Markets for public decision-making
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Markets for public decision‑making Nikhil Garg1 · Ashish Goel1 · Benjamin Plaut1 Received: 28 October 2018 / Accepted: 30 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
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.
1 Introduction Fair and transparent public decision-making is a key element of a democratic society, but many public decisions are made by government officials behind closed doors. In this paper, we investigate mechanisms for large-scale public decision-making * Benjamin Plaut [email protected] Nikhil Garg [email protected] Ashish Goel [email protected] 1
Stanford University, Stanford, USA
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where citizens directly vote on a set of issues at the same time, focusing on the case where each issue has exactly two alternatives. In particular, we examine connections to private goods allocation (i.e., standard resource allocation). One can think of each issue that is under consideration as a “good”, and public decision-making as “allocating” the good to one of the alternatives. We allow randomized outcomes, where the outcome can put nonzero probability on multiple alternatives: this is analogous to divisible private goods, where a good can be split among multiple agents1. The fundamental difference is that in private goods allocation, each agent’s utility depends only on the bundle of goods she receives; in public decision-making, the group makes a single decision that affects all agents. Market economies are one of the longest-studied areas in the distributions of private goods. The simplest market model is that of a Fisher market (see Brainard
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