How can voting rules ensure fair candidate rankings?
Characterizations of voting rules based on majority margins
This paper explores margin-based voting rules, where the outcome depends solely on the pairwise comparisons between candidates (how many voters prefer candidate A to B, B to C, and so on). It establishes a connection between these rules and several axioms related to voter equality and preference balancing, especially "Preferential Equality," which means if two voters swap adjacent rankings, the outcome changes consistently regardless of which voter swapped. These results could inform the design of fair and robust aggregation mechanisms in multi-agent systems where LLMs act as agents by representing voter preferences as rankings or comparisons and using margin-based rules as a method for collective decision-making. The focus on pairwise comparisons and axioms like Preferential Equality can enhance the transparency and fairness of LLM-based multi-agent interactions.