Probability calculations under the IAC hypothesis

TL;DR

This paper demonstrates how advanced algorithms for counting lattice points and calculating convex polyhedron volumes can be applied to compute probabilities in social choice theory, providing new computational tools for the field.

Contribution

It introduces a novel application of geometric algorithms to social choice probability calculations, bridging computational geometry and social choice theory.

Findings

Algorithms effectively compute probabilities of social choice events.

Multiple illustrative examples showcase practical applications.

The approach enhances computational efficiency in social choice analysis.

Abstract

We show how powerful algorithms recently developed for counting lattice points and computing volumes of convex polyhedra can be used to compute probabilities of a wide variety of events of interest in social choice theory. Several illustrative examples are given.