On the stability of choice processes

Abstract

Decisions researchers generally agree that the method of elicitation – be it task format or response mode – has a huge impact on people's responses: different task formats, such as probabilities and frequencies (Gigerenzer and Hoffrage, 1995) – or decisions from description and experience (Hertwig et al., 2004), trigger drastically different behavior. Different response modes, such as choosing, pricing, and matching, have been shown to prompt substantial discrepancies in people's preferences (e.g., Lichtenstein and Slovic, 1971; Tversky et al., 1988). While these streams of research have received much attention, much less is known about the effects of task format in decisions from description, which have been the staple for decision researchers. Here the underlying assumption seems to be that task format has little or no effect on the choice process (Birnbaum, 2004; Birnbaum et al., 2008). When choices differ across experiments, such instabilities can always be modeled by (a) using flexible multi-parameter models that allow for the description of strikingly different choice data (see Brandstatter et al., 2008 for a discussion), or by (b) situating an editing phase prior to the selection phase (Kahneman and Tversky, 1979). In both attempts the core process – the weighting and summing of information – remains unaffected. I argue that both attempts seem unsatisfactory, since different task formats trigger fundamentally different choice processes in decisions from description. Instead of advocating single calculus models I propose an adaptive tool box view of risky choice (Gigerenzer et al., 1999; Brandstatter et al., 2008). The crucial question thus becomes: which task format triggers which choice process? To answer this question I concentrate on decisions from descriptions and on two fundamentally different accounts of risky choice: expected utility theory and its modifications, and the priority heuristic (Brandstatter et al., 2006). Expected utility theory and its modifications are historically rooted in the work of Daniel Bernoulli, and these models rest on the assumption of weighting and summing of information. Examples are expected utility theory (von Neumann and Morgenstern, 1947), cumulative prospect theory (Tversky and Kahneman, 1992), and the transfer of attention exchange model (Birnbaum et al., 2008). Interpreted as process theories, expected utility theory, for example, predicts that people value payoffs with a utility function, multiply the utilities by the probabilities, sum the products, and finally select the gamble with the higher sum of weighted values. These theories, therefore, predict that people process information within each gamble, such that an overall evaluation for each gamble is made. The priority heuristic, which represents a different class of models, builds on the work of Luce (1956), Simon (1957), Tversky (1969), and Selten (2001). It is a simple lexicographic semiorder strategy that implies several classic violations of expected utility theory that had previously been accounted for by modifications of expected utility theory (Brandstatter et al., 2006; Katsikopoulos and Gigerenzer, 2008). Across four different data sets with a total of 260 problems, the priority heuristic predicted the majority choice better than each of three modifications of expected utility did. A process test using reaction times further confirmed the heuristic's process predictions (Brandstatter et al., 2006). To illustrate the heuristic, consider a choice between two simple gambles where each offers “a probability p of winning amount x and a probability (1−p) of winning amount y.” A choice between two such gambles contains four reasons for choosing: the maximum gain, the minimum gain, and their respective probabilities; because probabilities are complementary, three reasons remain: the minimum gain, the probability of the minimum gain, and the maximum gain. For choices between gambles having two non-negative outcomes (all outcomes are zero or positive), the heuristic consists of the following steps: Priority rule. Go through reasons in the order of minimum gain, probability of minimum gain, maximum gain. Stopping rule. Stop examination if the minimum gains differ by 1/10 (or more) of the maximum gain; otherwise, stop examination if probabilities differ by 1/10 (or more) of the probability scale. Decision rule. Choose the gamble with the more attractive gain (probability). One-tenth of the maximum gain represents the aspiration level for gains, and 0.1 that for probabilities1. Note, the aspiration level for gains is not fixed but changes with the maximum gain of the problem. For probabilities, which are bound between 0 and 1, the aspiration level of 0.1 is fixed. The term “attractive” refers to the gamble with the higher (minimum or maximum) gain and to the lower probability of the minimum gain. The heuristic does not use any non-linear transformations of outcomes and probabilities but takes both in their natural currencies (i.e., objective cash amounts and objective probabilities). Unlike the expectation-type models, the priority heuristic predicts that people process information between rather than within gambles. For gambles involving losses, the term “gain” is replaced by “loss.” For gambles with more than two outcomes, and gambles involving gains and losses (“mixed gambles”), see Brandstatter et al. (2006). To illustrate the conceptual difference between an expectation-type model such as prospect theory and the priority heuristic (for details see Brandstatter and Gusmack, submitted), consider the following choice problem (Kahneman and Tversky, 1979). A: 6,000 with p = 0.001 0 with p = 0.999 B: 3,000 with p = 0.002 0 with p = 0.998 Most people (73%) chose Gamble A. How does prospect theory explain this majority choice? The standard value function is concave for gains, which implies that the larger amount of 6,000 is devalued more than the smaller amount of 3,000 (i.e., compared to a linear value function). The standard value function, thus, predicts B but not A. Prospect theory must explain the choice of A by the overweighting of small probabilities. That is, the overweighting of 0.001 (compared to 0.002) must be stronger than the devaluation of 6,000 (compared to 3,000). Because the weighting function is not well-behaved near the endpoints (Kahneman and Tversky, 1979), consider the other possibilities of (a) underweighting, (b) linear weighting, and (c) ignoring small probabilities. Underweighting of small probabilities (captured by an S-shaped rather than an inverse S-shaped probability weighting function) implies the choice of B but not of A – as does a linear weighting function (due to the value function). Ignoring small probability outcomes predicts guessing, because the zero outcomes remain. None of these additional possibilities, therefore, can account for the choice of A. The same reasoning holds for cumulative prospect theory, since both prospect theories are identical for two-outcome gambles. According to (cumulative) prospect theory, only the minute difference between 0.001 and 0.002 can cause the choice of A. For the priority heuristic, this difference is neglected. The heuristic first compares the minimum gains (0 and 0). Because they do not differ, the probabilities (0.999 and 0.998 or their logical complements 0.001 and 0.002) are compared. This difference falls short of the aspiration level (i.e., smaller than 0.1) and people are predicted to choose A, because of its higher maximum gain. Thus, the priority heuristic captures the majority choice by using comparisons between rather than within gambles. Both the priority heuristic and prospect theory can model the majority choice. In the following I will investigate which of these two models better captures the majority choice. We will see that task format plays a key role in this endeavor. In the light of both models, I also investigate the effect of salience on people's choice processes.