What is decidables?

The decidables project is a collection of explorable explanations of decision making. The focus is on quantitative theories from the field of cognitive psychology:

Explorable explanations

Explorable explanations combine interactive elements with supporting text. The goal is to help the learner understand a concept through an active process of engagement. Victor (2011) explains this as an “environment to think in” instead of just “information to be consumed”.

The term “explorable explanation” was first used in a related context by Brusilovsky (1994), but was popularized by Victor (2011), and has been championed by Case (2015/2022) with the wonderful Explorable Explanations (https://explorabl.es/) website, which has links to examples, readings, tutorials, and tools (“Explorable Explanation,” 2021).

Cognitive psychology

As a central human activity, decision making can be studied from many different perspectives, which provide diverse and complementary insights. Here we concentrate on quantitative models from cognitive psychology, which attempts to understand the relationship between thoughts and behavior using an information processing approach. We can think about the environment presenting a situation that potentially invites a decision. Information about that situation acts as input to an individual’s mind. This information is integrated with ongoing processes and representations in the mind, potentially leading to a response as output. A quantitative theory of decision making describes the relationship between input and output in terms of the intervening processes and representations.

Quantitative modeling

Each of the explorables in this project starts with a decision-making task which the learner can partake in. This provides empirical input and output. The explorable then explains how the theory attempts to account for the relationship between input and output through a quantitative model of cognition.

Central to each of these explorables are interactive simulations for model exploration (i.e. “exploring the hypothesis space” or “proof of sufficiency”, McClelland, 2009; Stafford, 2009; Zuidema et al., 2020), fitting (i.e. “parameter estimation”, Lewandowsky & Farrell, 2010; Wilson & Collins, 2019), and prediction (i.e. “simulation”, Stafford, 2009; Wilson & Collins, 2019):



d′etectable explores signal detection theory (SDT). The task is to detect coherent motion in a random dot kinematogram. Is the motion stimulus present or absent? Building on early work studying radar operators, SDT mathematically models our choices in terms of our detection sensitivity and response bias (Peterson et al., 1954; Tanner & Swets, 1954).


prospectαbλe explores cumulative prospect theory (CPT). The task is to choose between a sure option of intermediate value and a gamble with a larger and a smaller option. Do you prefer the sure thing, or the chance to win more? CPT describes mathematical transformations of objective probabilities and values into decision weights and subjective values which we combine on a relative scale (Kahneman & Tversky, 1979; Tversky & Kahneman, 1992).


diskountable explores hyperbolic temporal discounting. The task is to choose between a smaller immediate value and a larger value in the future. Would you rather have less now or more later? Hyperbolic discounting describes how our subjective perception of value changes with time (Ainslie, 1991; Berns et al., 2007).