Open AccessPattanaik’s axioms and existence of preferred with probability at least half winners
Author(s) -
Somdeb Lahiri
Publication year - 2021
Publication title -
badania operacyjne i decyzje/operations research and decisions
Language(s) - English
Resource type - Journals
eISSN - 2081-8858
pISSN - 1230-1868
DOI - 10.37190/ord210205
Subject(s) - axiom , mathematics , transitive relation , probability distribution , coherence (philosophical gambling strategy) , mathematical economics , set (abstract data type) , probability measure , discrete mathematics , combinatorics , statistics , computer science , geometry , programming language
In this paper we show that three conditions due to Pattanaik, when satisfied by a given profile of state-dependent preferences (linear orders) on a given and fixed set of alternatives and a probability distribution with which the various states of nature occur, are individually sufficient, for the non-emptiness of the set of alternative(s) which are individually preferred to all alternatives other than itself with probability at least half. Prior to this, we show that since each axiom individually implies Sen-Coherence, then, as a consequence of a result obtained earlier, each axiom along with asymmetry of the ‘preferred with at probability at least half” relation implies the transitivity of the relation. All the sufficient conditions discussed here are required to be applicable at least to all those otherwise relevant events that have positive probability. This observation also applies to a sufficient condition for the non-emptiness of the set of alternative(s) which are individually preferred to all alternatives other than itself with probability at least half, called Generalised Sen Coherence introduced and discussed in earlier research.