The Panel Complexity of Sortition: Is 12 Angry Men Enough?

TL;DR

This work investigates how large a randomly selected panel must be (the panel complexity) to ensure that sortition-based decisions are representative and reliable for the whole population. It introduces a Wasserstein-distance-based notion of $\,\\epsilon$-representative panels and develops a general framework to analyze how panel size transfers desiderata such as welfare efficiency, core fairness, and low outlier probability from the panel to the population. The authors provide near-tight guarantees for two canonical social choice settings: divisible participatory budgeting and facility location, including finite and continuous spaces, and extend results to multiple facilities and the line. The results have practical implications for designing citizens' assemblies and other random-deliberation bodies, offering principled bounds on panel size that balance representativeness, fairness, and logistical considerations, while highlighting open directions for non-uniform sampling and broader problem domains.

Abstract

Sortition is the practice of delegating public decision-making to randomly selected panels. Recently, it has gained momentum worldwide through its use in citizens' assemblies, sparking growing interest within the computer science community. One key appeal of sortition is that random panels tend to be more representative of the population than elected committees or parliaments. Our main conceptual contribution is a novel definition of representative panels, based on the Wasserstein distance from statistical learning theory. Using this definition, we develop a framework for analyzing the panel complexity problem -- determining the required panel size to ensure desirable properties. We focus on three key desiderata: (1) that efficiency at the panel level extends to the whole population, measured by social welfare; (2) that fairness guarantees for the panel translate to fairness for the population, captured by the core; and (3) that the probability of an outlier panel, for which the decision significantly deviates from the optimal one, remains low. We establish near-tight panel complexity guarantees for these desiderata across two fundamental social choice settings: participatory budgeting and facility location.

Figures (1)

• Figure 1: Illustration of the reductions described in \ref{['lem:reduction_main', 'lem:further_line_reduction']}, as used in the proof of \ref{['thm:tail_bound']}. In subfigure (i), the solid black circle represents the optimal facility location $q^\star$, while the empty circles indicate the agent locations in $\mathcal{X}$. In subfigure (ii), the dashed lines show the mapping of agent locations from the original metric space $\mathcal{X}$ to their corresponding positions in the metric space $\mathcal{Y} = [0, T]$.

Theorems & Definitions (75)

• Theorem : Panel Complexity for Welfare Maximization in Participatory Budgeting; see \ref{['thm:pbeffub']}
• Theorem : Panel Complexity for Core Fairness in Participatory Budgeting; see \ref{['thm:core_ub']}
• Theorem : Panel Complexity for Bounding Panel Outliers in Facility Location; see \ref{['thm:tail_bound']}
• Theorem : Panel Complexity for Welfare Maximization in Facility Location; see \ref{['thm:assouad']}
• Theorem : Panel Complexity for Multiple Facility Location on the Line; see \ref{['thm:line']}
• Definition 2.1: Wasserstein Distance
• Definition 2.2: Representative Panels
• Lemma 2.2: Reduction to Independent Sampling
• Lemma 2.2: Concentration Inequality
• Theorem 2.3: Panel Complexity of Representativeness