Generalized Sen-Coherence and Existence of Preferred With Probability At Least Half Winners

Lahiri, Somdeb

《International Journal of Operations Research》 17卷3期 (2020/09) Pp. 93-99

https://doi.org/10.6886/IJOR.202009_17(3).0002

摘要

In this paper, we provide two sufficient (though not necessary) conditions under which for a given profile of state-dependent preferences (linear orders) on a given and fixed set of alternatives, the set of alternatives alternative(s) which are individually preferred to all alternatives other than itself with probability at least half, is non-empty. We thereby extend the domain of decision making under uncertainty from state-dependent utility functions to the domain of state-dependent rankings whose informational requirements are considerably more parsimonious. The first sufficient condition-valid under a mild asymmetry condition- is the well-known Sen Coherence. The second sufficient condition which is valid unconditionally is a generalisation of Sen Coherence. It says that there exists at least one alternative which is never at the end of a particular structure (sigma) associated with a preference profile. The scientific contribution of this second property-apart from its novelty- as we show by means of two examples is that it is applicable even when Sen Coherence is not.

關鍵字

state-dependent preferences ； preferred with probability at least half ； fixed set of alternatives