Finding Common Ground in a Sea of Alternatives

Abstract

We study the problem of selecting a statement that finds common ground across diverse population preferences. Generative AI is uniquely suited for this task because it can access a practically infinite set of statements, but AI systems like the Habermas machine leave the choice of generated statement to a voting rule. What it means for this rule to find common ground, however, is not well-defined. In this work, we propose a formal model for finding common ground in the infinite alternative setting based on the proportional veto core from social choice. To provide guarantees relative to these infinitely many alternatives and a large population, we wish to satisfy a notion of proportional veto core using only query access to the unknown distribution of alternatives and voters. We design an efficient sampling-based algorithm that returns an alternative in the (approximate) proportional veto core with high probability and prove matching lower bounds, which show that no algorithm can do the same using fewer queries. On a synthetic dataset of preferences over text, we confirm the effectiveness of our sampling-based algorithm and compare other social choice methods as well as LLM-based methods in terms of how reliably they produce statements in the proportional veto core.

Figures (9)

• Figure 1: Our experiment setup. We generate statements conditioned on synthetic persona, and build preference profiles from voters conditioned on synthetic persona. We then evaluate various voting rules, including those powered by LLMs, and compare their critical epsilons.
• Figure 2: CDF of critical epsilons for the chosen alternatives of various voting rules for the three polarizing topics. The smaller the epsilons (the closer the line is to the top-left corner), the better at finding common ground the voting method is.
• Figure 3: Critical epsilons for the winners of various generative voting rules on conservative voters for polarizing topics. Generative voting rules consistently do worse than VBC and sometimes even the random baseline.
• Figure 4: Likert scores of 100 voters on 100 generated statements. Higher Likert scores indicate higher agreement. The most polarizing topics have average Likert scores close to 5 and a wide spread. The top 3 topics by polarization are abortion, Electoral College, and healthcare. The bottom 3 polarizing topics are environment, policing, and public trust in elections.
• Figure 5: CDF of critical epsilons across various topics (top three topics by degree of polarization). The leftmost subplot (Persona) allows for clearer analysis than other alternative generation methods.

Theorems & Definitions (38)

• Definition 2.1
• Definition 2.2
• Proposition 3.1
• proof : Proof sketch
• Corollary 3.2
• proof
• Proposition 3.3
• proof
• Theorem 3.4
• proof : Proof Sketch