A Natural Adaptive Process for Collective Decision-Making

TL;DR

This paper introduces a natural, adaptive process for collective decision-making that converges to a maximal lottery voting rule, blending ideas from biology, physics, chemistry, and machine learning.

Contribution

It presents a novel, biologically inspired process that approximates maximal lotteries, providing a flexible alternative to traditional voting rules.

Findings

The process converges exponentially to maximal lotteries.

The method is more adaptable than traditional voting rules.

It draws parallels with natural processes in various scientific fields.

Abstract

Consider an urn filled with balls, each labeled with one of several possible collective decisions. Now, let a random voter draw two balls from the urn and pick her more preferred as the collective decision. Relabel the losing ball with the collective decision, put both balls back into the urn, and repeat. Once in a while, relabel a randomly drawn ball with a random collective decision. We prove that the empirical distribution of collective decisions produced by this process approximates a maximal lottery, a celebrated probabilistic voting rule proposed by Peter C. Fishburn (Rev. Econ. Stud., 51(4), 1984). In fact, the probability that the collective decision in round $n$ is made according to a maximal lottery increases exponentially in $n$. The proposed procedure is more flexible than traditional voting rules and bears strong similarities to natural processes studied in biology, physics, and chemistry as well as algorithms proposed in machine learning.