On quantum models for opinion and voting intention polls

TL;DR

This paper develops a quantum-inspired mathematical framework to predict election outcomes from opinion polls, introducing a density operator approach and a numerical method validated on real election data.

Contribution

It establishes a novel connection between quantum voting models and opinion polls, proposing a density operator method for election result prediction.

Findings

Successfully applied the method to synthetic data

Validated approach with French 2012 presidential election data

Demonstrated potential of quantum models in electoral analysis

Abstract

In this contribution, we construct a connection between two quantum voting models presented previously. We propose to try to determine the result of a vote from associated given opinion polls. We introduce a density operator relative to the family of all candidates to a particular election. From an hypothesis of proportionality between a family of coefficients which characterize the density matrix and the probabilities of vote for all the candidates, we propose a numerical method for the entire determination of the density operator. This approach is a direct consequence of the Perron-Frobenius theorem for irreductible positive matrices. We applyour algorithm to synthetic data and to operational results issued from the French presidential election of April 2012.