Analysis of Iterative Process for Nauru Voting System

Abstract

Game theory is a popular area of artificial intelligence in which the voter acknowledges his own desires and favors the person he wants to be his representative. In multi-agent systems, social choice functions help aggregate agents’ different preferences over alternatives into a single choice. Since all voting rules are susceptible to manipulation, the analysis of elections is complicated by the possibility of voter manipulation attempts. One approach to understanding elections is to treat them as an iterative process and see if we can reach an equilibrium point. Meir et al. proposed an iterative process to reach a stable outcome, i.e., Nash Equilibrium. This technique, explored in previous work, converges to a Nash equilibrium for plurality voting, along with a tie-breaking rule that chooses a winner according to a linear order of preferences over candidates. Almost all the scoring rules have been studied in previous work, we identified the iterative processes of the Nauru voting system. We analyzed the Nauru voting system with Copelands and lexicographic rule for tiebreaking. Nauru is the modified version of Borda counting. Like Borda counting, Nauru voting system scores each candidate with different points. In the iterative behavior analysis of the Nauru voting system, when two or more winning candidates have the same score, a tie occurs. To break the tie, we use the Copeland method, which is a pairwise comparison to rank the candidates. If there is still a tie, we break it using the traditional linear ordering method, the lexicographic rule. We have observed cycles for different manipulative moves.