A new paper on separable vs entangled stochastic choice

[Victor Aguiar]

Dear all, 

My coauthors and I just finished this new short paper 

https://www.researchgate.net/publication/378938384_Entangled_vs_Separable_Choice

Abstract:

We study joint probabilistic choice rules that describe the behavior of two decision-makers, each facing a possibly different menu. These choice rules are separable when they can be factored into autonomous choices from each individual solely correlated through their individual probabilistic choice rules. Despite recent interest in studying such rules, a complete characterization of the restrictions on them remains an open question. A reasonable conjecture is that such restrictions on separable joint choice can be factored into individual choice restrictions. We name these restrictions separable and show that this conjecture is true if and only if the probabilistic choice rule of at least one decision maker uniquely identifies the distribution over deterministic choice rules. Otherwise, entangled choice rules exist that satisfy separable restrictions yet are not separable. The possibility of entangled choice complicates the characterization of separable choice since one needs to augment the separable restrictions with the new emerging ones.

p.s. We use Bell Inequalities used to detect entanglement in quantum physics to be able to characterize our separable model. 

Best

V

[Victor Aguiar]

Dear all, 

We have updated our paper with a full characterization of the separable model. 

Abstract:

We investigate joint probabilistic choice rules describing the behavior of two decision makers, each facing potentially distinct menus. These rules are separable when they can be decomposed into individual choices correlated solely through their respective probabilistic choice rules. Despite its significant interest for the study of peer effects, influence, and taste variation, a complete characterization of these rules has remained elusive (Chambers, Masatlioglu, and Turansick, 2021). We fully characterize separable choices through a finite system of inequalities inspired by Afriat's theorem. Our results address the possibility of entangled choices, where decision makers behave as if they do not communicate, yet their choices are not separable. More generally, we establish that separable joint choice restrictions can be factored into individual choice restrictions if only if at least one decision maker's probabilistic choice rule uniquely identifies the distribution over deterministic choice rules. The no communication condition and the individual restrictions are no longer sufficient in the absence of this uniqueness. Our results offer robust tools for distinguishing between separable decision-making and behaviors beyond mere peer effects such as imitation and cheating. 

https://www.researchgate.net/publication/378938384_Entangled_vs_Separable_Choice

Best

V