Savage-Type Decision Theory

In order to describe a decision under uncertainty, Savage-type decision theory distinguishes:

• Acts

• States of the world

• Consequences

For example, the act might be applying to a university, the relevant state of the world is whether the university is disposed to accept your application, and the consequence is whether you underwent the effort and are accepted.Footnote ¹⁰ We can express this situation in Table 1.

One might assume that you prefer expending the effort and being accepted to not expending the effort and not being accepted, which might still be better than having wasted the effort without getting accepted.Footnote ¹¹ According to standard decision theory, whether you should apply then depends on the strength of your preferences and the probability you assign to the university being disposed to accept your application.

What we introduced here as the strength of preferences is more commonly described using a utility function. A utility function, U(·), takes an alternative as input and returns a real-value number as output. If one takes a mental realist perspective on utilities, they can be understood as degrees to which the alternative is wanted. We do not commit ourselves to such a perspective, but it provides an intuitive means to understand the following key formulas linking preferences:

$A\succcurlyeq B\leftrightarrow \text{U}\left(A\right)\ge U\left(B\right).$

Alternative A is at least as preferred as B if and only if A’s utility is at least as large as B’s.

$A\succ B\leftrightarrow U\left(A\right)>U\left(B\right).$

Alternative A is preferred to B if and only if A’s utility is larger than B’s.

$A\sim B\leftrightarrow U\left(A\right)=U\left(B\right).$

Alternative A is equally preferred as B if and only if A’s utility is identical to B’s.

These connecting biconditionals can still be posited from a non-realist perspective on utility, which considers it a formal tool. Formally, a utility function can be derived from preferences, provided they fulfil certain conditions, including those discussed in the previous section (see Reference SavageSavage 1954; Reference KrepsKreps 1988). In light of this derivation, one might consider the utility function as a useful shorthand for describing them.Footnote ¹²

The Savage framework has two utility functions: the utility function over outcomes and the expected utility (EU) function. The fundamental utility function ranges over the consequences, such as the case where someone has applied to a university and been accepted. The EU function ranges over the acts and provides the average utility of the outcomes for this act weighted by the probability of the state of the world for that outcome.

To illustrate this concept, we have assigned arbitrary numbers in our example that allow us to calculate the EU (Table 2).

In the outlined case, the state of the world where the university is disposed to accept has a probability of 40 per cent (i.e. P(Disposed to Accept) = 0.4). The utility for spending the effort and getting accepted is 20 on our scale. Based on these numbers, we can calculate the EU for both acts:

EU(Apply) = P(Disposed to Accept) × U(Accepted & Effort) + P(Disposed to Accept) × U(Not Accepted & Effort) = 0.4 × 20 + 0.6 × −10 = 8 – 6 = 2

EU(Not Apply) = 0.4 × 0 + 0.6 × 0 = 0.

Assuming that EU is to be maximised, this calculation suggests that you should put in the effort and apply (2 > 0).

The EU functions, however, can be altered. Savage-type decision theory thereby distinguishes between a preference change over acts (apply vs. not apply) due to a new utility function (a change in the utility functions over outcomes) or Bayesian updating (a change in subjective probabilities).

This distinction has played a major role in debates about preference change, especially because it limits the types of preference changes that can exist. Therefore, we will return to it later.

While the framework of Savage-type decision theory is useful for many purposes, and we will draw on it accordingly, it unduly restricts the discussion of preference change.Footnote ¹³

First, Savage-type decision theory precludes all discussions of preference changes over alternatives for which the framework does not assign a preference order. For example, there are no preferences over states of the world. Such a limitation does not seem psychologically required. For example, you might prefer that a university be disposed to accept you, even if the question of applying is left out of the picture. It is not obviously wrong to want the world to be a certain way, even if it being this way does not affect any choices or outcomes.

Second, preference change is limited by the dependence relations postulated by Savage’s framework. Specifically, the framework requires the utility of consequences to be independent of both the state of the world in which they are realised and the action. The preferences over actions derive from the preferences over consequences (and the probabilities assigned to states) and not vice versa. However, at least at first glance, a consequence might become more appealing by virtue of the action that leads to it. For example, one might get another university degree because one’s preferences regarding studying over working in the industry have changed. A preference change of this sort would be ruled out by the framework, at least while one describes studying as an action.

While one can often solve such issues by re-describing the decision problem (i.e. by specifying its ontology differently), it can become unwieldy or unintuitive to do so. In such cases, the decision theory developed by Richard Jeffrey and Ethan Bolker is often more appropriate.

Jeffrey-Type Decision Theory

The Jeffrey–Bolker framework is very flexible because it takes propositions as its basic elements rather than consequences, states, and acts. Therefore, preferences in this framework describe which propositions an agent would rather see realised. For example, an agent might prefer the proposition that the university is disposed to accept an application over the proposition that the university is not disposed to accept an application. Given the generality of propositions, this leads to a more general decision-making theory.Footnote ¹⁴

Furthermore, instead of a utility and EU function, Jeffrey-type decision theory introduces what is called a desirability function, which maps propositions to real-value numbers. The differences between the desirability and standard utility functions can be relatively subtle. In the standard interpretation of utility, a high utility indicates that the consequence is highly wanted or, in the case of EU, that the act is highly choice-worthy. Desirability, however, is often interpreted as a news-value indicator, meaning that the more the news of a certain proposition being true is wanted, the higher the proposition’s desirability.Footnote ¹⁵ Therefore, the desirability for a logical truth would be zero since such a proposition being true cannot be news (for a logically omniscient agent).

Unlike the Savage-type framework, there is one desirability function and, therefore, no correspondence to the distinction between the utility and EU function (see Reference Bradley and StefánssonBradley and Stefánsson (2017: 492–493) for an interesting interpretation of desirability measures). The unified ontology of propositions also leads to this result.

Despite these differences between utility and desirability, the two types of functions can nonetheless be treated as largely equivalent for our purposes because the formulas connecting preferences and utility also apply to the desirability function. More particularly, writing v(·) for the desirability function, it is the case that

$A\succcurlyeq B\leftrightarrow v\left(A\right)\ge v\left(B\right)$

and so on for strict preference and indifference.

Generally, we try as much as possible to adhere to the vocabulary of preferences instead of the utility or desirability function. However, since the literature on preference change also frequently uses these functions, we will use them whenever it simplifies the overall presentation.

Following these introductions, we turn to preference change, especially the difference between derived and fundamental preference change.

Preference-Logic Models of Preference Change

Multiple preference logic-based approaches to preference change exist, but we focus on an AGM-based model.Footnote ²⁶ The AGM model was originally a model of belief change and is named after three eminent researchers (Reference Alchourrón, Gärdenfors and MakinsonAlchourrón et al. 1985). Only later have its ideas been used to model preference change.

Hansson and Grüne-Yanoff have offered some of the most prominent applications of the AGM model to preference change (Reference HanssonHansson 1995; Reference Grüne-Yanoff, Hansson, Grüne-Yanoff and HanssonGrüne-Yanoff and Hansson 2009; Reference Grüne-YanoffGrüne-Yanoff 2013).Footnote ²⁷ The bases for these applications are the formal preference relations discussed in chapter 1, which are then incorporated in propositional logic without addressing uncertainty, as the Savage- and Jeffrey-type decision theories do.

We start with a set of alternatives, A, which might, for example, be a set of book genres over which an agent has preferences:

$A=\left\{\text{SciFi},\text{Fantasy},\text{Crime}\right\}.$

In this context, we can represent a preference relation R as a set of tuples, each comprising two alternatives that are compared. For example, if Lane prefers science fiction (SciFi) to crime and fantasy literature and also prefers crime to fantasy literature, then her preference ranking can be represented as follows:

$R_{\text{Lane}}=\{〈\text{SciFi},\text{Fantasy}〉,〈\text{SciFi},\text{Crime}〉,〈\text{Crime},\text{Fantasy}〉,〈\text{SciFi},\text{SciFi}〉,〈\text{Crime},\text{Crime}〉,〈\text{Fantasy},\text{Fantasy}〉\}.$

Each tuple ranks the first option at least as highly as the second. In this example, Lane is shown to have a reflexive and transitive weak preference relation.

Such a preference relation R then renders valid a set of preference sentences [R] similar to the semantics of propositional logic (see again Reference HanssonHansson 1995: 8; Reference Grüne-YanoffGrüne-Yanoff 2013: 2626). For example, the tuple ⟨SciFi, Fantasy⟩ validates the proposition that Lane weakly prefers SciFi to Fantasy (i.e. the preference sentence ‘SciFi ≽ Fantasy’). Expressed formally:

$〈A,B〉\in R\leftrightarrow A\succcurlyeq B\in \left[R\right].$

The absence of a preference sentence, represented by the variable α, from the set of sentences validates its negation:

$\alpha \notin \left[R\right]\leftrightarrow \neg \alpha \in \left[R\right].$

Hansson and Grüne-Yanoff also used the connectives of propositional logic (i.e. conjunction, disjunction, and the material conditional). The formal description of conjunction would be:

$\alpha \in \left[R\right]\wedge \beta \in \left[R\right]\leftrightarrow \alpha \wedge \beta \in \left[R\right].$

In essence, the basic preference sentences express a simple (weak) preference for one alternative over another and further sentences are constructed using negation and standard logical connectives.

Representing a preference relation as a set of tuples and the associated sentences allows for incomplete, intransitive, and further unusual preferences. However, despite this flexibility, Hansson and Grüne-Yanoff consider such a set of tuples insufficient to represent certain plausible states of mind. Specifically, agents might be in a state where they hold one or another preference but have not settled on one yet.

Consider a case in which the agent knows that they prefer either The Dispossessed (D) or The Lord of the Rings (LotR) to Death on the Nile (DotN) but cannot remember which one it was. Here, the preference sentence D ≻ DotN v LotR ≻ DotN holds, but neither D ≻ DotN nor LotR ≻ DotN holds.Footnote ²⁸ Regarding the present formalism, the disjunction of two preference sentences might be valid without either being valid. To solve this problem, Hansson introduced a set R of preference relations and defined that a preference sentence holds for R if and only if all R in R validated it. In the case of the three books, R might be a set of two preference relations, R₁ and R₂, where the first validates the first disjunct (D ≻ DotN) and the second validates the second (LotR ≻ DotN).

The formal apparatus allowed Reference HanssonHansson (1995: 10, Reference Hansson2001: chapter 4) to describe four elementary types of preference change:

1. 1. Revision: a new preference sentence (e.g. A ≽ B) is included in the preference model R.

2. 2. Contraction: a preference sentence is lost from the preference model R.

3. 3. Addition: a new alternative becomes available for the preference model R.

4. 4. Subtraction: an alternative for the preference model R is lost.

Hansson provides a complete description of these types, but we will limit ourselves to a largely informal discussion of how to make the four types of preference change specific. After all, there are many ways to include a sentence in a preference model.

To visualise the problem, consider a case where an agent neither weakly prefers the movie Totoro to Bambi nor vice versa. Assume that their R includes only the preference relations R₁ and R₂, where the first one validates only Totoro ≽ Bambi and the second only Bambi ≽ Totoro, but neither validates both. If the agent undergoes a revision that Totoro ≽ Bambi is validated for them, then the second relation (R₂) has to be different. However, it could be changed so that:

• Totoro ≽ Bambi is only added to what R₂ makes true, in which case the R₂ would specify indifference between the two movies.

• Or the earlier Bambi ≽ Totoro in R₂ would be lost, in which case the agent represented by R now strictly prefers Totoro.

The description given so far does not settle which version is correct.

To make the four types of preference change specific, Hansson suggests that the preference model before the change should be maximally similar to that of the model afterwards. Put differently: the change should be conservative. This move requires a notion of distance. Many such notions can be defined simply by counting how many preference sentences were true for the first model but not the second and vice versa and then adding those two counts together. The maximally similar model is the one for which the added count is the smallest.

However, Reference HanssonHansson (1995: 12) suggests a slightly more complex distance metric, where some preferences change before others. Specifically, he proposes that the revision operation includes a so-called priority index that specifies alternatives that are ‘loosened’ during the revision. When multiple ways to undergo preference change are open, the change that concerns the loosened alternatives should occur with priority. For example, when Lane re-reads The Lord of the Rings and concludes that it is better than Dune, her experience might loosen her preferences for SciFi and Fantasy books but not travel guides. On Hansson’s account, that means that if a change in Lane’s preferences over genre novels can help avoid a preference change over travel guides, then the first change will occur. Her preferences over genre novels have been loosened and so should have priority in change.

The general conservative constraints imposed by Hansson and Grüne-Yanoff can be motivated in at least three ways (see Reference Grüne-YanoffGrüne-Yanoff 2013: 2629). First, the change process might have cognitive costs. Presumably, the agent seeks to ensure that the resulting new preferences are consistent and fulfil various prior commitments. The smaller the preferences change, the fewer the ways of newly violating these restrictions.

Second, the existing preferences might have been reached through an investment, either cognitively or otherwise, and therefore can be seen as a form of ‘accumulated capital’ (Reference Grüne-YanoffGrüne-Yanoff 2013: 2629). Regarding biographies, Rory might prefer The Power Broker to The Life of Johnson because she spent months reading both volumes and evaluating their multifaceted qualities. Given the effort it takes to establish such well-considered preferences on the matter, they should not be discarded without need.

Third, the functioning of preferences in human conduct might require stability. Grüne-Yanoff highlights the role of preferences in personal identity and long-time planning. Some social coordination functions might also be better served by stability than fluctuations not forced by the preference change-inducing event.

All three considerations are most easily understood and supported if preferences are assumed to be cognitively real. If preferences were merely used to describe behaviour, there would be no cognitive cost, and it would be challenging to see how they would accumulate cognitive capital or play a direct function in cognitive life. Recovering these three reasons from a behaviourist perspective would require considerable conceptual work. Therefore, the arguments by Hansson and Grüne-Yanoff illustrate the deep intertwinement between the ontology of preferences and theories of preference change. This intertwinement is also between descriptive and normative modelling. The cognitive roles ascribed by these arguments are a matter of descriptive inquiry and modelling, but they are used to impose normative constraints.

As the name suggests, preference logic deals with preferences, but decision theorists prefer to work with utility or desirability functions. We now discuss how Bayesian decision theorists can deal with fundamental preference change.

Bayesian Models of Preference Change

The flexibility of the Bayesian framework makes it comparatively easy to introduce fundamental preference change into Jeffrey-type decision theory. While the conditioning approach was initially intended to deal with new evidence, there is no reason to limit it in such a way. Reference BradleyBradley’s (2017) work on conditioning explicitly covers changes in preferences, including what he describes as desire-driven changes. Given the variety of ways of conditioning, not all of them can be covered; instead, we focus here on what Bradley calls ‘generalised conditioning’.

Let P and V stand for the old degrees of belief and desirability and Q and W for the new degrees of belief and desirability (i.e. the degrees after the change has occurred). Furthermore, we need the notion of a partition of the alternatives, which are in the Jeffrey-framework propositions. A partition of a set of propositions is a set of subsets that do not share any elements but together include all elements in the original set of propositions. So, if the propositions are:

• tomorrow I read The Power Broker,

• tomorrow I will work on preference change, or

• tomorrow is a Sunday,

then one partition would be the set: {{Tomorrow I read The Power Broker, Tomorrow is Sunday}, {Tomorrow I will work on preference change}}. For brevity, we write the partition A = {α_i}, where α₁, α₂, and so on are the various members of the partition, which are themselves sets of propositions.

Given this notation, the new pair of degrees can be obtained from the old by generalised conditioning if and only if for all propositions β and for all α_i in A (such that P(β|α_i) > 0), the following equations hold (2017: 202):

$Q\left(\text{β}\right)=\sum _{i}P\left({\text{β|α}}_i\right)\cdot Q\left({\text{α}}_i\right).$

This first equation describes the new degrees of beliefs. They result from multiplying the previous conditional probabilities for the proposition β with the new probabilities for the partition elements across the partition. More important for our purposes is the second equation describing the new degrees of desirability:

$W\left(\text{β}\right)=\underset{i}{{\sum }^{\text{}}}\left[V\left({\text{β|α}}_i\right)+W\left({\text{α}}_i\right)\right]\cdot Q\left({\text{α}}_i\text{|β}\right).$

Given the connection between desirability and preferences (i.e. an alternative is weakly preferred to another if and only if it has at least as high a desirability), the second equation describes a type of preference change. These equations might appear opaque, and we cannot provide here all of the well-developed justification in Reference BradleyBradley’s (2017) book and (2007) paper. However, to hint at some of the intuition regarding the desirability equation, note that $V\left(\text{β}|{\text{α}}_i\right)+W\left({\text{α}}_i\right)=W\left({\text{βα}}_i\right)$ . That is, deriving the new desirability for $\text{β}$ involves taking the new joint desirability for $\text{β}$ with each proposition from the partition and then weighing this joint desirability by the new conditional probability of the relevant proposition from the partition given $\text{β}$ . Roughly, we consider the new desirability of all ways in which $\text{β}$ could be true and weigh them by the relevant probability.

Generalised conditioning covers cases where preferences over a given set of alternatives change direction. Not covered are cases where:

1. 1. an agent acquires or loses a preference between two alternatives;

2. 2. an agent becomes aware or loses awareness of an alternative.

In his effort to make Bayesian decision theory more realistic, Bradley has provided a way of dealing with these cases. The core idea will be broadly familiar since it also takes inspiration from the AGM model of belief change (see Reference BradleyBradley 2017: 245). As we did in our discussion of Hansson and Grüne-Yanoff, we will provide a broad outline without all the formal details.

To address the loss and gain of preferences, Bradley introduces the notion of avatars. The main intuition is that an agent can be thought of as a group of agents, called avatars, that disagree amongst themselves. If Rory has not yet settled on the desirability of various courses she might pick this term, she can be modelled as having multiple avatars that differ regarding the desirability of these courses while sharing attitudes regarding other alternatives on which Rory has a settled state of mind.Footnote ²⁹ For example, Rory₁, her first avatar, might assign V(biology) = 10 and V(sociology) = 5, while Rory₂ might assign the numbers in reverse (i.e. V(biology) = 5 and V(sociology) = 10). If Rory the person settles on the first desirabilities, this can be modelled as her losing the second avatar that was previously in contradiction with this assignment.

The avatar approach greatly resembles the preference-logic approach of having a preference model R that is a set of multiple preference relations R₁, R₂, …, R_n. In both cases, the represented agent is said to prefer one alternative over another if and only if all components (i.e. all avatars or all preference relations) validate such a preference. Nonetheless, there are considerable differences. First, Bradley’s avatars are taken to have desirability and probability functions, which impose stricter criteria on the avatars than the existence of a preference model R requires. Second, Bradley’s approach does not include the notion of preference sentences, which could then be extended using logical connectives.Footnote ³⁰

These differences could be addressed by extending and adapting Hansson’s preference logic and Bradley’s Bayesian approach. One could require the preference model R to be such that the relations it includes allow the construction of desirability functions, and one might define a language of preference sentences for Bradley’s framework. However, there are reasons not to do so. The two approaches have different purposes. The preference-logic approach is better suited to cases where the modeller wants to make minimal assumptions. Bradley’s extension is appropriate in cases where the full power of Bayesian decision theory is required.

Having covered losing or acquiring a preference state, the option of becoming aware or losing awareness of an alternative remains. To model such changes in awareness, Bradley distinguishes the modeller’s domain from the agent’s. Simply put, there is a truly available set of alternatives and a subset of which the agent is aware. From the perspective of Bradley’s project, the question is which restrictions rationality imposes on extending and restricting the agent’s domain of awareness. Reference BradleyBradley (2017: 255–60) primarily endorses conservative criteria that describe the preservation of attitudes. In the case of domain extension, the agent’s new probabilities and desirabilities should be the same as the original unconditional probabilities and desirabilities. In the case of domain restriction, the new probabilities and desirabilities should be the same as the old probabilities and desirabilities conditioned on what is to become the new smaller domain of alternatives. Put differently, when extending one’s domain, the previous attitudes are preserved as attitudes conditioned on the previous domain. In contrast, when restricting one’s domain, the previous attitudes conditioned on the sub-domain are preserved as unconditional attitudes.

We have already encountered conservative requirements in discussing Hansson’s and Grüne-Yanoff’s approaches. However, as with the case of avatars and preference models, there are significant differences. Reference Grüne-YanoffGrüne-Yanoff (2013) has criticised in detail that Bradley’s approach does not include a similarity measure between desirability functions, which would govern the change of such desirabilities. It is not the case in Bradley’s approach that an agent will necessarily develop the most similar desirability function, given the required changes and constraints of rationality. The rigidity that Bradley formalised using conditional attitudes does not have the same restrictive force. While similarity measures could also be introduced into Bradley’s approach, doing so is not without challenges (see Reference Grüne-YanoffGrüne-Yanoff (2013) for details).

Reason-Based Decision Theory

When Ishmael told us that ‘Queequeg, for his own private reasons, preferred his own harpoon’, he implied that our preferences could be grounded in reasons. Developed by Reference Dietrich and ListDietrich and List (2013a, Reference Dietrich and List2013b, Reference Dietrich and List2016b), reason-based decision theory captures how shifts in such motivating reasons induce preference change.

You might be motivated by the appeal of being famous and therefore prefer a career as a social media influencer to that of a decision theorist one day, while the next day, being famous does not serve as a motivating reason to you anymore, and your preference reverses. You stopped considering that reason, and, as a result, your preferences are no longer the same.Footnote ³¹

In order to model such preference changes, reason-based decision theory postulates:

1. 1. an underlying set of motivationally salient properties;

2. 2. a weighing relation over the power set of properties.

Together, they ground the fundamental preferences of each agent.

Let us start with a set, called P, of potentially motivating properties for a university course:

$P=\left\{\text{includes lots of mathematics }\left(\text{LM}\right),\text{ taught by a great professor }\left(\text{GP}\right)\text{, …}\right\}.$

Only some of these properties will be motivationally salient for each human agent who has to choose between courses. Dietrich and List call the set of motivationally salient properties the agent’s motivational state. We can think of the motivational state as specifying the agent’s motivating reasons. Formally, the agent’s motivational state, M, is a subset of the set of all properties, P (i.e. M ⊆ P).

Many combinations of properties can be motivating (i.e. many Ms that form a set of all potential motivational states). Let M denote this set of all motivational states that are psychologically possible. In our case, M would be as follows:

$M=\{\left\{\text{L}\text{M},\text{G}\text{P}\right\},\left\{\text{G}\text{P}\right\},\left\{\text{L}\text{M}\right\},\{\}\dots \}.$

For example, Paris might be motivated to choose a university programme because it is taught by a great professor (GP) and/or includes lots of mathematics (LM); then, we can write for Paris that M = {LM, GP}.

Furthermore, Dietrich and List introduce a binary relation ≥, called the weighing relation, over M. For example, the weighing relation might put the singleton set of being taught by a GP over the empty set. If and only if the (weak) weighing relation ranks one set of properties over another, the higher-ranked set is at least as choice-worthy as the other.

A complete weighing relation allows for deducing the agent’s preferences over alternatives for each possible motivational state in M as follows: for each alternative, one identifies the set of motivationally salient properties it instantiates and then finds the place of this set in the weighing relation. That place specifies the rank of the alternative.Footnote ³²

We will illustrate this with the case of Paris choosing between university programmes which can be described as combinations of two properties: being taught by a GP and including LM. The options are:Footnote ³³

• Medicine is taught by a GP but does not include LM (GP, not LM).

• Physics includes LM but is not taught by a GP (LM, not GP).

• Biology has neither of the two properties (not LM, not GP).

As already mentioned, Dietrich and List further postulate an underlying ordering of the possible motivational states given by the agent’s weighing relation. In Paris’ case, this ordering might look like this:Footnote ³⁴

$\left\{\text{L}\text{M},\text{G}\text{P}\right\}>\left\{\text{G}\text{P}\right\}>\left\{\text{L}\text{M}\right\}>\left\{\right\}.$

The set of all properties is ranked above the sets containing one property and the empty set. This ordering induces a preference ordering for the three programmes, given a motivational state in which Paris could find herself (Table 3). Assuming both properties are salient, Paris strictly prefers Medicine to Physics and Physics to Biology. By contrast, if Paris is not motivated by any of the two reasons that could guide her choice, then she will simply be indifferent between all available options. If no properties are motivationally salient, then no alternative can instantiate a motivationally salient property.

Dietrich and List’s framework combines reasons, as commonly discussed in philosophical investigations of practical rationality, with decision theory. The framework clearly draws upon the philosophical literature and has both normative and description ambitions.

Given the framework’s versatility, it is unsurprising that Dietrich and List have developed it in multiple directions. One of them was to propose it as an answer to the question of where preferences come from (see the title of Reference Dietrich and ListDietrich and List (2013b)). A comprehensive answer to this question requires a theory of preference change, and we will evaluate reason-based decisions only regarding this requirement. Specifically, we will address two issues:

• Can it cover all cases of preference change?

• Is the reason-based framework a theory of fundamental preference change?

The Role of Commitment in Preference Change

As a capstone for our discussion of sources-of-change models, we want to connect them to the input-assimilation model of Hansson and Grüne-Yanoff, which distinguishes two tiers of alternatives during revision. Some preferences were loosened and were, therefore, less robust during the change.Footnote ³⁷

Since Hansson and Grüne-Yanoff were working within the framework of input-assimilation models, they only addressed the question of what form a change in preferences should take given a specific input, not whether any change should happen. We want to fill this gap, and for that purpose, we propose a connection between ranking preferences by how easily they change and whether change occurs. Why would one individual’s preferences change when another individual’s do not?

To formalise the problem, consider the story of Doyle and Paris. Our protagonists face a choice over what to study: physics or medicine. In the beginning, they share a strict preference for medicine over physics. Therefore, Doyle and Paris enrol in the medicine course. Full of excitement, they start their studies, learn numerous Latin names for bones, and have first patient contact. At this point, they both experience the tragic death of a patient. This experience has transformative potential and leads Doyle to undergo preference change. His preference between medicine and physics reverses. Doyle switches degrees. Paris has had precisely the same experience. However, this does not lead to a preference reversal in her case. She still prefers medicine over physics and is continuing her degree. Why did Doyle undergo preference reversal but Paris did not?

It seems that the difference between Doyle and Paris cannot be explained by new information learned from the patient’s death.Footnote ³⁸ They both knew that patients tragically die, and we can expect they had a good sense of how this would feel. In essence, we stipulate that their experience brings no relevant information about either course of study. Nevertheless, their preferences might differ in stickiness, or so we suggest.

Crucially, Paris’ preference is more robust than Doyle’s despite them sharing relevant preferences and undergoing the same experience. A preference is more robust than another if, ceteris paribus, it takes a more intense experience to change it. A more intense experience is needed to override Paris’ preference for medicine than Doyle’s.

The story of Doyle and Paris undergoing a potentially preference-changing experience is just one example among many that our framework covers. As the following example illustrates, not all these experiences must be life-changing.

Rory and Jess prefer William S. Burrough to Ernest Hemingway, but they both read The Old Man and the Sea for school. While they have read it before on their own, the novel speaks much more to them on this occasion. They have an intense positive experience, despite receiving no new information about the book or its content.Footnote ³⁹ This positive experience leads Rory to undergo motivational change. She now prefers Hemingway to Burrough, while Jess remains a Burrough fan.

Importantly, neither scenario can be covered by the approach of Hansson and Grüne-Yanoff, since the input-assimilation model always a priori assumes that preference change occurs. What is needed is a theory that connects the robustness to not only how preference change occurs but also whether it occurs. To fill this gap, we propose what we call the commitment-based theory of preference change.

The main idea of the commitment-based theory of preference change is that the robustness of an agent’s preferences results from how committed they are to these preferences. Commitments are mental properties explaining motivational dynamics. In this way, commitment resembles entrenchment in the AGM modelling literature. Reference Grüne-Yanoff, Hansson, Grüne-Yanoff and HanssonGrüne-Yanoff and Hansson (2009) have also discussed such an entrenchment-inspired proposal but without taking the idea very far.Footnote ⁴⁰

We develop our framework for modelling these commitments in five steps:

1. 1. Presenting the basic assumptions about alternatives and preferences.

2. 2. Outlining the newly introduced commitment function.

3. 3. Developing our representation of experience.

4. 4. Introducing the ‘commitment-preservation identity’ as a condition describing which preference ordering would result if an experience caused preference change.

5. 5. Finally, introducing the intensity inequality that determines whether an experience is intense enough to cause this change.

Alternatives and Preferences

Our framework requires a set of alternatives and preference states held over these alternatives.Footnote ⁴¹ In the example of Doyle and Paris, the set of alternatives might simply be a set of available university courses:

$A=\left\{\text{physics,medicine,…}\right\}.$

For the purposes of our overview, we do not settle on the specific nature of the alternatives: they could be Savage-type consequences or Jeffrey-type propositions. However, we assume that A is the set of alternatives over which the fundamental preferences range. These fundamental preferences are taken to be well-described by a preference ordering that is represented as a set of preference states, P:

$P=\{\text{medicine}\succ \text{physics},\text{physics}\sim \text{physics},\dots \}.$

All preference orderings we consider will be complete, in that a preference state of strict preference or indifference holds between each pair of alternatives, including alternatives paired with themselves.

In our overview, we only consider preference changes in which agents replace indifference or strict preference between alternatives with the same two types of state. We will overlook other types of preference change, such as when a preference is withdrawn between two alternatives without indifference or a reversed preference takes its place, or when alternatives are lost or discovered.

Commitments and the Commitment Function

‘Commitment’ is used in many ways.Footnote ⁴² We add to this collection and use ‘commitment’ in a further technical sense: commitments determine the robustness of an agent’s preferences in response to experiences. This general idea can be given two interpretations: strong and weak.

In the strong interpretation, commitments are mental states that govern the robustness of preferences in the light of experiences. These mental states would have the function, presumably due to evolutionary selection, to ensure that preferences do not change haphazardly. If some process would affect a preference with strong commitment, the strong commitment state will act as a defence.

In the weak interpretation, commitments are just the robustness of preferences. According to this view, they are a dispositional property of preference states. Preferences are more or less fragile.

The two interpretations can be compared to two ways of explaining why a porcelain plate might not break during transport: either it has been packaged well in dampening materials, which are in this analogy equivalent to the commitment states, or it is not disposed to break, presumably due to its intrinsic properties. For the present purposes, we will not settle on one interpretation. In either interpretation, commitments to preferences are irreducible to the preference ordering, and our conditions can be applied to the dynamics of preferences.

While both Doyle and Paris initially prefer medicine to physics, they differ in their commitment to this preference. Importantly, their commitment is not reducible to the strength of their preference since it might be derived from their utility functions. That is, Paris being more committed to the preference for medicine over physics does not simply mean that the difference in utility between these two options is larger for her than for Doyle.Footnote ⁴³ In our example, Paris and Doyle initially wanted to study medicine and physics to the same degree.

We do not consider the distinction between the strength and robustness of a preference to be particularly controversial once appropriately considered.Footnote ⁴⁴ Fickle agents with strong desires (i.e. individuals who strongly want their preferred alternatives but nonetheless undergo substantial motivational change over time) are common. We have all heard of the fickle lover who desires with all their heart to be with the object of their love rather than anyone else, only to change their mind a day or two later. Their preference is strong but not robust.

The converse is also possible. Human agents exhibit anaemic but persistent preferences, which require intense experiences to be changed. A trivial example is a ceteris paribus preference for having $1010 rather than $1000 in one’s bank account. Most of us would not be willing to do much to realise this preference. Yet, it would take an extremely intense experience, perhaps a conversion to a religion of poverty, to reverse this preference. The strength of preferences understood in terms of utility functions cannot account for such cases. Since robustness is distinct from strength, we postulate that commitment is distinct from desirability.

Based on this informal understanding, one can develop rigorous models that describe the role of commitment in preference change. However, there are multiple ways to develop such a framework. One key question is at which scale one should represent commitment. On an ordinal scale, commitments would only be taken to specify whether one preference is more robust than another but not how much more robust. A ratio scale allows such a specific comparison.Footnote ⁴⁵

Justifying a response to this question goes beyond what we can accomplish here. For the purpose of illustration, we will settle on a ratio-scale representation of commitment in the following since its power simplifies the presentation. However, at opportune moments, we will remark on how one could develop the framework differently.

Given the suggested representation of alternatives and preferences, commitments can be represented by a function from the set of preferences P to an appropriate interval. Specifically, we suggest that the function takes the form:

$\text{c}\text{o}\text{m}:P\to ℝ.$

For example, Paris’ commitment might be 8 while Doyle’s is only 6. We would write this as:

${\text{com}}_{\text{Paris}}(\text{medicine}\succ \text{physics})=8$

${\text{com}}_{\text{Doyle}}(\text{medicine}\succ \text{physics})=6.$

Intuitively, the higher the commitment to a preference relation, the more intrinsically robust the preference is (some special cases are treated in Appendix B). More precisely, we need to turn to the representation of experience.

Representing Experience

We have stipulated in our example that Doyle and Paris experienced the death of a patient in the same way, but one might inquire what it means for two experiences to be the same. It cannot be sufficient that the agents live through the same events because then a difference in how they interpret these events could explain the difference in preference change. Instead, it is required that the internal representation of the events is the same, at least insofar as the representation matters for the dynamics of preferences (cf. Reference BradleyBradley 2017: 185–86).

Experiences can be extremely rich and their processing highly complex, but we make the simplifying assumption that only two aspects of an experience matter for commitment-based preference change, which we call:

• Substantial component

• Intensity

First, an experience suggests changing particular preferences, and this suggestive part of the experience we call the ‘substantial component’. For example, the substantial component of Doyle and Paris’ experience suggests preferring physics over medicine, which can be represented as the singleton set {physics ≻ medicine}. The substantial component specifies which preferences are to be considered because of what has happened to the agent. This aspect of the experience mirrors the proposal by Hansson and Grüne-Yanoff, although we are not operating with general preference sentences.

Second, every experience has an intensity. Good experiences, such as enjoying a book by Hemingway, and bad experiences, such as witnessing a patient’s death, have an intensity. We propose that the intensity of the experience can be represented by a real number on a ratio scale, meaning that such experiences can be more or less intense. In the case of Doyle and Paris, the experience is intense because it is highly tragic. In the case of Rory and Jess reading Hemingway, the experience is presumably of lower intensity.

As with the representation of commitment, one can – and should – question whether the intensity of experiences, such as the experiences of Doyle and Paris, is

1. 1. representable by real numbers on a ratio scale;

2. 2. whether intensities are commensurable across agents.

Defending these assumptions in all detail goes beyond the confines of our Element, and we will later outline how to model intensity on an ordinal scale instead. However, for now, we want to offer a potential path for approximately operationalising ratio-scale intensity.

The intensity of an experience might be approximated using the experience’s degree of absolute pleasurability (i.e. treating both highly pleasing and highly displeasing experiences as intense and neutral experiences as lacking intensity).Footnote ⁴⁶ Psychological research has provided evidence that experiences share a hedonic degree. For example, Reference Kahneman, Kahneman, Diener and SchwarzKahneman (1999) proposes that every experience can be characterised by a value on a single good/bad dimension because the good experience of, for example, reading a book by Hemingway and the bad experience of the death of a patient share an attribute of goodness/badness. When the good/bad commentary is conscious, it is experienced as pleasure or distress, with a corresponding acceptance or rejection of the stimulus. If we determine the value of an experience affectively rather than cognitively (e.g. Reference ZajoncZajonc 1980) and the affective evaluation works on pleasant/unpleasant dimensions (e.g. Reference Kahneman, Kahneman, Diener and SchwarzKahneman 1999; Reference KauppinenKauppinen 2015), the hedonic degree suggests itself as a proxy measure for intensity. Therefore, if two agents experience an event with the same intensity, they experience the same absolute hedonic degree. The intensity can then be represented by a function:Footnote ⁴⁷

$I:E\to [0,\infty ),$

where E is the set of experiences, and the range starts at zero because it reflects the absolute hedonic degree (i.e. there is no negative intensity).

Accepting that intensity is on a ratio scale, an experience can be represented by an ordered pair with the substantial component (i.e. a set of preference relations suggested by the experience as the first member and the intensity as the second). For example, the experience of Doyle and Paris can be written as:

$〈\{\text{physics}\succ \text{medicine}\},7〉.$

The experience suggests a specific preference (i.e. to prefer physics over medicine), and it does so with a specific intensity.Footnote ⁴⁸ That Doyle and Paris have the same experience means that the experience is correctly represented by the same tuple for our purposes. Both the substantial content and the intensity of the experiences are identical.

Condition 1: The Commitment-Preservation Identity

Given this formalisation of experiences, we propose that one equation specifies which preferences are changed if preference change occurs. The idea is simply that preferences are changed to minimise overall violation of commitments.

Assume an experience changes an agent’s preferences. If Q represents the new preference ordering and C represents the set of all preference orderings over the set of alternatives that are rational and compatible with the substantial component of the experience, then the identity is:

$Q=\underset{C\text{in}C}{\text{argmin}}\left(\sum _{R\text{in}P\backslash C}\text{com}\left(R\right)\right).$

This identity specifies that the new preference ordering is the one that is compatible with the experience and, at the same time, minimises the sum of violated commitments.Footnote ⁴⁹ Specifically, the commitment-preservation identity requires that the new preference ordering is the ordering of C that minimises the commitment of preferences that must be abandoned (i.e. that are in P but not in Q). If the commitment to a preference state, R, is higher than others, it is less likely to be abandoned. Therefore, the identity selects the compatible preference ordering, minimising the commitment values of the preferences in the original but not the new preference ordering.

In the case of Doyle and Paris, the following two preference orderings might be amongst the candidates, one that only ranks physics over medicine and one that also ranks biology over medicine, where all preference states subsumed in the ellipses are identical:

1. 1. {physics ≻ medicine, medicine ≻ biology, physics ≻ biology, …}

2. 2. {physics ≻ medicine, biology ≻ medicine, biology ≻ physics, …}

If Doyle previously preferred both medicine and physics over biology and had positive commitments to these preferences, the first preference ordering would always have a lower overall violation of commitments. Therefore, it will be selected over the second candidate.

Interpreting the identity normatively, a rational agent should undergo preference change in such a way as to minimise the violations of commitments. Intuitively, a rational agent should not go overboard in accommodating an experience. In this regard, the commitment-preservation follows a similar motivation as Hansson and Grüne-Yanoff’s model. However, there are important differences.

The most obvious difference is that our suggested model includes a ratio scale of commitment. However, one can also envision an ordinal version of our framework that could follow the model of Hansson and Grüne-Yanoff. That is, instead of requiring that the sum of the commitments be minimised, one can require that as few preferences of the highest commitments be changed as possible, and then as few preferences as possible of the second tier, and so on.

A more profound difference is that in the Hansson and Grüne-Yanoff model, the revision operation specifies loosened alternatives and, thus, preferences that have priority when it comes to change. In our approach, commitments hold across preference transformations and determine the robustness of preferences. What is a property of the experience in their model is a property of the agent’s cognitive system in ours. Despite starting with highly similar motivations, the variation in assumptions about what governs motivational dynamics leads to quite divergent models. The difference between them will become even more apparent with the second condition.

Condition 2: The Intensity Inequality

Having described how preferences change with the commitment-preservation identity, we propose that whether preference change occurs also depends on commitments. To capture this, we propose the inequality condition.

If I(e) represents the intensity of an experience e and C represents the set of all preference orderings compatible with the substantial component of the experience, again represented using strict preference and indifference states, the inequality describing the condition under which preference change occurs is:

$\text{I}\left(e\right)\ge \underset{C\text{in}C}{\text{min}}\left(\sum _{R\text{in}P\backslash C}\text{com}\left(R\right)\right).$

Informally, preference change happens if and only if the intensity of the experience overcomes the sum of violated commitments. Therefore, we can describe the difference between Doyle and Paris. For Doyle, the intensity of the patient-death experience is greater than the sum of the commitments for the preferences that are abandoned. Put more informally: the experience hits him harder than the degree to which he hangs on to his preferences. Given that the experience is represented as ⟨{physics ≻ medicine}, 7⟩, we can write for Doyle:

$\text{7}\ge \underset{C\text{in}C}{\text{min}}\left(\sum _{R\text{in}P\backslash C}\text{com}\left(R\right)\right).$

In contrast, for Paris, the condition is not fulfilled due to her greater commitment to the preference for medicine over physics:

$\text{7}<\underset{C\text{in}C}{\text{min}}\left(\sum _{R\text{in}P\backslash C}\text{com}\left(R\right)\right).$

This formalism encompasses the examples of Doyle and Paris’ life-changing experience and Rory and Jess’ experience with Hemingway. In both examples, the agent who undergoes preference change fulfils the inequality condition, while the other does not.

Interpreting the inequality condition normatively, a rational agent should not change their preferences because they had a bad experience but because they also had a sufficiently intense experience. Interpreting the inequality condition descriptively, an agent will not undergo preference change whenever an adverse experience occurs, but they will if it is sufficiently intense.

The inequality condition requires the commensurability of the intensity of experiences with commitments for both its normative and descriptive tasks. Only then can we say that Doyle was hit harder by the experience than he was committed to his preferences. Accepting our story of Doyle and Paris, this claim appears natural to us.

To use the example of Shakespeare’s Hamlet instead of our tale, assuming commensurability allows us to take at face value the following assertions: Hamlet’s experience was more intense than his interest in society could withstand. While he strongly held social preferences before, never wavering in them, the experience was greater than them.

These assertions assume that Hamlet had persistent preferences to engage in social interaction over other activities and that these preferences were held to some degree. Furthermore, they assume the experience of his father’s death and mother’s remarriage to the murderer was greater than this degree. It is probably not the only way to read Shakespeare, but it seems intuitive enough to suggest that we have a grasp on the commensurability between experiences and commitment. Such a grasp, we suggest, arises from our acquaintance with similar situations.

These considerations appear to us sufficiently strong to provisionally base our model on this commensurability, albeit with the caveat that the overall model requires further empirical investigation.Footnote ⁵⁰

Postulating and justifying commensurability between experience intensity and commitments is one thing; formalising this commensurability is another. To simplify this formalisation, we assume that both the commitment function and the intensity of an experience are on a shared ratio scale. For example, we assume that if an agent is twice as committed to a set of preferences, then the experience of changing these preferences also has to be twice as intense. Unlike an ordinal scale, the ratio scale can offer such a straightforward interpretation. We find it plausible, especially since we believe an experience can hit one person twice as hard as another and therefore have twice the impact.

Nonetheless, one could also develop an ordinal version of our proposal, which would preserve a more limited commensurability. For example, experiences could have a maximal commitment level that they can overturn. Therefore, one might explain why Paris’ preference is more robust than Doyle’s by:

1. 1. postulating three levels of commitments to preferences: high, medium, and low;

2. 2. ascribing a high commitment level to Paris’ preference for medicine ≻ physics but a medium to low commitment level to Doyle’s same preference.

Then, the experience ⟨{physics ≻ medicine}, medium⟩ would lead to a preference change for Doyle but not Paris.

This explanation does not require a full ratio scale. However, it still requires commensurability between intensity and commitment and between persons. Without the commensurability between persons, it would no longer be valid to assert that Doyle and Paris had the same experience since the intensity level of the experience would no longer be comparable.

If one went further and rejected the intrapersonal commensurability between intensity and commitment, the inequality condition could no longer be specified, even for one person. Therefore, the commensurability assumption is required even on the ordinal variant of our proposal.

The Challenge to Decision Theory

There are different ways to formulate Paul’s challenge to decision theory and rationality more broadly understood.Footnote ⁵³ Reference PettigrewPettigrew (2015, Reference Pettigrew, Lambert and Schwenkler2020) argues that Paul challenges a deliberative conception of decision theory. According to the deliberative conception, an agent uses the decision-theoretic models to deliberate and make a rational choice according to their preferences. According to this conception, being rational means the deliberation preceding the choice fulfils certain rationality criteria. If you choose the best outcome without deliberating according to the formal decision theory framework, you are still irrational in the deliberative conception.

Transformative choices pose a problem for the deliberative conception of decision theory because they threaten the usefulness of decision-theoretic models for deliberation. Consider Paul’s example of the decision of whether to have a (first) child. Applying Savage-type decision theory, one would proceed as follows.

First, one identifies the set of available actions. Let us suppose there are two options: having a child and not having a child (ignoring any difficulties regarding conception). Second, one assigns a utility to each potential outcome. The number of potential outcomes depends on the relevant states of the world. For illustration, assume that only the following states of the world matter for the decision: the relationship works out or falls apart, and one’s financial situation is stable or unstable. Therefore, there are four relevant states of the world:

1. 1. The relationship holds, and the financial situation is stable.

2. 2. The relationship holds, and the financial situation is unstable.

3. 3. The relationship falls apart, and the financial situation is stable.

4. 4. The relationship falls apart, and the financial situation is unstable.

In this scenario, one determines the utility of eight potential outcomes (each action will lead to one of four different outcomes): the utility of having children given that the relationship holds and the financial situation is stable (Utility 1), the utility of not having children given that the relationship holds and the financial situation is stable (Utility 2), the utility of having children given that the relationship falls apart and the financial situation is unstable (Utility 3), and so on. We can express this as shown in Table 4.

Third, one multiplies each outcome’s utility by how probable the state of the world is (i.e. one’s level of confidence that the outcome will occur given the action) and calculates the EU of having a child and the EU of not having a child by adding up the utilities of the corresponding outcomes weighted by the subjective probability of the associated state of the world. Lastly, one chooses the action with the highest EU.

According to Paul, step 2 fails when the decision is transformative (Reference VilligerVilliger 2021): one cannot even approximately assign any reliable utility to the outcome of having a child (Reference PaulPaul 2014: 19–23; Reference Paul2015a: 3–5) because one does not have access to it (Reference PettigrewPettigrew 2015). Denying any epistemic access raises the question of which notion of utility Paul presupposes.

Paul’s concept of subjective value is crucial in this regard. While Reference PaulPaul (2014: 25) recognises that non-subjective values, such as objective moral and prudential values, can hold importance in some decisions, she sets them aside for the first-personal transformative choices of interest to her. Paul argues that even if the value of a non-phenomenal outcome can be evaluated, its unknown phenomenal value may be so positive or negative that it outweighs its known non-phenomenal value (Reference PaulPaul 2015c: 165 and footnote 4).

The centrality of subjective values in decision-making has been challenged (e.g. Reference ChangChang 2015; Reference KauppinenKauppinen 2015; Reference Bykvist and StefánssonBykvist and Stefánsson 2017; Reference KhanKhan 2021). Reference Bykvist and StefánssonBykvist and Stefánsson (2017) argue that assessing non-subjective values is crucial for agents who are not ‘texture fetishists’. As defined by Bykvist and Stefánsson (2017: 131), texture fetishists are agents for whom the experience of an outcome largely determines its value.

The crucial aspect for us is the subjective aspect of experiencing or, as Reference CampbellCampbell (2015) and Reference PaulPaul (2015b: 807) put it, living out the outcome, which ultimately determines its perceived value. With this in mind, we can draw upon the existing research in psychology to interpret Paul’s understanding of utility.

Reference Kahneman, Lichtenstein and SlovicKahneman (2006) distinguishes between decision utility, experienced utility, and predicted utility.Footnote ⁵⁴

• Decision utility is equivalent to modern decision theory’s concept of utility; it is the weight assigned to an outcome (Reference Kahneman, Lichtenstein and SlovicKahneman 2006: 489).

• Experienced utility is the positive or negative feeling corresponding to the chosen option. On a hedonistic interpretation, the experienced utility is the degree of pleasure or pain in the actual experience of an outcome, but other interpretations are possible.

• The predicted utility of an outcome is the agent’s beliefs about the experienced utility at some future time.

Simplifying, we use Paul’s concept of subjective value and the concept of experienced utility interchangeably. We do not mean to interpret Paul as a hedonist by this, but the notions of positive and negative feeling can be broadly construed as more than sensory pleasures and pain (e.g. a generally positive sense of having achieved one’s goals).

Leaving experienced utility aside, predicted utility also plays a key role in Paul’s examples: the prediction of one’s experienced utility fails (at least, the prediction is not sufficiently reliable) because what she calls cognitive modelling fails.

On this reconstruction, Paul’s challenge to deliberative decision theory can be understood as follows:

1. 1. One does not have epistemic access to a transformative outcome’s future experienced utility.

2. 2. Therefore, it is impossible to determine the EU of a transformative choice.

3. 3. Therefore, it is impossible to determine whether one prefers the transformative option (being a parent) or the non-transformative option (living a childless life).

4. 4. Therefore, transformative decisions fall outside the realm of deliberative decision theory.

Reconstruction and Interpretation of Paul’s Argument and Solution

In the previous section, we saw that there is a connection between Paul’s work and the psychological literature on the gap between decision utility and experienced utility (i.e. mischoices in which we fail to choose the option that leads to the best experience) and the gap between predicted utility and experienced utility (i.e. mispredictions in which we fail to predict what will make us happy). Psychologists have described various causes for mischoices and mispredictions (see Reference Buehler and McFarlandBuehler and McFarland 2001; Reference Gilbert, Wilson, Driver-Linn, Barett and SaloveyGilbert et al. 2002; Hsee and Zang 2006: 505):

• Agents might overlook important things.

• Agents might have incorrect beliefs.

• Agents over-predict external rewards, such as income.

• Agents underestimate intrinsic values, such as contact with friends.

Given this wealth of psychological research an agent could read, why does Paul claim that agents cannot access a transformative outcome’s future experienced utility? According to her, the usual way one determines an outcome’s utility is cognitive modelling, which she characterises as using a mental simulation to put oneself ‘in the shoes’ (i.e. the first-person perspective) of a future self. To determine what it would be like for oneself to have a child or to continue living without one, the agent creates a sort of mental cinema: ‘In the first movie, one does have a child. In the second film, one lives a childless life’ (Reference Mathony and MesserliMathony and Messerli forthcoming: 2). Crucially, the agent not only imagines what they will do but also how the experience of being a parent would feel.

From Paul’s viewpoint, the prescribed procedure of mental simulation is essential for the decision to be authentic. The notion of authenticity is integral to Paul’s theory, and she would consider its abandonment highly unsatisfactory (Reference PaulPaul 2014: 112). Even if an agent were to know the transformative outcome’s future experienced utility without undergoing mental simulation, the decision arrived at through such means would lack authenticity.Footnote ⁵⁵

However, in the case of transformative experiences, Paul argues that cognitive modelling fails (see Reference PaulPaul 2014: 124). As discussed earlier, such transformative experiences have a personal component insofar as they can change an individual’s core preferences while simultaneously having an epistemically transformative component that puts up an ‘epistemic wall’. According to Paul, we cannot penetrate this wall through imagination, testimony, or scientific investigation. One might think that scientific data could show what experiences result from becoming a parent. However, Paul argues that aggregated statistical data do not provide sufficiently fine-grained information on how one will experience having a child (Reference PaulPaul 2014: 131–32). She holds that the experience of being a parent only becomes accessible through becoming one.

When deliberating about whether to become a parent, one does not know, for example, one’s career ambitions. As we understand Paul, the problem of personal transformation is, therefore, twofold:

1. 1. Do present preferences (e.g. career is more important than family) or future preferences (e.g. family is more important than career) matter more?

2. 2. One does not know one’s future, transformed preferences.

Therefore, there is not only the problem of whether current or future preferences should guide one’s choice but also the problem that one’s potential preferences after a transformative experience are inaccessible.Footnote ⁵⁶

In addition to raising the challenge, Paul offers her own solution: a rational agent should base transformative decisions on the so-called revelatory value. That is, instead of basing a transformative choice on a prediction regarding one’s experienced utility, one should make such a decision by asking oneself how one values new experiences and new selves. According to Paul, we can rationally choose transformative experiences. However, such a choice requires resources not usually part of decision theory, such as a desire to undergo such experiences.

As part of her solution, Paul reformulates the structure of the decision problem so that the outcomes do not involve experiencing but rather discovering the transformative outcome. If you deliberate about epistemic transformative choices, such as trying durian fruit for the first time, the relevant outcomes are discovering the taste of durian and avoiding discovering the taste of durian. In Paul’s view, these outcomes are independent of the experienced taste, which one cannot predict. Similarly, if you deliberate about personal transformative choices, such as being a parent for the first time or studying medicine, the crucial question is how much you value discovering what it is like to be a parent or a doctor: which Paul calls the revelatory value.Footnote ⁵⁷

However, it is questionable whether Paul’s solution is successful. Some authors have claimed to spot tension in it (e.g. Reference KauppinenKauppinen 2015; Reference ShupeShupe 2016; Reference Bykvist and StefánssonBykvist and Stefánsson 2017). While Paul initially disregards non-phenomenal values such as those of prudence and morality and focuses on the issue of subjective values, she later proposes a solution that appears to be based on a non-phenomenal value: the revelatory value. As noted by Reference Bykvist and StefánssonBykvist and Stefánsson (2017), this presents a challenge for Paul since she must argue that the revelatory value is subjective despite facing difficulties in doing so.Footnote ⁵⁸

We provide an interpretation that identifies a related tension in Paul’s solution, drawing upon prior research on this subject. Our argument has three steps.

First, as mentioned earlier, Paul proposes that a transformative choice should be taken authentically.

Second, for Paul, authenticity means ‘authentic self-governance informed by knowledge via experiential or imaginative acquaintance with objects of deliberation’ (Paul’s characterisation of her concept of authenticity in her Teaching Guide to Transformative Experiences: 9; see also Reference PaulPaul (2015b: 807)). Note that Paul’s perspective regarding what constitutes an authentic choice has thereby been subject to criticism.Footnote ⁵⁹ As Reference KhanKhan (2021) noted, Paul posits that a transformative decision can only be deemed authentic if it involves mental simulation. Our interpretation aligns with Reference KhanKhan’s (2021) assertion that Paul’s definitions of rational and authentic preferences both entail imaginative acquaintance with potential outcomes (i.e. in Paul’s view, an authentic choice necessitates cognitive modelling).

Third, the revelatory value is determined independent of forecasting/cognitive modelling in Paul’s framework: one uses cognitive modelling to find out what an experience is like, but one does not use cognitive modelling to find out whether one wants to discover what the experience is like or to avoid discovering it. In other words, according to Paul, a choice based on the revelatory value does not involve cognitive modelling.

Therefore, a choice based on the revelatory value cannot be authentic. In summary, the tension is that Paul claims that a transformative choice should be taken authentically, but her own solution leads to the choice not being taken authentically. Therefore, Paul’s solution appears unsatisfactory.

Multi-Criteria Decision-Making

Reference Reuter and MesserliReuter and Messerli’s (2018) approach is based on standard multi-criteria decision-making science (e.g. Reference Ishizaka and NemeryIshizaka and Nemery 2013). The idea is that rational decision-making involves two components:

1. 1. Value: the extent to which a criterion favours a certain outcome.

2. 2. Weight: a criterion’s relative importance.

To illustrate, imagine that you have to choose between buying one or another apartment, and suppose two criteria matter: price and location. First, each of the two criteria has a weight. If you consider both criteria equally important, their respective weights are 0.5. Second, both apartments have value regarding price and location. If one apartment is cheaper, it has a higher value regarding price. According to this approach, the overall utility of an action, such as buying an apartment, is determined by a weighted average of how much each criterion is fulfilled.

However, unlike standard multi-criteria decision science, Reuter and Messerli’s approach allows decision criteria to be unknown. For example, you might not know whether you value one apartment more than another regarding location. This approach allows agents to form a preference ranking over acts even if values are unknown, for example, because they depend on the experienced utility of a transformative outcome.

To illustrate how the models work, we consider the transformative decision of whether to have a child. Assume that three criteria influence our agent’s choice:

1. 1. whether the agent’s partner wants to have a child;

2. 2. the agent’s financial situation;

3. 3. the experienced utility of what it is like to have a child.

Furthermore, these criteria differ in importance to the agent. The partner’s opinion accounts for 40 per cent of the decision process (w_partner = 0.4), while financial impact contributes 35 per cent (w_financial = 0.35), and experience 25 per cent (w_experience = 0.25). For illustration, we assign the following values: v_{partner/pro-child} = 1 and v_{partner/contra-child} = 0 (i.e. the opinion of the partner speaks totally in favour of becoming a parent), v_{financial/pro-child} = 0.5, and v_{financial/contra-child} = 0.5. Notably, the experienced utility is unknown, so v_{experience/pro-child} = ? And v_{experience/contra-child} = ? A summary is provided in Table 5.

Table 5 Multi-criteria decision-making

Criteria	Weight	Value for a child	Value against a child
Partner wants to have a child	0.40	1	0
Financial situation	0.35	0.5	0.5
Experienced utility of having a child	0.25	?	?

By calculating the overall utility for both acts – and only using the known weights and values – one arrives at:

$U\left(\text{having a child}\right)=0.4\times 1+0.35\times 0.5=0.575$

$U\left(\text{not having a child}\right)=0\times 0.4+0.35\times 0.5=\mathrm{0.175.}$

Even if the experienced utility totally speaks against having a child (i.e. v_{experience/contra-child} = 1), the overall utility of not having a child would be at most U(not having a child) = 0.425 (0.175 + 0.25), which is still much lower than U(having a child) = 0.575. Therefore, preference ordering is possible, even if the experienced utility is unknown, provided w_experience < 0.5.

Of course, one might maintain that the weight w_experience is generally >0.5. However, Reference Reuter and MesserliReuter and Messerli (2018) conducted an empirical investigation asking individuals to weigh a range of values in terms of importance regarding questions such as whether or not to have a child. They found that the importance individuals assign to the weight w_experience does not make it impossible, or even improbable, that they will form a rational decision and act towards what they prefer most. Indeed, because how an experience will feel does not have sufficient weight or, alternately, because other criteria are together sufficiently important, individuals faced with a transformative choice will make a rational decision much of the time.Footnote ⁶¹

A more serious problem would arise if the weights could be changed due to the personally transformative character of the experience. If so, the weights assigned to what it will feel like to be a parent, for example, might increase so that an agent would have decided differently. Then, the decision would have arguably failed to be rational. Put simply: the worry is that the weights might also be outcome-dependent. However, the empirical data that Reference Reuter and MesserliReuter and Messerli (2018) have collected from individuals who already have children (and, therefore, have already had the transformative experience and the possibly changed weights) are relatively robust (i.e. the weights of the decision criteria look similar to those who had not undergone the experience).

Reuter and Messerli’s solution has been criticised on both theoretical and empirical grounds. One theoretical critique refers to the fundamental assumptions of multi-criteria decision-making models. Most such models assume (a) the separability of the decision criteria (to avoid double-counting); (b) the numerical ascertainability of the criteria weights; (c) the value and weight attributions range between 0 and 1; and (d) that for each criterion, v_{outcome 1} + v_{outcome 2} = 1 (e.g. v_{experience/contra-child} + v_{experience/pro-child} = 1). Assumption (c) is particularly controversial (see Reference VilligerVilliger (forthcoming b)) for a critique). For instance, why can values not be >1? The reason is that values can be taken to represent whether a criterion is fulfilled in multi-criteria decision-making models. For example, if one’s partner wants to have a child, the respective criterion is fulfilled (v_{in favour of child} = 1).

One justification for imposing a normalisation on values can be found in the satisficing theory (Reference SimonSimon 1955). While there are significant differences between the satisficing and multi-criteria decision-making models, Simon’s rationale for satisficing can also be extended to multi-criteria decision-making: the classical conception of rationality embodied in standard decision theory is overly demanding demands on decision-makers. A normalised multi-criteria approach is easier for us as limited human beings to handle.Footnote ⁶²

Reference VilligerVilliger (forthcoming b) also argues that Paul’s challenge explicitly refers to Savage-type EU theory. However, it is unclear why one must stick to this version of decision theory. After all, the important question is which theory is more plausible for deliberation. Crucially, Paul seems to accept Reuter and Messerli’s theoretical choice model for making rational transformative decisions (Reference Chituc, Paul and CrockettChituc et al. 2021).

Instead, Reference Chituc, Paul and CrockettChituc et al. (2021) criticise Reference Reuter and MesserliReuter and Messerli (2018) on empirical grounds. They argue that the so-called evaluability bias explains Reuter and Messerli’s empirical findings. The idea is that participants attach more weight to the decision criteria they can know, and since they cannot know w_experience, they attach less weight to it.Footnote ⁶³ While the evaluability bias might indeed play a role in explaining participants’ responses, we should remember that a preference ordering in Reuter and Messerli’s model is possible as long as w_experience < 0.5. Furthermore, more research is needed regarding the normative relevance of the objection (is the evaluability bias always irrational?) and the relationship between subjective and non-subjective values in general (how should a decision-maker weigh experiential values relative to non-experiential values?).

Present Preference Solution

Reference IsaacsIsaacs (2020: 1074) claims that Anne’s change of preferences is not problematic since decision theory does not depend on future utilities. He writes, ‘It is easy to say what an agent should do in the face of potentially changing utilities – maximise EU relative to his current credences and current utilities’ (Reference IsaacsIsaacs 2020: 1078).Footnote ⁶⁷ In Isaacs’ view, current Anne should prevent future Anne from getting what she wants if what she wants is diametrically opposed to what current Anne wants.Footnote ⁶⁸ Therefore, Anne should continue travelling without having a baby.

One way to elaborate is to argue that rational choice is limited to an individual’s current preferences and beliefs because standard decision theory aims to formalise means-end rationality. According to this view, it is not means-end rational to choose means to attain goals that the agent has discarded or has not yet embraced. However, note that a means-end interpretation is not universally accepted since decision theory does not necessarily involve an instrumental conception of practical rationality (e.g. Reference Nida-RümelinNida-Rümelin 1994).

Another way to elaborate is to argue, like Paul, that we cannot predict our own future preference changes (e.g. Reference ElsterElster 1983).Footnote ⁶⁹ Consequently, present preferences are all Anne has when making a choice. This response suggests that Anne simply has no idea whether her future preferences will diverge from her current ones. For example, Anne cannot predict whether her future self will enjoy settling down with a baby more than travelling. After all, a significant percentage of individuals regret parenthood (e.g. Reference DonathDonath 2015; Reference Geißler and LaudeGeißler and Laude 2016), and some individuals travel with babies. Furthermore, preferences may change unexpectedly even if Anne chooses the non-transformative option. Anne’s desire to travel may weaken or disappear even if she tries to avoid transformation.

While some uncertainty is to be expected, humans nonetheless seem able to base their choices on possible future preferences and anticipate them to a certain extent. The idea that preference change can be foreseen is especially plausible if – contrary to Paul – one considers testimony and that one’s values are socialised (i.e. created through socialisation processes). In Anne’s case, consulting testimony could be informative.

Reference Geißler and LaudeGeißler and Laude (2016) stated that approximately one-fifth of parents regret parenthood. Assuming that nothing about Anne renders her especially similar to these regretful parents, she would most likely not regret the choice to have a child. Therefore, she can somewhat confidently predict the probability distribution of her future preferences and could reasonably act upon them.

A further option to justify the present preference solution would be to argue that our present preferences already appropriately consider our future preferences, or at least should do so. When Luke realises that his future self will prefer to retire and go fishing instead of continuing to work, this might change Luke’s present preferences for future retirement, perhaps even his current preferences regarding how much money to save each month. Our present preferences are not causally independent from our beliefs regarding our future preferences. Provided the present and future self are appropriately related to each other, considering each other in their standard preferences, there is no need to consider more than the present preferences. Otherwise, the future preferences would just be accounted for twice.

However, it seems to us that sometimes agents disagree, even conflict, with their future selves. Luke might resent his future self for wanting to go fishing rather than continue the working lifestyle he currently values. He might even save less money to ensure his future self cannot fulfil its preference. While such extreme cases of disagreement might be less common, it seems to us that more than the present preference solution is needed to address them.

Higher-Order Preference Solution

Reference Ullmann-MargalitUllmann-Margalit (2006) proposes that Anne should base her choice on higher-order preferences (preferences over preferences). To illustrate the concept of higher- and lower-order preferences, consider Reference FrankfurtFrankfurt’s (1971: 8) example of a drug addict. A drug addict might have a first-order preference to consume drugs instead of abstaining but a higher-order preference not to have the preference to consume drugs.

According to Reference FrankfurtFrankfurt’s (1971: 7) view, Anne’s ability to reflect on her preferences allows the formation of higher-order preferences. When confronted with a choice that might lead to a change of some preferences, Anne should therefore ask herself which of these preferences she would prefer to have: does she want to become the person that prefers having a child or remain the person that prefers travelling (Reference Ullmann-MargalitUllmann-Margalit 2006: 167)?Footnote ⁷⁰

Advocates of a higher-order preference solution have to address at least two challenges. First, the normativity challenge concerns the normative power of higher-order preferences and questions whether higher-order preferences are worthier than first-order preferences. The second challenge highlights that higher-order preferences can also change: Anne’s higher-order preference for settling down might reverse when she experiences motherhood. We call this the higher-order change challenge. We briefly discuss both challenges, beginning with the normativity challenge.

One possible response to the normativity challenge is to assert that low-order preferences backed up by higher-order preferences typically promote an agent’s well-being more than those lacking such backing. This promotion of well-being would then justify giving them priority.

There are two problems with this argument. First, it is questionable whether there are objective facts about what is valuable for each comparison of goals or preferences (Reference PettigrewPettigrew 2019: 47). For example, it seems dubious that there is an objective fact regarding whether studying business administration is more valuable than studying art.Footnote ⁷¹ Second, it is questionable whether lower-order preferences backed up by higher-order preferences necessarily promote an agent’s well-being more. While this may be true in the case of Frankfurt’s drug addict, it might be false in the case of Anne. It is entirely possible that Anne has a higher-order preference for a first-order preference for being a mother and that the satisfaction of this preference will decrease her well-being. Indeed, there is empirical evidence that parents’ levels of life satisfaction decrease on average and stay below their previous childless levels of life satisfaction for several years (e.g. Reference Luhmann, Hofmann, Eid and LucasLuhmann et al. 2012). One may interpret this as evidence that parents’ well-being decreases on average.

Another argument is that only higher-order preferences reflect who we want to be and what we consider meaningful. In this view, Anne’s higher-order preference for becoming a mother reflects what she considers a meaningful life. However, this approach is also controversial. Assume that Anne becomes extremely unhappy as a settled-down mother who does not perceive her parental duties as meaningful. In this case, the preference for settling down with a child over travelling might be backed up by a higher-order preference – she would prefer to have such a preference – but it is unclear whether acting on this preference reflects what is more meaningful to Anne.

In addition to the questions about the normative force of higher-order preferences, the higher-order change challenge looms. If future higher-order preferences differ from current ones, how should we choose between them? Reference PettigrewPettigrew (2019: chapter 4) seems correct that the higher-order preference solution, which he calls ‘the Utility of Utility Solution’, does not solve the challenge of changing selves but pushes the problem to a higher-order level. Why should Anne prioritise present higher-order preferences rather than possible future higher-order preferences?

Therefore, it is clear that both the present and higher-order preference solutions face problems. Nevertheless, Anne’s preferences will likely change when she gets older, regardless of which option she chooses. Therefore, Anne must face the challenge of how to choose in light of future preferences that likely differ from her current ones.

Pettigrew’s Aggregate Utility Solution

Reference PettigrewPettigrew’s (2019) aggregate utility solution is based on the idea that Anne’s past, present, and future selves can be treated as a group of individuals whose attitudes must be aggregated. In other words, Anne is a collective entity comprising diverse selves whose attitudes must be aggregated. While Anne’s current self is making a choice, she must decide on behalf of all three selves since each self contributes to the person Anne. So, when Anne decides, she should base her choice not only on her present utilities but also on those of her past and possible future selves matter, although to different degrees.Footnote ⁷² From this metaphysical perspective, Pettigrew can use social choice theory tools to address the problem of choosing to change selves.Footnote ⁷³

Of course, much is to be said about how exactly this aggregation will be modelled, and many options exist. For example, one could use majority voting instead of Pettigrew’s weighing scheme. In light of this universe of options, Pettigrew spends much effort justifying his exact aggregation model, but we will limit ourselves to presenting the final results of his theory. The key points can be summarised as follows:

• The aggregation occurs on the levels of utilities and subjective probabilities (rather than preferences or beliefs, for example).

• The aggregation takes the form of a weighted average. That is, the final value function should average the utility function of each relevant self, weighted by how much that self’s mental state should matter.

• To determine the weights, Pettigrew makes recourse to Derek Parfit’s contribution to ethics and the personal identity debate. In particular, the degree of connectedness between individuals plays a role in specifying the average’s weights.

Applying this strategy, Pettigrew would argue that Anne should base her choice on a weighted average of past, present, and potential future utilities. This weighted average should then determine the evaluation of acts and inform her decision.

To illustrate how Pettigrew’s solution works, we ignore uncertainty and just ask how Anne should calculate the utilities for the outcome of settling down with a child over a life of travelling. In this case, Anne should proceed in two steps to make a rational choice.

In the first step, Anne determines the utilities of the outcomes: the extent to which her past, current, and future selves value this choice, multiplied by the weights assigned to the respective selves. Simplifying, by only taking one future self into account, for now, we can represent this as follows:

• Past Anne’s utility in future Anne settling down with a child: U_Past(settling down)

• Current Anne’s utility for the same future option: U_Present(settling down)

• Future Anne’s utility: U_Future(settling down)

The indices concern the utility of which self is considered, while the option is always considered to be in the future.

Our case study, in which future Anne would prefer having a baby but current Anne would prefer travelling, indicates that: U_Present(settling down) < U_Present(travelling). Nonetheless, it might be the case that the future self assigns a larger utility to settling down: U_Future(settling down) > U_Future(travelling). This relation might be shared by the past self so that U_Past(settling down) > U_Past(travelling). After all, Anne and John have dreamed of starting a family.

A situation like this can be summarised as shown in Table 7 if we assign utilities to how Anne’s selves evaluate the corresponding outcome.

To signify that these different utilities add up to one individual’s utility, we have the weights for them add up to 1. For illustration: if the weight of current Anne’s utility is 0.6 and the weight of future Anne’s utility is 0.3, then the weight of past Anne’s utility is 0.1.

Using these weights, U_Overall(settling down) would be 0.1 × 2 + 0.6 × 1 + 0.3 × 2 = 1.4 and U_Overall(travelling) would be 0.1 × 1 + 0.6 × 2 + 0.3 × 1 = 1.6. In this scenario, the overall utility for settling down turns out to be smaller, but we have only considered one future Anne so far. There might very well be a second possible future Anne that assigns U_Future(settling down) = 5. Assuming that the future Anne’s split the overall weight of the future and keeping all other utility assignments identical, we arrive at U_Overall(settling down) = 0.1 × 2 + 0.6 × 1 + 0.15 × 2 + 0.15 × 5 = 1.85.

In the second step, Anne should calculate which act maximises her EU. At this stage, we could reintroduce uncertainty (i.e. Anne would have to multiply the overall utilities of the outcomes with the respective probabilities that the outcomes will occur). Since this step would follow the procedure of Savage-type decision theory, we will not describe it again.Footnote ⁷⁴

Thus far, we have illustrated how aggregation, including weights, works.Footnote ⁷⁵ How to determine the weights is another question. Pettigrew follows Parfit and accepts that connectedness is more important than personal identity and sympathises with the following principle: the more connected a self is to Anne’s present self, the more the weight that should be attached to it.

The crucial question for us is what being connected means when applied to different selves. Pettigrew makes three claims. First, Anne’s past self is connected to her present self in that Anne now benefits from her past sacrifices. One can imagine, for example, that Anne previously saved money and worked hard to later be in a good position to have a child. According to Reference PettigrewPettigrew (2019: 172), Anne is therefore obliged to give a certain amount of weight to her past self.

Second, Anne is cognitively connected to her various selves, in that they share experiences and cognitive states, such as memories and beliefs. Following Parfit, Reference PettigrewPettigrew (2019: 187–192) argues that these cognitive connections are a legitimate reason to discount the future; the weaker the cognitive connection between a future self and Anne’s current self, the less the weight that should be given to that future self.

Third, Anne is connected to her selves, in that they share values; therefore, the closer the self’s values are to Anne’s current values, the more the weight that should be assigned to them (Reference PettigrewPettigrew 2019: 213). In other words, the more similar Anne’s different selves’ utilities are to her present self’s utility, the higher the weight it should be assigned. In Pettigrew’s view, agents feel less alienated the more they base their decisions on commonly shared values. To illustrate this idea, consider a student who does not value money but studies business instead of art because they expect to care about money in the future. If our student despises individuals who consider money important but nevertheless assigns a great weight to their potential future self, they will feel alienated.

The aggregate utility solution seems to be a more promising approach than the present or higher-order preference solution. Nonetheless, we will briefly hint at two concerns: unknown past utilities and constraints on weights.

Regarding the first concern, it is helpful to recall that the challenge of transformative experiences not only consists of the question of whether present or future values matter more but also of the fact that one does not know one’s future values. Therefore, Anne does not know her future self’s utility of having a child. Pettigrew proposed the fine-graining technique as a solution (see the ‘Uncertain Utilities – The Fine-Graining Solution’ section). Applied to our example, this means that future Anne’s utility can be replaced by the aggregate of the utilities of Anne’s several possible future selves. In this way, Pettigrew offers a method to address unknown future utilities. However, he underestimates that one might not know one’s past utilities either. The main reason past utilities might be unknown is that memory is unreliable and often inaccurate.

In the context of this debate, the episodic memory of what an experience was like and how one valued it seems to be crucial. Let us call the memory of what an experience was like ‘qualitative memory’ (Reference MonteroMontero 2020) and the memory of how one valued what it was like ‘evaluative memory’ (Reference Kahneman, Lichtenstein and SlovicKahneman 2006). For example, remembering that giving birth was painful differs from remembering how the pain felt. Both qualitative and evaluative memory are problematic in their own ways, but qualitative memory is especially so. While mothers remember that they felt pain during childbirth, they often cannot remember how this pain felt.

To give a more mundane example, consider the rollercoaster ride experience. If one had a perfect qualitative memory of this experience, one would only need to experience it once. To experience the thrill of a rollercoaster ride again, one could simply remember the already-experienced ride. Luckily for rollercoaster operators, recalling qualitative memories is not so simple: one must go for another ride. However, it is not only qualitative but also evaluative memory that is flawed (Reference Kahneman, Lichtenstein and SlovicKahneman 2006). If this is true (i.e. past utilities cannot be remembered accurately), it is questionable whether Anne can make an intertemporal and, in a way, interpersonal utility comparison between her past, present, and future selves (see Reference Ahmed and PettigrewAhmed 2021b: 485–87).

In response, Pettigrew might question whether imperfect memory is a problem specific to his solution. He could argue that the problem of imperfect memory applies to all relevant forms of decision theory. Let us again consider the rollercoaster example to illustrate this idea. In order to know whether one should prefer a rollercoaster ride to a museum visit, one needs to assess the two different experiences. For this, one must typically either have experienced such a ride to assess its utility value or be able to ask others who have experienced the ride. While in some cases there might be other evidence, such as based on scientific investigations, usually somebody must have had the experience and know about it. Consequently, if nobody accurately remembers how they valued the experience, the option’s utility value cannot be assessed, and decision theory does not help us choose. While this would be a disappointing outcome for decision theory (and sounds slightly absurd), it is not a criticism specific to Pettigrew.

Another option would be for Pettigrew to propose using retrospective expectations. Just as in the case of the future, agents would consider multiple epistemically plausible past versions of themselves.Footnote ⁷⁶ However, this attempted solution might appear to neglect an important difference between past and future, at least from the perspective of an agent about to choose: only one past has occurred to them, while many future paths appear open. Why should pasts matter that are not even actual options anymore?Footnote ⁷⁷ Some of the standard arguments for EU, where we also use expectations, might be applicable, but not straightforwardly, if at all.

Any such justification must address the fact that some of Pettigrew’s (Reference Pettigrew2019: 169) reasons for considering the past, such as to account for past effort, appear to depend on only considering the actual past. The past effort in achieving a degree matters when deciding whether to stay in university now because it was actually spent, not because it could have been spent. Otherwise, Anne would have to consider all the effort spent by a possible past Anne to become a mother!

Pursuing this argument further, if only one case matters, is then expectation really the best way to consider the past? This question may be addressed, but as of yet, it points to a gap in the aggregate utility solution.

The second concern relates to the constraints on weights. According to Reference PettigrewPettigrew (2019: 159), there are few strict rationality constraints on how an agent should weigh their past, present, and future selves. However, one might worry whether the weights will end up determinate enough to allow changing selves to choose rationally. To achieve determinacy, Pettigrew explicitly goes beyond the rationality requirements of decision theory and considers a more general notion of reasonable weights.

Introducing the concept of reasonable weights is a further step away from traditional decision theory than providing formalism for accounting for past and future preferences. Preferences are at least the type of objects that usually have their home in decision theory, while the considerations that Pettigrew now brings into the discussion do not. For example, in decision theory, we do not typically accuse individuals who abandon their present values of having ‘sold out’ (Reference PettigrewPettigrew 2019: 210–211) or believe that morally better options should get higher weight (Reference PettigrewPettigrew 2019: 35–36).

While allowing to assign more specific weights, introducing such broadly moral considerations also invites further controversy. Can Anne only rationally choose to have a child after reflecting on her ethical obligations to her future self? Is a strong moral anti-realist unable to rationally choose as a changing self? In light of such issues, one might hesitate to introduce moral considerations into a theory of how instrumentally rational agents whose preferences change should choose.

We have outlined the two concerns in broad terms only to showcase active areas of engagement. Much remains to be said on both Pettigrew’s approach and the challenge of choosing to change selves in general.

While we cope daily with changes in what we want, appearing to act as practical agents that broadly realise their preferences, our theories of how we face the problem of choosing to change selves are heavily debated and will remain so for the foreseeable future. We do not need a theory of knowledge to know, and we do not need a complete account of practical agency to be practical agents. However, when faced with troubling decisions and the prospect of changing preferences, it would at least provide some peace of mind if we could refer back to well-developed and well-founded theories of our agency. We hope our discussion of the various debates has made progress towards this purpose. Since your authors strongly prefer changing their minds in light of new arguments, we look forward to further developments in these debates.