Implementation of an Innovative Method in the Field Of Social Choice Theory Based on the Geometric Mean

Abstract

Social choice theory, also known as voting methods theory, studies the mechanisms for aggregating individual preferences within a group into a collective decision. Among classical approaches, approval voting stands out for its simplicity and interesting theoretical properties. With the aim of improvement, particularly in terms of consensus and acceptability, the MVMG method (Voting Method based on the Geometric Mean) has been proposed. It combines assent voting with an aggregation function based on the geometric mean. However, its applications have so far been limited to small-scale cases (  candidates and  voters). In this paper, we propose a generalized algorithmic implementation of the MVMG method, designed to overcome these limitations. The approach developed is based on a modular architecture in Python, organised into three modules. A main module coordinates the other three to create a readable and well-structured programme. After validation on simple cases, simulations were carried out on large data sets (up to 20 candidates and 10 000 000 voters). The results provided by our implementation are consistent with the analytical calculations performed in the literature. Furthermore, the polynomial complexity of the programme paves the way for practical applications, particularly in online voting systems or large-scale decision-making processes.