A deterministic electoral system satisfying Arrow's four conditions in an easily approached limit

TL;DR

This paper introduces a deterministic electoral system that satisfies Arrow's conditions in a specific limit, providing a novel approach that aligns with stronger social choice criteria.

Contribution

It presents a new deterministic electoral method satisfying stronger conditions, bridging the gap between Arrow's impossibility and Gibbard-Sonnenschein's probabilistic approach.

Findings

The method satisfies Arrow's four conditions in a certain limit.

Provides a reference implementation in C for Linux and Windows.

Demonstrates a deterministic approach compatible with stronger social choice conditions.

Abstract

In 1950 Arrow famously showed that there is no social welfare function satisfying four basic conditions. In 1976, on the other hand, Gibbard and Sonnenschein showed that there does exist a unique probabilistic social welfare method that satisfies a different set of strictly stronger conditions. In this paper we discuss a deterministic electoral method satisfying those same stronger conditions in an appropriate sense; it is not a counterexample to either of these theorems. We attach a simple reference implementation written in C with executables for Linux and Windows.