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What if you fail? Confidence as a special kind of probability
When pondering whether to engage in a given course of action or project, such as growing an orange tree to eventually produce orange juice, one aspect that individuals typically consider is the subjective value of the various possible outcomes (e.g., within the next five years, a healthy tree and litres of delicious orange juice, or, a healthy tree yet barely any orange, or, a dying tree and no orange in sight). As we have seen above, individuals also consider the overall cost entailed by this course of action (e.g. the money to buy the tree, the time and effort to take care of it). Another crucial judgment generated during the decision process is about the subjective probability that the course of action will lead to each of the different envisaged outcomes. In many instances, as in the orange tree scenario, these outcomes are at least partly contingent on the individual’s specific behaviour (or, in this context, performance), and can be situated with respect to a “success” or “correctness” (more or less arbitrary) criterion. In the above example, one may be a seasoned gardener and estimate that he is very likely to succeed (where his success threshold would be, e.g., keep the tree healthy and harvest oranges within five years) or he might be inexperienced but overestimate his skills and have the same prediction. In any case, as we have seen earlier, expected utility theory postulates that the subjective value of each outcome is multiplied with its subjective probability (before being summed and discounted by the cost of action). Thus, according to this framework, and since “successful” outcomes are in general higher valued than “unsuccessful” ones, the more confident a decision-maker is in his endeavour being successful, the higher the overall expected utility of the course of action, and the likelier he is to initiate it.
What it means to be correct
We can distinguish (at least) two ways in which one can be correct, or successful: 1) epistemically, 2) behaviourally. The first case applies to a judgment, belief or prediction one has internally committed to or will commit to (e.g., thinking to yourself: “he will be at least five minutes late”), and being correct means that this judgment is in line with some ground truth or observable state. The second case applies to a behaviour, or behavioural sequence, one has performed or will perform, and being correct or successful means that either the behaviour per se, or its outcome, belongs to a set of correct or success states. The criteria defining truth, or correctness or validity can be more or less arbitrary, either defined externally (e.g. by encyclopaedias, the rules of a sport) or internally (e.g., by your own appreciation of what a “good soufflé” is) and applying to objective variables (e.g. where the tennis ball lands, how puffy a soufflé is) and/or subjective ones (e.g. the elegance of a move or the deliciousness of a soufflé). Thus, generating confidence judgments typically implies a discretization (and often even a binarization) of the variable(s) of interest. This is not as artificial as it may seem, because in many natural situations, the value distribution of possible outcomes tends to be multinomial, discrete, or even binary (to take a rather extreme example, if you try to jump across a deep rift, either you reach the other side and survive — although you may have twisted your ankle in the process — , or you don’t, and die).
A typology of confidence
There can be many ways to classify confidence judgments into subtypes, but we will only propose two distinctions here, as (hopefully) useful landmarks in the confidence field which we can refer to later.
The first one, expounded in the previous paragraph, is the distinction between epistemic and behavioural confidence. It can be noted, however, that in many recent studies about confidence, these two notions are basically treated as one and the same. These studies use paradigms in which the subject is required to make a perceptual or mnemonic — often binary —decision (e.g.: Is this cloud of dots moving to the left or to the right? Has this word been presented to you earlier?) and to report it explicitly, for instance by pressing a key on a keyboard. Then, subjects are typically prompted to make a confidence (“second-order”) judgment about their perceptual (“first-order”) answer. Therefore, in such cases, confidence is both about the correctness of their behaviour (pressing key A rather than key B) and that of their internal perceptual judgment (i.e., belief, or epistemic state), since there is a systematic mapping between both. One could argue, though, that what this kind of experiments probes is, in essence, epistemic confidence. (Bang & Fleming, 2018; Boldt, Gardelle, & Yeung, 2017; Gardelle & Mamassian, 2014; Hainguerlot, Vergnaud, & Gardelle, 2018; Lebreton et al., 2018; Rutishauser, Aflalo, Rosario, Pouratian, & Andersen, 2018; Wagner et al., 1998).
Putting it all together: a current framework of value-based action selection
In the present work, we adhere to modern frameworks of value-based decision-making, which themselves draw on earlier formalizations by economists and psychologists. The currently dominant view on action selection (Rangel et al., 2008) is that it is contingent on action valuation, which itself derives from an internal representation of internal (e.g. hunger) and external states (e.g. month of the year) of the agent, as well as (of course) the set of feasible actions, and previous experiences of action-outcome associations.
A methodological parenthesis: eliciting decisional variables
Over decades of experimental investigation, behavioural economists and psychologists have come up with several methods to elicit and measure the components entering the computation of action value, i.e., decisional variables.
Importantly, the measurement can be made before or after the outcome is owned or consumed, or the action is performed, thus prompting either an a priori or a posteriori evaluation.
The most straightforward way to probe a decisional variable — whether it is the subjective value (be it positive or negative) attached to a given outcome, its subjective probability, or the subjective cost attached to an action — is to ask explicitly: “How much do you like this cookie?”, “How likely is it that you will draw a winning card?”, “How costly do you find it to climb six flights of stairs?“. Typically, in experimental settings, the question is displayed on a computer screen, and the answer is made by placing a cursor on a rating scale, which is bounded and features either numeric or verbal labels, such as “Not at all” and “Extremely”. This is arguably the most frequent approach to the measurement of decisional variables in modern cognitive neuroscience research. Likeability or pleasantness ratings have been used in a large number of studies over the past fifteen years (O’Doherty, Dayan, et al., 2003; Lebreton et al., 2009; Tobler et al., 2009; Rushworth et al., 2011; Lebreton et al., 2015; Genevsky et al., 2017; Schmidt et al., 2017; Vinckier et al., 2019), as have effort ratings (Schmidt et al., 2009; Rollwage et al., 2018), probability ratings (e.g. Genevsky et al., 2017; Lebreton et al., 2015; Sharot, Korn, & Dolan, 2011; Szpunar & Schacter, 2013), and confidence ratings (Aridan, Malecek, Poldrack, & Schonberg, 2019; Bang & Fleming, 2018; Berg et al., 2016; Gardelle & Mamassian, 2014; Sanders, Hangya, & Kepecs, 2016).
Table of contents :
Acknowledgements
Summary
Résumé
Chapter I: Introduction
A. Decisional variables: the cognitive components of action selection
1) Apples and oranges: the science of choice and value in its early days
2) Will the tree bear fruit? Incorporating uncertainty in choice problems
3) The reconciliation of economics and psychology
4) Seeing the bigger picture: from options to actions
5) A methodological parenthesis: eliciting decisional variables
B. Neural correlates of action selection
1) Anticipated & experienced value of outcomes
2) Probability & confidence
3) Effort cost
C. Interferences within and between decisional variables
1) Intra-dimensional interferences
2) Inter-dimensional interferences
D. Summary & directions
Chapter II: Study 1
Chapter III: Study 2
Chapter IV: Study 3
Chapter V: General discussion
1) Overview
2) What have we learned?
3) Limitations & Perspectives
References
Appendix
