Issue: 2021/Vol.31/No.2, Pages 109-122
PATTANAIK’S AXIOMS AND THE EXISTENCE OF WINNERS PREFERRED WITH PROBABILITY AT LEAST HALF
Somdeb Lahiri
Cite as: S. Lahiri. Pattanaik’s axioms and the existence of winners preferred with probability at least half. Operations Research and Decisions 2021: 31(2), 109-122. DOI 10.37190/ord210205
Abstract
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. Before 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 apply 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.
Keywords: state-dependent preferences, preferred with probability at least half, fixed set of alternatives
Received: 28 September 2020 Accepted: 8 February 2021