Sequential Deliberation for Social Choice

TL;DR

Sequential deliberation is an iterative, decentralized method for large-scale social choice that approximates optimal social cost, ensuring efficiency, truthfulness, and scalability in complex decision spaces.

Contribution

The paper introduces sequential deliberation as a scalable, decentralized social choice mechanism with provable approximation guarantees and desirable strategic properties.

Findings

Achieves a 1.208-approximation to optimal social cost on median graphs.

Proves sequential deliberation is ex-post Pareto efficient and truthful.

Bounds the second moment of social cost distribution in general metric spaces.

Abstract

In large scale collective decision making, social choice is a normative study of how one ought to design a protocol for reaching consensus. However, in instances where the underlying decision space is too large or complex for ordinal voting, standard voting methods of social choice may be impractical. How then can we design a mechanism - preferably decentralized, simple, scalable, and not requiring any special knowledge of the decision space - to reach consensus? We propose sequential deliberation as a natural solution to this problem. In this iterative method, successive pairs of agents bargain over the decision space using the previous decision as a disagreement alternative. We describe the general method and analyze the quality of its outcome when the space of preferences define a median graph. We show that sequential deliberation finds a 1.208- approximation to the optimal social cost on such graphs, coming very close to this value with only a small constant number of agents sampled from the population. We also show lower bounds on simpler classes of mechanisms to justify our design choices. We further show that sequential deliberation is ex-post Pareto efficient and has truthful reporting as an equilibrium of the induced extensive form game. We finally show that for general metric spaces, the second moment of of the distribution of social cost of the outcomes produced by sequential deliberation is also bounded.