Markets for Public Decision-making

TL;DR

This paper introduces a novel approach called pairwise issue expansion that transforms public decision-making problems into Fisher markets, enabling the analysis of equilibria that maximize social welfare and revealing deep connections between public and private market models.

Contribution

The paper presents a new technique to convert public decision problems into Fisher markets, allowing for equilibrium analysis that maximizes Nash welfare and addressing limitations of previous pricing methods.

Findings

Market equilibria with a single common price can be arbitrarily poor.

Pairwise issue expansion transforms public decision problems into Fisher markets.

Equilibrium prices in the transformed market maximize Nash welfare.

Abstract

A public decision-making problem consists of a set of issues, each with multiple possible alternatives, and a set of competing agents, each with a preferred alternative for each issue. We study adaptations of market economies to this setting, focusing on binary issues. Issues have prices, and each agent is endowed with artificial currency that she can use to purchase probability for her preferred alternatives (we allow randomized outcomes). We first show that when each issue has a single price that is common to all agents, market equilibria can be arbitrarily bad. This negative result motivates a different approach. We present a novel technique called "pairwise issue expansion", which transforms any public decision-making instance into an equivalent Fisher market, the simplest type of private goods market. This is done by expanding each issue into many goods: one for each pair of agents who disagree on that issue. We show that the equilibrium prices in the constructed Fisher market yield a "pairwise pricing equilibrium" in the original public decision-making problem which maximizes Nash welfare. More broadly, pairwise issue expansion uncovers a powerful connection between the public decision-making and private goods settings; this immediately yields several interesting results about public decisions markets, and furthers the hope that we will be able to find a simple iterative voting protocol that leads to near-optimum decisions.