Exploring Fairness in District-based Multi-party Elections under different Voting Rules using Stochastic Simulations

Many democratic societies use district-based elections, where the region under consideration is geographically divided into districts and a representative is chosen for each district based on the preferences of the electors who reside there. These representatives belong to political parties, and the executive powers are acquired by that party which has a majority of the elected district representatives. In most systems, each elector can express preference for one candidate, though they may have a complete or partial ranking of the candidates/parties. We show that this can lead to situations where many electors are dissatisfied with the election results, which is not desirable in a democracy. The results may be biased towards the supporters of a particular party, and against others. Inspired by current literature on fairness of Machine Learning algorithms, we define measures of fairness to quantify the satisfaction of electors, irrespective of their political choices. We also consider alternative election policies using concepts of voting rules and rank aggregation, to enable voters to express their detailed preferences without making the electoral process cumbersome or opaque. We then evaluate these policies using the aforementioned fairness measures with the help of Monte Carlo simulations. Such simulations are obtained using a proposed stochastic model for election simulation, that takes into account community identities of electors and its role in influencing their residence and political preferences. We show that this model can simulate actual multi-party elections in India. Through extensive simulations, we find that allowing voters to provide 2 preferences reduces the disparity between supporters of different parties in terms of the election result.