FSS-ECON Seminar: A Complexity Hierarchy for Stochastic Choice
Speaker: Prof. Erya YANG, Assistant Professor, Business School, Sun Yat-sen University
Date:11 September 2024 (Wed)
Time:14:00 – 15:15
Venue: E21B-G002
Language: English
Abstract: We develop a hierarchy of families of stochastic choice rules in terms of increasing complexity based on the concepts of a conditional probability space (R’enyi, 1955) and a dimensionally-ordered system of measures (R’enyi, 1956). The levels of our hierarchy are: single-valued or point conditional probability spaces (PCPS’s); conditional probability spaces; probabilistic mixtures of PCPS’s; mutually absolutely continuous mixtures of PCPS’s; absolutely continuous mixtures of PCPS’s; and signed probability mixtures of PCPS’s. We show at a general measure-theoretic level that the first five levels are strictly nested. In the finite case, the sixth level nests all the other levels (the general case here appears to be open). Our hierarchy organizes various well-known axioms for stochastic choice and identifies some new relationships among them. It also offers a precise definition of contextuality in stochastic choice and, from this, a new classification of some leading behavioral effects in choice.
