Decision by sampling: The role of the decision environment in risky choice

Abstract

Decision by sampling (DbS) is a theory about how our environment shapes the decisions that we make. Here, I review the application of DbS to risky decision making. According to classical theories of risky decision making, people make stable transformations between outcomes and probabilities and their subjective counterparts using fixed psychoeconomic functions. DbS offers a quite different account. In DbS, the subjective value of an outcome or probability is derived from a series of binary, ordinal comparisons with a sample of other outcomes or probabilities from the decision environment. In this way, the distribution of attribute values in the environment determines the subjective valuations of outcomes and probabilities. I show how DbS interacts with the real-world distributions of gains, losses, and probabilities to produce the classical psychoeconomic functions. I extend DbS to account for preferences in benchmark data sets. Finally, in a challenge to the classical notion of stable subjective valuations, I review evidence that manipulating the distribution of attribute values in the environment changes our subjective valuations just as DbS predicts.

Keywords:

• Decision by sampling
• Decision under risk
• Judgement and decision making
• Expected utility
• Subjective probability

I thank the EPS for their invitation to write this article. The article follows the EPS Prize Lecture delivered at UCL in January 2008. I would like to thank all of my collaborators, but must especially thank Gordon D. A. Brown and Nick Chater, to whom I am greatly indebted. Thanks also to Nigel Harvey and an anonymous reviewer.

This research was supported by ESRC Grant RES-062–23–0952.

Notes

¹ In fact, Kahneman and Tversky (1979) maintained a difference between subjective probability and decision weighting. A subjective probability is the psychophysical transform of the objective probability. A decision weight is the emphasis given to the corresponding outcome. So one might have an accurately calibrated subjective probability for an objectively unlikely event (e.g., knowing winning the lottery is very unlikely), but still behave as if the event is more likely than it really is because one weights the associated outcome too heavily (e.g., by buying a ticket).

² If data outside the range in Figure 4 are used, so that the DbS subjective value function is extended to cover the full range of values in Figure 3, the best-fitting exponent drops to 0.11: Plotted in log–log space, the subjective value function is initially linear with slope 0.47, but then the slope reduces to zero above about £10,000, so the subjective values of large amounts are all the same. This breakdown, I think, reflects the limits of using these current account data and assuming people randomly sample from them. For example, when considering an annual salary or the price of a house people are more likely to sample other similarly large amounts rather than the costs of cups of coffee or weekly shops. Scale invariance in the world and in memory (Chater & Brown, 2008) is likely to lead to similar-shaped utility functions across a range of magnitudes.

³ ipoints is an online reward scheme. ipoints can be redeemed for a large range of goods.

⁴ Adaptation level theory (Helson, 1964) represents perhaps the first attempt to account for contextual effects. In adaptation level theory, stimuli are judged against the mean of the distribution in which they are encountered. Range-frequency theory goes further in accounting for the effects of higher moments, like the variance and the skew.