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

Abstract

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 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.

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