Nature and statistics of majority rankings in a dynamical model of preference aggregation

TL;DR

This paper investigates a complex dynamical model of preference aggregation, revealing how interaction range influences the probability of transitive social rankings and identifying a counterintuitive enhancement with larger numbers of alternatives.

Contribution

It introduces a novel dynamical model for preference aggregation that shows how interaction range affects transitivity probability, with new insights into the role of the number of alternatives.

Findings

Probability of transitive ranking peaks at large interaction ranges for S>4

Increasing the number of alternatives S enhances the transitivity probability

A microscopic mechanism explaining the counterintuitive results is proposed

Abstract

We present numerical results on a complex dynamical model for the aggregation of many individual rankings of S alternatives by the pairwise majority rule under a deliberative scenario. Agents are assumed to interact when the Kemeny distance between their rankings is smaller than a range R. The main object of interest is the probability that the aggregate (social) ranking is transitive as a function of the interaction range. This quantity is known to decay fast as S increases in the non-interacting case. Here we find that when S>4 such a probability attains a sharp maximum when the interaction range is sufficiently large, in which case it significantly exceeds the corresponding value for a non-interacting system. Furthermore, the situation improves upon increasing S. A possible microscopic mechanism leading to this counterintuitive result is proposed and investigated.