Cognitive Choice Modeling by Zheng Joyce Wang

Author:Zheng Joyce Wang
Language: eng
Format: epub
Tags: Utility theory; random utility models; signal detection theory; sequential sampling models; dynamic models; stochastic models; reinforcement learning models; decision neuroscience; quantum cognition models;Cognitive psychology; stochastic choice models; probability theory; random variables;decision weights; utility axioms; expected utility rule; decision paradoxes;Random utility; Thurstone choice model; Luce choice model; Elimination by aspects model;Maximum likelihood estimation, Bayesian estimation; model comparison methods;Signal detection task; sensitivity; bias; confidence;Random walk; diffusion model; threshold bound; decision time; speed – accuracy trade-off; Attention weights; preference accumulation; Ornstein -Uhlenbeck process;Mutli-atlernative choice; mult-attribute choice; choice paradoxes; model comparisons;Reinforcement learning; description-experience gap; Markov decision problems;Dopamine; orbital prefrontal cortex; functional magnetic resonance imaging; electrophysiological recording;Quantum probability; unitary evolution; quantum measurement; interference effects;Rationality; model complexity; theory integration
Publisher: MIT Press

7.3    Applications to Binary Choice Findings

DFT has been shown to quantitatively fit choices between gambles better than popular choice models such as a probabilistic version of prospect theory (Rieskamp, 2008), and it also fits choices between consumer products better than another recently introduced cognitive model called the proportional difference choice model (Scheibehenne, Rieskamp, & Gonzalez-Vallejo, 2009). Next, we present some important qualitative predictions used to test the theory.

Variance effect    An important principle of DFT is that the variance of the valence changes across choice pairs depending on the payoffs assigned to each action. Recall that the standardized mean drift rate parameter, d = (δ /σ), is a ratio of the mean valence divided by the standard deviation, σ, of the valence, and the latter changes depending on the payoffs of the actions. Considering table 7.1, we can manipulate the variance of action A by changing the range of payoffs for option A (i.e., changing the range across {rA1, rA2, rA3}).

If we ignored the standard deviation (or assumed that it was constant across all pairs of actions), then this model would satisfy both strong stochastic transitivity and choice independence. Many authors have in fact assumed such a restrictive choice model (e.g., Stott, 2006). However, this is problematic because, as reviewed in chapter 3, there is extensive empirical evidence demonstrating the effect of heterogeneous variance across choice pairs (Blavatskyy, 2007; Hey & Orme, 1994; Erev & Barron, 2005; Busemeyer, 1985; Wilcox, 2011). As reviewed in chapter 3, this heterogeneity in variance produces systematic violations of both strong stochastic transitivity and choice independence. Ignoring heterogeneity in variance across conditions can distort other parameter estimates in a model (Wilcox, 2011). Therefore, it is important to include the change in variance across pairs of actions to account for these robust findings in the choice literature.

Consider, for example, the violation of binary choice independence reported by Busemeyer (1985) and discussed in chapter 3. Option A was a gamble producing normally distributed payoffs with a mean equal to zero and a standard deviation equal to 5 cents. Option B was a gamble producing normally distributed payoffs with a mean equal to zero and a standard deviation equal to 50 cents. Option C delivered a loss of 3 cents for sure, and option D delivered a gain of 3 cents for sure. The results found by Busemeyer (1985) were as follows:

p(A | {A, C}) = .88 > p(B | {B, C}) = .62,

but

p(A | {A, D}) = .11 < p(B | {B, D}) = .27.

The reversal of the two inequalities shown here indicates a violation of binary choice independence. DFT accounts for this finding using the following simple explanation: For the first inequality, the mean advantage is δ = 3 for choosing A over C, and this is also the case for B over C. However, this mean advantage is easier to discriminate with the A, C choice pair than the B, C choice pair because the variance is much smaller for the A, C choice (σ = 5) than

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