Salience driven value integration explains decision biases and preference reversal

Abstract

Human choice behavior exhibits many paradoxical and challenging patterns. Traditional explanations focus on how values are represented, but little is known about how values are integrated. Here we outline a psychophysical task for value integration that can be used as a window on high-level, multiattribute decisions. Participants choose between alternative rapidly presented streams of numerical values. By controlling the temporal distribution of the values, we demonstrate that this process underlies many puzzling choice paradoxes, such as temporal, risk, and framing biases, as well as preference reversals. These phenomena can be explained by a simple mechanism based on the integration of values, weighted by their salience. The salience of a sampled value depends on its temporal order and momentary rank in the decision context, whereas the direction of the weighting is determined by the task framing. We show that many known choice anomalies may arise from the microstructure of the value integration process.

Fig. 1.

Decision task and results in experiment 1. (A) The timeline of a trial. At the end of the presentation, participants decided which sequence had the highest average. The unbalanced conditions (B) consisted of two sequences generated from Gaussians with different means. In the balanced condition (C), the sequences corresponded to equal mean Gaussians, with one alternative sampled from the lower range (gray) during the first half, and from the higher range (black) during the second half of the trial (and conversely for the other alternative). (D) The decision accuracy in the unbalanced trials improves with sequence length. (E) The preference for the alternative associated with higher values at the end of the sequence shows recency, increasing with sequence length. Error bars correspond to 95% confidence interval. Red symbols (dashed line) correspond to leaky integration fits (Eq. 1), and square symbols (solid gray line) to fits of the full model (Eq. 2).

Fig. 2.

Experiment 2 conditions and results. Observers decided between two alternatives, each characterized by a sequence of 12 values, presented as pairs at a rate of 2/s. In two unbalanced conditions (A and B), either the broad or the narrow distribution had the highest mean, whereas in the equal condition both distributions had equal mean and different variance (C). (D and E) Decision accuracy and (F) preference for the risky alternative, associated to the broad distribution. Purple circles indicate the fits of the rank-weighted model (Eq. 2). Individual data are given in Fig. S2A. Error bars correspond to 95% confidence interval.

Fig. 3.

Two-stage decision task and results in experiment 3. (A) Participants saw 12 triples presented at a rate of 750 ms and were first asked to eliminate one of them (stage 1), and then to select one from the remaining two (stage 2), which were presented as a second sequence of 12 pairs at a rate of 500 ms. (B) In the first stage, the rejection rate of the risky alternative was higher than chance (33%); in the second stage, the selection rate for it was also higher than chance (50%), consistent with an account that weighs different sides of the distribution depending on the task framing (C and Eq. 2). Purple circles indicate the fits of the rank-weighted model (Eq. 2). Individual data are given in Fig. S2B. Error bars correspond to 95% confidence interval.

Fig. 4.

Experiment 4: creating analogs of the attraction and similarity effects (A, B) using the fast value integration task with three alternatives. Each alternative is associated with two distributions, one red and one blue (colors for illustration purposes only), and at each frame the values for all three alternatives are sampled from either the red or the blue Gaussian distributions (randomly determined; see Table 1 and B for exact values). (C) Four frames from one experimental trial in the attraction condition. (D) Results for the four conditions, showing reversal effects in the decoy conditions. Individual data for the decoy conditions are given in Fig. S2C. Purple circles indicate the fits of the rank-weighted model (Eq. 3). Error bars correspond to 95% confidence interval.