Application of Voting Geometry to Multialternative Choice

Application of Voting Geometry to Multialternative Choice Anouk S. Schneider (asschneider@princeton.edu) Department of Psychology, Green Hall Princeton, NJ 08540 USA Daniel M. Oppenheimer (doppenhe@princeton.edu) Department of Psychology, Green Hall Princeton, NJ 08540 USA Greg Detre (gdetre@princeton.edu) Department of Psychology, Green Hall Princeton, NJ 08540 USA Abstract may attempt to maximize payoff while others prefer to minimize risk. We argue that the big three decision anomalies come about as a natural consequence of aggregating preferences across different agents. This paper presents an application of voting geometry to individual decision making. We demonstrate that a number of decision anomalies can arise as a natural consequence of the aggregation of preferences of different neural systems. We present a proof of existence of a set of voting procedures that can account for the attraction effect, the similarity effect and the compromise effect, and provide an example of one such procedure in the form of a modified Borda count. The result is an original closed form computational model of multialternative choice. The Big Three A very simple laboratory example will be used to represent human decision-making in real life (c.f. Roe et al., 2001). In this example, the choice set includes a limited number of choice options that vary on two attributes. This representation simplifies the demonstration of the anomalies and makes it easier to analyze decision-outcomes, but the findings are applicable to more complex real-life choice problems as well (Roe et al., 2001). The choice options are represented in terms of different pairs of shoes that vary on two attribute dimensions: comfort and style. The ideal shoe would be closest to the upper right hand corner of the diagram, where the shoes are most stylish and at the same time most comfortable. Figure 1 represents the “shoe” - choice set, which will be used throughout the entire paper. Keywords: Voting theory; decision-making; Borda count; multilaternative choice; Introduction For nearly 50 years, psychologists have been cataloguing violations of the standard assumptions of economic theory: that humans exhibit rational, stable, and ordered preferences. As the field has come to a consensus that the rational model is a poor descriptor of human behavior, researchers have moved from documenting anomalies to attempting to model them. To date, the most successful attempt to model decision anomalies has been Decision Field Theory (DFT), introduced by Busemeyer and Townsend (1993). Using a sequential sampling approach, DFT can account for three of the most puzzling decision anomalies: compromise effects, attraction effects, and similarity effects. Busemeyer and his colleagues have proven that there exists no weighting function for a utility model that can effectively capture all three of these phenomena (Roe, Busemeyer, Townsend, 2001). While DFT remains the premier computational approach for multi-attribute choice, recent criticism about the biological plausibility of the model (Usher & McClelland, 2004) has led researchers to try and account for the big three decision anomalies using different techniques. In this paper we propose a model for multi-attribute choice derived from the principles of voting geometry. We assume a number of neural systems within an individual's brain (i.e. agents ), which differentially respond to different attributes of choice. For example, some agents Figure 1: The choice set Figure 1 provides a geometric representation of a hypothetical choice set. Options A, S, and D are in the upper left hand corner, which means that they are high on the style attribute but low on comfort. D is completely dominated by A, while S is similar to A but slightly better in style and