2. Aggregating desire-satisfaction

In this section, building on previous works of Barrett (Reference Barrett2019, Reference Barrett2022) and Van der Deijl and Brouwer (Reference Van der Deijl and Brouwer2021), I describe four aggregation principles that an adherent of a desire-satisfaction theory of well-being could adopt and show how they can be formalized. I then argue that one of these four principles is implausible on numerous counts. As I will show in the following sections, the other three aggregation principles are vulnerable to the objection from trivially satisfied desires.

Broadly following Barrett (Reference Barrett2019), we can formally represent an individual's desire for a feature of an outcomeFootnote ¹ at some point in time as a function D_I,t(x) = r, mapping an individual I, a point in time t, and a feature x onto a desire strength r.Footnote ² If an individual has no desire for a feature x, this can be represented by D_I,t(x) = 0. Barrett's view is that we should call D_I,t(x) with negative strength aversions toward x, and that these constitute a phenomenon psychologically distinct from desires. Alternatively, one might have the view that aversions toward x are simply (positive) desires that x not obtain, which could be represented formally as an additional constraint for all I, t, x that D_I,t(x) ≥ 0. As we will see, aversions slightly complicate some aggregation principles. However, nothing in my objection from trivially satisfied desires turns on the status of aversions.

Following Van der Deijl and Brouwer (Reference Van der Deijl and Brouwer2021), we can represent the degree to which a desire for x is satisfied at some point in time t as a function S_t(x) = s, where 0 ≤ s ≤ 1. This allows desires to be partially satisfied, although again, nothing in the following argument depends on this assumption. Alternatively, one could require that S_t(x) has to assume either the value of 0, when the desire for (or the aversion toward) x is not realized, or 1, when it is realized.Footnote ³

Which aggregation principles could desire-satisfactionists adopt? There seem to be four broadly plausible answers: totalism, proportionalism, differentialism, and anti-frustrationism. The most straightforward view may be totalism (Barrett Reference Barrett2022; Van der Deijl and Brouwer Reference Van der Deijl and Brouwer2021): the view that the degree of an individual's well-being consists in the sum of the strength of her satisfied desires. Totalism can be considered a variant of what Parfit (Reference Parfit1984: 497) calls “summative theories.” On totalism, an individual I's degree of well-being W_I(t) at a point in time t can be represented formally as follows:

$$W_I( t ) = \mathop \sum \limits_x D_{I, t}( x ) S_t( x ) $$

This sums over all features x toward which the individual I has a desire or aversion, i.e., where D_I,t(x) ≠ 0. Since we have formalized aversions toward x as having a negative strength D_I,t(x), this view subtracts an individual's realized aversions from her satisfied desires, if we allow for aversions. If we deny the existence of aversions as a welfare-relevant psychological phenomenon distinct from desires, all D_I,t(x) will be non-negative and so will be the total degree of an individual's well-being.

A second possible aggregation principle can be called proportionalism (Barrett Reference Barrett2022). Proportionalism claims that the degree of an individual's well-being is the proportion of her satisfied desires relative to all her desires, weighted by their strength. In contrast to totalism, this view tries to incorporate the “Epicurean Intuition” (Van der Deijl and Brouwer Reference Van der Deijl and Brouwer2021: 778) that gaining a new unsatisfied desire is intrinsically bad (and conversely, losing an unsatisfied desire is intrinsically good) for an individual. Van der Deijl and Brouwer (Reference Van der Deijl and Brouwer2021), modulo some slightly different notation, formalize it as follows:

$$W_I( t ) = \displaystyle{{\mathop \sum \nolimits_x D_{I, t}( x ) S_t( x ) } \over {\mathop \sum \nolimits_x \vert {D_{I, t}( x ) } \vert }}$$

Proportionalism represents the degree of well-being of individuals on a scale between −1 and 1. If an individual has no aversions and only fully satisfied desires, her well-being is 1. On the other hand, if all aversions of an individual are fully realized and if she has no desires, her well-being according to proportionalism is −1.Footnote ⁴ This points to the implausible implication that an individual with the worst possible well-being −1 actually becomes better off if she forms an unsatisfied desire. More generally, this is the case when starting from any negative level of well-being, which means that proportionalism actually violates the Epicurean intuition for individuals with negative welfare. Conversely, on proportionalism, gaining even unrealized aversions decreases one's well-being slightly if it was positive before. This is because gaining a new unrealized desire or aversion will increase the denominator of the fraction while holding the numerator constant. Thus, on proportionalism, whether forming a new unrealized desire or aversion is good or bad for an individual depends on her prior well-being.

In addition to these two aggregation principles identified by Van der Deijl and Brouwer (Reference Van der Deijl and Brouwer2021), two more possible aggregation principles are sometimes alluded to in the literature. Heathwood (Reference Heathwood2006: 548) and Parfit (Reference Parfit1984: 496) can be read as suggesting a variant of totalism which satisfies the Epicurean intuition. In contrast to proportionalism, this principle does not appeal to the proportion of satisfied desires to all desires, but to the difference of satisfied and unsatisfied desires and could therefore be called differentialism. Differentialism can be formalized as followsFootnote ⁵:

$$\eqalign{W_I( t ) = & \mathop \sum \limits_x D_{I, t}( x ) S_t( x ) -\mathop \sum \limits_x D_{I, t}( x ) ( {1-S_t( x ) } ) \cr = & \mathop \sum \limits_x D_{I, t}( x ) ( {2S_t( x ) -1} ) } $$

Like totalism, differentialism claims that forming a new satisfied desire is good for an individual. But unlike totalism, it satisfies the Epicurean intuition that gaining a new unsatisfied desire is not neutral, but actively bad for one. As stated, this view also implies that if we allow for aversions, unrealized aversions add toward an individual's well-being. One might consider this an implausible implication – if I now form a strong aversion to eating blue apples, does this really make me better off?Footnote ⁶ Differentialists may therefore want to deny aversions as an independent welfare-relevant phenomenon, as Heathwood seems to do. Alternatively, one could treat aversions asymmetrically, counting unsatisfied desires as negative but unrealized aversions as neutral toward an individual's welfare.

A fourth and final aggregation principle has been called anti-frustrationism (Fehige Reference Fehige, Fehige and Wessels1998). Peter Singer (Reference Singer1993: 128–29) has tentatively advocated this principle in the past, calling it the “moral ledger” view. This view thinks “of the creation of an unsatisfied preference as putting a debit in a kind of moral ledger that is merely cancelled out by the satisfaction of the preference” (Singer Reference Singer1993: 128). As a first approximation, it can be formalized as follows:

$$W_I( t ) = {-}\mathop \sum \limits_x D_{I, t}( x ) ( {1-S_t( x ) } ) $$

Basically, the anti-frustrationist agrees with the differentialist that having unsatisfied desires decreases an individual's well-being but disagrees that having satisfied desires increases it. In the naive formulation above, where aversions are straightforwardly treated like desires with negative strength, anti-frustrationism has a similar potential problem with unrealized aversions as differentialism: it implies that forming an unrealized aversion makes one better off. Moreover, formalized as above, anti-frustrationism would imply that realized aversions are neutral toward one's well-being. To avoid these implications, anti-frustrationism could be revised as follows:

$$W_I( t ) = {-}\mathop \sum \limits_{\{ {x{\rm \vert }D_{I, t}( x ) > 0} \} } D_{I, t}( x ) ( {1-S_t( x ) } ) + \mathop \sum \limits_{\{ {x{\rm \vert }D_{I, t}( x ) < 0} \} } D_{I, t}( x ) S_t( x ) $$

This revised version counts unsatisfied desires and realized aversions as negative toward one's welfare, while satisfied desires and unrealized aversions are seen as neutral. But anti-frustrationism as represented above has another potential problem: it holds that individuals' well-being is always negative. We may think that the zero-point in a theory of well-being should represent the point above which life, to use Parfit's (Reference Parfit1984: 358) description, is (intrinsically and prudentially) “worth living.” Taken as formalized above, anti-frustrationism would then imply that a life full of desire-satisfaction which also contains one single weak unsatisfied desire is not worth living. Singer (Reference Singer1993: 129) has proposed to avoid this implausible implication by specifying a baseline of desire-frustration at which an individual's well-being is zero. This second revised version of anti-frustrationism can be formalized as follows, where the positive number L represents the compensation for the baseline amount of desire-frustration:

$$W_I( t ) = L\;-\mathop \sum \limits_{\{ {x{\rm \vert }D_{I, t}( x ) > 0} \} } D_{I, t}( x ) ( {1-S_t( x ) } ) + \mathop \sum \limits_{\{ {x{\rm \vert }D_{I, t}( x ) < 0} \} } D_{I, t}( x ) S_t( x ) $$

However, as Singer (Reference Singer1993: 129, Reference Singer, Fehige and Wessels1998) concedes, introducing such a zero-level seems ad hoc. If desire-frustration is what fundamentally makes individuals' lives go badly on anti-frustrationism, and there is nothing on the other side of the ledger which fundamentally makes lives go well, then it seems natural to conclude that individuals' well-being is always negative, i.e., a life that contains even one unsatisfied preference is not worth living. Fehige (Reference Fehige, Fehige and Wessels1998: 521–23), who advocates anti-frustrationism, concurs with the latter conclusion.

As we have seen, the four aggregation principles have different strengths and weaknesses. Besides the potential problems discussed above, another test is how aggregation principles handle cases like depression (Spaid Reference Spaid2020; Van der Deijl and Brouwer Reference Van der Deijl and Brouwer2021). Depressed individuals typically lose many of their previously held desires. Consider Anna, an individual who has lost all her desires and aversions and is left with a single satisfied desire, the desire to lie in bed all day. Proportionalism implies that if this desire is satisfied, Anna is as well-off as possible, having a well-being of 1 (Van der Deijl and Brouwer Reference Van der Deijl and Brouwer2021: 778–79). The same conclusion holds for anti-frustrationism, on which Anna has the best possible well-being level 0 (L in Singer's revised version). That some depressed individuals are considered very well-off appears to be a very unpalatable implication. It is also an avoidable one. Neither totalism nor differentialism implies that Anna is nearly as well-off as possible, although they do imply that her well-being is positive.

Anti-frustrationism in particular seems to have many issues. We have already seen anti-frustrationism's forced choice between the implication that no one's life is worth living and an ad-hoc zero-level, as well as its implausible verdicts in some cases of depression. In addition, since anti-frustrationism claims that losing an unsatisfied desire is as good as satisfying it, the principle is vulnerable to an adaptiveness objection. Consider the following case:

If Beth is only concerned with her own well-being, should she take the pill? It appears that anti-frustrationism would recommend that she does. The pill is certain to increase her well-being by removing her unsatisfied desire to be free, whereas the attempt to break out carries a small risk of failure. But this seems absurd, and none of the other aggregation principles have this implication. All in all, anti-frustrationism seems to be an implausible view. I think desire-satisfactionists should reject it. For the remainder of this article, I therefore set aside anti-frustrationism. Since the other three aggregation principles imply that the proliferation of new satisfied desires is good for the desirer, I call them proliferationist principles. I suggest that proliferationist principles suffer from the problem of trivially satisfied desires.

Desire-satisfactionists might hope that there is an entirely different aggregation principle out there that avoids these problems. But this seems unlikely: it appears that all plausible non-proliferationist aggregation principles will yield counterintuitive verdicts in some cases of depression. Recall Anna, a depressed person who has lost all her desires and aversions and is left with a single satisfied desire, the desire to lie in bed all day. On plausible non-proliferationist aggregation principles, there seems to be nothing that can make Anna better off: forming new aversions or unsatisfied desires will surely not increase her well-being; she has no unsatisfied desires that could be satisfied in order to make her better off; and forming and satisfying new desires is not good for her by stipulation on non-proliferationism. So, aggregation principles that are prima facie plausible may face a dilemma: either they yield unacceptable verdicts in some cases of depression, or they face the problem of trivially satisfied desires. If this is the case, then the search for a new aggregation principle seems unlikely to solve the problems for desire-satisfaction theories of well-being discussed here. In the following sections, I examine the second horn of the dilemma: the problem of trivially satisfied desires faced by proliferationist principles.

3. Defining trivially satisfied desires

In this section, I define trivially satisfied desires and argue that having such desires is psychologically realistic. I call a desire that an individual forms at a certain point in time t trivially satisfied if the desire is already satisfied at t. Examples of desires that would be trivially satisfied if I were to form them right now include the desire that 1 + 1 equal 2, the desire that I live to more than 5 years old, and (hopefully) the desire that my friends like me.

I call a desire trivially future-satisfied if it is not satisfied when it is formed at t, but will almost certainly be satisfied at some point in time after t even when nobody intentionally acts toward fulfilling this desire. Examples of trivially future-satisfied desires include the desire that the sun rise tomorrow and the desire that my blood type stay the same over the coming week. Trivially future-satisfied desires are, by definition, not trivially satisfied (because they are not satisfied at the time of their formation). In this article, my main argument is about trivially satisfied desires, not about trivially future-satisfied ones. But it will sometimes be useful to have the concept of trivially future-satisfied desires at hand.

One might think that having trivially satisfied desires is psychologically unrealistic. Can we really desire that 1 + 1 equal 2? If we could not realistically have such desires, one might argue that our intuitions about these cases could plausibly be mistaken, or at the very least, that they do not have any practical import. However, on reflection, it seems that we can have desires very similar to the desire that 1 + 1 equal 2. When I was in high school, a friend told me that e^iπ + 1 = 0. When he told me this, I formed a desire that this mathematically beautiful identity be true. Later, when I learned about proofs of Euler's identity, I found out that this desire of mine was in fact (trivially) satisfied. Other psychologically realistic desires that may well be trivially satisfied include a moral philosopher's desire that ethical egoism be false and an American businessperson's desire to live (presently) in a capitalist economy. These examples seem to show that human beings can have desires that are trivially satisfied.

In response, one might retreat to the claim that an individual can only realistically have a trivially satisfied desire while she is not aware of the satisfaction of this desire. Once someone comes to learn that her desire is in fact trivially satisfied, one might think, she cannot plausibly continue to have that desire. But first, this is only relevant to the claims about well-being at issue if the belief or knowledge that one's desires are satisfied, rather than just their actual satisfaction, matters to an individual's well-being – a non-standard subjectivist view (see Footnote footnote 14). Second, and more importantly, I in fact continue to desire that e^iπ + 1 equal 0 even after having learned that this desire is satisfied. When I imagine finding out that my belief that e^iπ + 1 = 0 were mistaken, I feel like a (relatively weak) desire of mine would be frustrated. Similarly, an individual may very well form the desire that her friends like her while knowing this to be the case. These states of mind seem not at all psychologically unrealistic. It thus appears that it is psychologically possible to have trivially satisfied desires even while knowing that these desires are satisfied.

Finally, one might argue that what I have called a trivially satisfied desire is really not a desire at all, and that the class of trivially satisfied desires as defined above is therefore an empty set. Perhaps, trivially satisfied “desires” are insufficiently action-guiding to count as desires. But we seem to have a lot of desires that we do not, or even cannot, do anything about. Or maybe a feature can only be desired if it does not obtain. But this would implausibly imply that desires can never be satisfied. In general, this line of argument does not seem promising. Examples like the desire that the number of atoms in the universe be prime or the desire that Napoleon's favorite color was blue – desires very similar in structure to some trivially satisfied desires that may well be trivially satisfied themselves – are taken as perfectly valid instances of desires in the literature on “pointless desires,” even by those who defend desire-satisfactionism against this objection (Bruckner Reference Bruckner2016; Heathwood Reference Heathwood2006; Lukas Reference Lukas2010).Footnote ⁷ If the desire-status of the apparent desire that the number of atoms in the universe be prime is not questioned by anyone, then it seems that the status of trivially satisfied desires should also be uncontroversial. All in all, there appear to be trivially satisfied desires that are psychologically realistic. In the next section, I explore how the proliferationist aggregation principles reconstructed above deal with them.

4. Proliferationist aggregation principles imply that gaining trivially satisfied desires is good for individuals

On the aggregative views introduced above, what happens when an individual – let us call her Claire – forms a new desire that is trivially satisfied? For the sake of simplicity, I assume that the only change to Claire's desire set and to the degree of satisfaction of her existing desires at the point in time t is gaining a new trivially satisfied desire for a feature x with strength D _Claire,t(x). Then, on totalism and differentialism, Claire's well-being increases by the strength of her new trivially satisfied desire D _Claire,t(x). On proportionalism as well, it increases,Footnote ⁸ except in the edge case where Claire's prior degree of welfare is the perfect score of 1 (i.e., where she has at least one satisfied desire, no unsatisfied desires, and no aversions at all). Prima facie, gaining a trivially satisfied desire therefore seems to increase an individual's welfare on the three proliferationist views.Footnote ⁹ However, there are several potential ways to resist this conclusion.

5. The view that gaining trivially satisfied desires is good for an individual is implausible

If the responses discussed in the preceding section fail, and if they exhaust the space of promising replies, the proliferationist has to hold that gaining trivially satisfied desires is good for individuals. How problematic is this? When I found out that my desire that e^iπ + 1 equal 0 was in fact satisfied, this felt good for a moment. This brief moment of pleasure may have been good for me. The proliferationist, however, is committed to a different, more implausible claim: the claim that my well-being increased the very moment I formed the desire that e^iπ + 1 equal 0, independent of any potential pleasure I might later get from my knowledge of its satisfaction.Footnote ¹⁴

One might think that the intuition that forming the desire that e^iπ + 1 equal 0 is not good for me is parasitic on another objection against desire-satisfaction theories: the objection from pointless desires. This objection appeals to the intuition that some desires are too strange in order for their satisfaction to be relevant to one's well-being. Common examples include the desire to count blades of grass (Rawls Reference Rawls1971: 432), the desire that the number of atoms in the universe be prime (Kagan Reference Kagan1998: 37), and the desire to make handwritten copies of War and Peace (Wolf Reference Wolf2010: 16). Although I will argue below that the existence of trivially satisfied desires may also render the objection from pointless desires more troubling for desire-satisfactionism, for now, we should consider the question whether gaining trivially satisfied desires can be good for an individual independently of this objection.

Arguably, though, the desire that e^iπ + 1 equal 0 is not pointless. I have argued above that it meets Bruckner's (Reference Bruckner2016) minimal accountability criterion that aims to filter out pointless desires, and there seems to be no reason to believe that it could not survive common idealizations such as full information. (In particular, the desire has already survived the information that it is satisfied.) Moreover, consider the very similar – and arguably to some degree trivially satisfied – desire that mathematical beauty obtains. When we judge whether this is a pointless desire, we have to do this independently of welfare considerations, i.e., without appealing to the fact that forming it does not seem to increase the desirer's well-being. Considering this, the desire that mathematical beauty obtain and the desire that e^iπ + 1 equal 0, which is similar in the relevant respects, like other desires for beauty, do not appear to be pointless.

However, because these desires are not self-regarding, an advocate of a restricted desire-satisfaction theory could still argue that gaining them is not good for the desirer. To show conclusively that trivially satisfied desires constitute a problem for proliferationist desire theories with any plausible restriction or idealization conditions, we should consider some desires as “innocuous” as possible, i.e., trivially satisfied desires that are non-adaptive, self-regarding, would survive idealization procedures, and appear non-pointless when formed at a time when they are not trivially satisfied. If even those trivially satisfied desires seem unlikely to contribute to an individual's welfare, then this would constitute a significant problem for proliferationist principles.

To this end, consider the desire to live to more than 70 years old. First, one might question whether this could be an intrinsic desire rather than a merely instrumental one. Of course, living to more than 70 years old may be instrumentally useful for satisfying many other desires. But we can certainly imagine an individual who considers it constitutive of a good life that it reaches a certain length, and therefore intrinsically desires this. Second, we need to consider whether this is a pointless desire regardless of the time of its formation, i.e., a desire that is “difficult to understand or appears downright inscrutable, extremely strange, unusual or maximally idiosyncratic” (Bruckner Reference Bruckner2016: 2). The fact that many people do have desires like this one (cf. Nussbaum Reference Nussbaum1992) seems to show that this is not the case. Third, the intrinsic desire to live to more than 70 years old is surely self-regarding. Fourth, it seems that the desire could survive idealization procedures such as full information or autonomy – at the very least, a fully informed individual could have this desire, and it could arise in a non-adaptive and autonomous way.

Now imagine Gertrude, who forms the desire to live to more than 70 years old when she turns 80. Could gaining this desire increase Gertrude's well-being? In order to answer this question, it is important to distinguish having a trivially satisfied desire from other states of mind. Desiring to live to more than 70 years old is different from feeling grateful, feeling glad, or consciously appreciating that one has lived to more than 70 years old. The latter states of mind are emotions which may intrinsically increase one's well-being. But in the same way that I can desire to sleep without any particular emotion being attached to this desire, we can imagine that Gertrude forms the intrinsic desire to live to more than 70 years old without feeling grateful, feeling glad, or consciously appreciating this. If we take this distinction into account, it seems implausible that merely forming this desire has increased her well-being. Imagine, furthermore, that Gertrude goes on to form the desires to live to more than 65, 60, 55 years old, and so on. All of these desires appear to satisfy the conditions given above, yet it seems even more absurd to say that Gertrude's well-being could increase each time she forms one of these desires.Footnote ¹⁵ If proliferationist aggregation principles are committed to this claim, then this is a serious problem for them.

Besides constituting an objection in itself, the phenomenon of trivially satisfied desires may also worsen other problems of desire-satisfactionism, such as the objection from pointless desires. One common strategy in response to this objection is to bite the bullet (Heathwood Reference Heathwood2005; Lukas Reference Lukas2010; see also Yu Reference Yu2022): imagine someone who is a passionate grass-counter. She simply desires to count blades of grass and does that for year after year of her life. Maybe grass-counting just is good for this quirky individual. And of course, such an individual might not even exist in the real world, which can make the cost of bullet-biting appear smaller. For example, our intuitions about the case might be unreliable since we might not be able to understand the grass-counter's psychology.

Now suppose that you are not interested in, and do not care at all about (but are not averse to) mathematics. According to proliferationist principles, if you could somehow gain the pointless desire that 396 + 575 equal 971, this would – other things being equal – make you better off. This makes bullet-biting substantially less attractive than on the classical version of the objection from pointless desires. Biting the bullet on the classical objection from pointless desires requires you to concede that satisfying a pointless desire is good for some quirky, possibly hypothetical individual who is into that kind of thing. Biting the bullet on the objection from trivially satisfied pointless desires requires you to concede that you, right now, could be (potentially a lot) better off by gaining (lots of) pointless trivially satisfied desires that you do not care about now. This seems very counterintuitive, and substantially more so than the classical objection from pointless desires. Now of course, there may be other strategies, such as restrictions, that can dispel the problem of pointless desires (see, e.g., Bruckner Reference Bruckner2016). I do not raise an objection to those strategies here. But to the extent that one is not entirely convinced that they succeed, the existence of trivially satisfied desires does seem to make the problem of pointless desires worse.