Choice functions on posets
Vladimir Danilov
TL;DR
This paper investigates choice functions on partially ordered sets, characterizing their structure through heredity and outcast conditions, and generalizing the Aizerman-Malishevsky theorem to a broader class of path-independent choice functions.
Contribution
It introduces a representation of choice functions satisfying heredity and outcast conditions as unions of elementary functions, extending existing theorems.
Findings
Choice functions can be decomposed into unions of elementary functions.
The paper generalizes the Aizerman-Malishevsky theorem.
Provides a structural characterization of choice functions on posets.
Abstract
In the paper we study choice functions on posets satisfying the conditions of heredity and outcast. For every well-ordered sequence of elements of poset, we define the corresponding `elementary' choice function. Every such a choice function satisfies the conditions of heredity and outcast. Inversely, every choice functions satisfying the conditions of heredity and outcast can be represented as union of several elementary choice functions. This result generalizes the Aizerman-Malishevsky theorem about structure of path-independent choice functions.
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Taxonomy
TopicsGame Theory and Voting Systems · Advanced Algebra and Logic