Extreme self-sacrifice in the context of phenomena, such as sports hooliganism, combines aspects of local and extended fusion. How can we best account for such phenomena in the light of the theory presented here, and how can we make a tangible distinction between the two types? I propose ways to explore and operationalize this distinction and the concept of fusion more generally.

A comprehensive explanation of extreme self-sacrifice would ideally clarify not only the proximate mechanisms leading to this behaviour, but also its developmental origins, its functions (if any), and its history. The theoretical framework set out in my target article has something to say about all of these dimensions, and many of the criticisms raised in the commentaries can therefore be addressed under those four main headings. In my response, I also discuss a set of proposals for further extending the framework. Finally, I conclude by distilling from the discussion a host of novel questions requiring further investigation.

Human perceptual decisions are often described as optimal. Critics of this view have argued that claims of optimality are overly flexible and lack explanatory power. Meanwhile, advocates for optimality have countered that such criticisms single out a few selected papers. To elucidate the issue of optimality in perceptual decision making, we review the extensive literature on suboptimal performance in perceptual tasks. We discuss eight different classes of suboptimal perceptual decisions, including improper placement, maintenance, and adjustment of perceptual criteria; inadequate tradeoff between speed and accuracy; inappropriate confidence ratings; misweightings in cue combination; and findings related to various perceptual illusions and biases. In addition, we discuss conceptual shortcomings of a focus on optimality, such as definitional difficulties and the limited value of optimality claims in and of themselves. We therefore advocate that the field drop its emphasis on whether observed behavior is optimal and instead concentrate on building and testing detailed observer models that explain behavior across a wide range of tasks. To facilitate this transition, we compile the proposed hypotheses regarding the origins of suboptimal perceptual decisions reviewed here. We argue that verifying, rejecting, and expanding these explanations for suboptimal behavior – rather than assessing optimality per se – should be among the major goals of the science of perceptual decision making.

Perceptual judgments are influenced by a multitude of factors in addition to the perceptual input. Particularly, the widely varying individual neurobiological endophenotypes and individual differences in the propensity for expectation-based illusory percepts make it unlikely that optimality is possible to define and defend by the type of abstract modeling approach criticized by Rahnev & Denison (R&D).

We concur with the authors’ overall approach and suggest that their analysis should be taken even further. First, the same points apply to areas beyond perceptual decision making. Second, the same points apply beyond issues of optimality versus suboptimality.

Suboptimality of decision making needs no explanation. High-level accounts of suboptimality in diverse tasks cannot add up to a mechanistic theory of perceptual decision making. Mental processes operate on the contents of information brought by the experimenter and the participant to the task, not on the amount of information in the stimuli without regard to physical and social context.

To deny that human perception is optimal is not to claim that it is suboptimal. Rahnev & Denison (R&D) point out that optimality is often ill defined. The fundamental issue is framing perception as a statistical inference problem. Outside of the lab, the real perceptual challenge is to determine the lawful structure of the world, not variables of a predetermined statistical model.

Rahnev & Denison (R&D) argue that human behavior is often described as “optimal,” despite many previous findings of suboptimality. We address how the literature handles these concepts and discuss our own findings on suboptimality. Although we agree that the field should embrace the “systematic weirdness of human behavior” (sect. 6, para. 1), this does not detract from the value of the Bayesian approach.

In the target article, Rahnev & Denison (R&D) use serial effects as an example of suboptimality. We show here that serial effects can be beneficial to perception, serving to reduce both error and response times in a near-optimal fashion. Furthermore, serial effects for stable attributes are positive, whereas those for changeable attributes are negative, demonstrating that they are engaged flexibly to optimize performance.

The target article uses a mathematical framework derived from Bayesian decision making to demonstrate suboptimal decision making but then attributes psychological reality to the framework components. Rahnev & Denison's (R&D) positive proposal thus risks ignoring plausible psychological theories that could implement complex perceptual decision making. We must be careful not to slide from success with an analytical tool to the reality of the tool components.

We disagree with Rahnev & Denison (R&D) that optimality should be abandoned altogether. Rather, we argue that adopting a normative approach enables researchers to test hypotheses about the brain's computational goals, avoids just-so explanations, and offers insights into function that are simply inaccessible to the alternatives proposed by R&D.

We argue that a radically increased emphasis on (bounded) optimality can contribute to cognitive science by supporting prediction. Bounded optimality (computational rationality), an idea that borrowed from artificial intelligence, supports a priori behavioral prediction from constrained generative models of cognition. Bounded optimality thereby addresses serious failings with the logic and testing of descriptive models of perception and action.

Systematically comparing models that vary across components can be more informative and explanatory than determining whether behaviour is optimal, however defined. The process of model comparison has a number of benefits, including the possibility of integrating seemingly disparate empirical findings, understanding individual and group differences, and drawing theoretical connections between model proposals.

Given the many types of suboptimality in perception, I ask how one should test for multiple forms of suboptimality at the same time – or, more generally, how one should compare process models that can differ in any or all of the multiple components. In analogy to factorial experimental design, I advocate for factorial model comparison.

Rahnev & Denison's (R&D) critique of optimality in perceptual decision making leads either to implicitly retaining optimality as a normative benchmark or disregarding the normative approach altogether. We suggest that “bounded rationality,” and particularly the “satisficing” criterion, would help dispense with optimality while salvaging normativity. We also suggest that satisficing would provide a parsimonious and robust explanation for perceptual behavior.

Optimality of any decision, including perceptual decisions, depends on the criteria used to evaluate outcomes and on the assumptions about available alternatives and information. In research settings, these are often difficult to define, and therefore, claims about optimality are equivocal. However, optimality is important in applied settings when evaluating, for example, the detection of abnormalities in medical images.

We show that the benchmark Bayesian framework that Rahnev & Denison (R&D) used to assess optimality is actually suboptimal under realistic assumptions about how noise corrupts decision making in biological brains. This model is therefore invalid qua normative standard. We advise against generally forsaking optimality and argue that a biologically constrained definition of optimality could serve as an important driver for scientific progress.

We agree with Rahnev & Denison (R&D) that to understand perception at a process level, we must investigate why performance sometimes deviates from idealised decision models. Recent research reveals that such deviations from optimality are pervasive during perceptual development. We argue that a full understanding of perception requires a model of how perceptual systems become increasingly optimised during development.

Within a multisensory context, “optimality” has been used as a benchmark evidencing interdependent sensory channels. However, “optimality” does not truly bifurcate a spectrum from suboptimal to supra-optimal – where optimal and supra-optimal, but not suboptimal, indicate integration – as supra-optimality may result from the suboptimal integration of a present unisensory stimuli and an absent one (audio = audio + absence of vision).

Rahnev & Denison (R&D) catalog numerous experiments in which performance deviates, often in subtle ways, from the theoretical ideal. We discuss an extreme case, an elementary behavior (reactive saccades to single targets) for which a simple contextual manipulation results in responses that are dramatically different from those expected based on reward maximization – and yet are highly informative and amenable to mechanistic examination.