Asymptotic Theory Of Stochastic Choice Functionals For Prospects With Embedded Comotonic Probability Measures

We introduce a monotone class theory of Prospect Theory's value functions, which shows that they can be replaced almost surely by a topological lifting comprised of a class of compact isomorphic maps that embed weakly co-monotonic probability measures, attached to state space, in outcome space. Thus, agents solve a signal extraction problem to obtain estimates of empirical probability weights for prospects under risk and uncertainty. By virtue of the topological lifting, we prove an almost sure isomorphism theorem between compact stochastic choice operators, and well defined outcomes which, under Brouwer-Schauder theory, guarantees fixed point convergence in convex choice sets. Along the way we introduce a risk operator in the Hoffman-Jorgensen class of lifting operators, and value function [averaging] operators with respect to Radon measure. In that set up, suitable binary operations on gain-loss space show that our risk operator is isometric for gains and skewed for losses. The point spectrum from this operator constitutes the range of admissible observations for loss aversion index in a well designed experiment.

Asymptotic Theory Of Stochastic Choice Functionals For Prospects With Embedded Comotonic Probability Measures

We introduce a monotone class theory of Prospect Theory's value functions, which shows that they can be replaced almost surely by a topological lifting comprised of a class of compact isomorphic maps that embed weakly co-monotonic probability measures, attached to state space, in outcome space. Thus, agents solve a signal extraction problem to obtain estimates of empirical probability weights for prospects under risk and uncertainty. By virtue of the topological lifting, we prove an almost sure isomorphism theorem between compact stochastic choice operators, and well defined outcomes which, under Brouwer-Schauder theory, guarantees fixed point convergence in convex choice sets. Along the way we introduce a risk operator in the Hoffman-Jorgensen class of lifting operators, and value function [averaging] operators with respect to Radon measure. In that set up, suitable binary operations on gain-loss space show that our risk operator is isometric for gains and skewed for losses. The point spectrum from this operator constitutes the range of admissible observations for loss aversion index in a well designed experiment.

Multi-parameter utility and drift-rate functions conflate attribute weights and choice consistency

Standard decision models include two components: subjective-value (utility) functions and stochastic choice rules. The first establishes the relative weighting of the attributes or dimensions and the second determines how consistently the higher utility option is chosen. For a decision problem with M attributes, researchers often estimate M-1 utility parameters and separately estimate a choice-consistency parameter. Instead, researchers sometimes estimate M parameters in the utility function and neglect choice consistency. I argue that while these two approaches are mathematically identical, the latter conflates utility and consistency parameters, leading to ambiguous interpretations and conclusions. At the same time, behavior arises from the interaction of utility and consistency parameters, so for choice prediction they should not be considered in isolation. Overall, I advocate for a clear separation between utility functions and stochastic choice rules when modeling decision-making, and reinforce the notion that researchers should use M-1 parameters for M-attribute decision problems.

Investigation of the Stochastic Choice under Risk using Experimental Data

This paper extends the analysis of the data from the experiment undertaken by Pradiptyo et al. (2015), to help explain the subjects’ behaviour when making decisions under risk. This study specifically investigates the relative empirical performance of the two general models of the stochastic choice: the random utility model (RUM) and the random preference model (RPM) where this paper specifies these models using two preference functionals, expected utility (EU) and rank-dependent expected utility (RDEU). The parameters are estimated in each model using a maximum likelihood technique and run a horse-race using the goodness-of-fit between the models. The results show that the RUM better explains the subjects’ behaviour in the experiment. Additionally, the RDEU fits better than the EU for modelling the stochastic choice.