Choice Deferral in Models of Preference Accumulation

Choice Deferral in Models of Preference Accumulation Sudeep Bhatia (s.bhatia@warwick.ac.uk) Behavioral Science Group, Warwick Business School, University of Warwick Coventry, United Kingdom attribute values are sampled sequentially and stochastically over the time course of the decision process. The values of these attributes are accumulated into preferences, and decisions are made when preferences cross a fixed threshold. Recently Jessup, Veinott, Todd and Busemeyer (2009) have assumed that choice is deferred within a DFT model, if the decision is not made by a certain time. They have shown that this time constraint based extension to DFT can explain the observed increase in deferral with size of the choice set 1 . While Jessup et al. provide a number of valuable insights regarding the psychological basis of choice deferral, they do not attempt to explain its relationship with option conflict and option desirability, or the effect of choice deferral on the choice probability of extreme options and on the incidence of the attraction and compromise effects. In this paper we imbed Jessup et al.’s (2009) time constraint mechanism, in the associative accumulation model (AAM) (Bhatia, 2013). AAM is a sequential sampling and accumulation theory of preference, which assumes that the probability of sampling a particular attribute depends on the composition of the choice set. AAM is able to explain conflict and alignability effects, effects relating to extreme options, and predict the emergence of the attraction and compromise effects. For this reason, AAM is a suitable framework with which to study the many diverse findings regarding deferred choice. Using the choice options and parameter values assumed in Bhatia (2013) we show that AAM, when combined with a deferral based time constraint, provides a comprehensive explanation for all of the deferral effects described above. Abstract This paper models choice deferral using a sequential sampling and accumulation theory of preferential choice. It assumes that choice options are accepted or rejected if accumulators reach an upper or lower threshold, and that choice is deferred if these thresholds are not crossed by a fixed time. The proposed model can explain a wide range of findings regarding the determinants and consequences of choice deferral, including the relationship of deferral with choice option conflict, choice option desirability, choice option extremity, and the attraction and compromise effects. Keywords: Choice deferral, Decision making, Sequential sampling, Associative accumulation, Context effects Introduction Cognitive models of preferential choice focus largely on predicting choice probabilities, decision times, and their dependence on task related factors such as decoy options, reference points, and anchors (Bhatia, 2013; Busemeyer & Townsend, 1993; Johnson & Busemeyer, 2005; Roe, Busemeyer & Townsend, 2001; Krajbich, Armel & Rangel, 2010; Rangel & Hare, 2010; Trueblood, Brown, & Heathcote, in press; Usher & McClelland, 2004). Largely absent from this is a comprehensive approach to modeling choice deferral, that is, the decision not to make any choice whatsoever (Gourville & Soman, 2005; Dhar, 1997; Dhar & Simonson, 2003; Iyengar & Lepper, 2000; Tversky & Shafir, 1992). The failure to decide is a fundamental feature of everyday decision making and formally studying its occurrence can provide many important insights regarding the cognitive underpinnings of the choice process. The past two decades have seen considerable empirical work outlining the determinants of choice deferral, and the consequences of allowing choice to be deferred. This work has established that the likelihood of choice deferral increases (paradoxically) with the size of the decision set: Adding choice options that are in conflict (i.e. are unalignable) with the options in the existing set, or that are equally desirable to the options in the existing set, can reduce the probability of making a choice (Dhar, 1997; Gourville & Soman, 2005; Tversky & Shafir, 1992). Additionally, the ability to defer choice has been shown to increase the choice probability of extreme options, compared to all-average options, and to increase the incidence of the attraction effect, but decrease the incidence of the compromise effect (Dhar & Simonson, 2003). There has been some theoretical work attempting to explain deferral using decision field theory (DFT) (Busemeyer & Townsend, 1993, Roe et al., 2001). DFT is a dynamic model of preferential choice, which assumes that Associative Accumulation Model In multi-attribute choice tasks, decision makers are asked to choose between two or more options defined on a number of different attributes. An example of such a task is a choice between two cars, each of which differs on attributes such as mileage, cost, fuel efficiency and so on. Jessup et al. also consider a number of other methods to model choice deferral. Many of these alternate methods are unable to predict the increase in deferral probability with the size of the choice set. Additionally Busemeyer, Johnson & Jessup (2006) present an alternate model of deferral. This model assumes that the possibility of choice deferral is processed as just another choice option, and that choice is deferred when this option is chosen. Busemeyer et al.’s (2006) model can explain deferral’s relationship with the attraction and compromise effect, but cannot, however, capture the observed increase in deferral with set size (see Jessup et al., 2009).