Coalitions and stability unite majoritarian and proportional election methods
Coalitions, Stability, and Majority Jackpots: Frameworks for Unifying Majoritarian and Proportional Allocation in Multiwinner Elections
Computer Science and Game Theory
Summary
Elections that pick multiple winners often try to be either fair to the majority or fair to all groups proportionally. The authors study systems in between these two extremes, such as majority jackpot systems. They introduce new ways to understand and analyze these approaches using ideas called coalitions and stability. Their work explains how these election systems behave mathematically and computationally, providing new insights into voting methods that haven't been well studied before.
What this means in practice
- •For election system designers: Design electoral systems that balance majoritarian and proportional goals using new coalition and stability frameworks.
- •For government policy teams: Analyze and improve majority jackpot voting methods in electoral reforms with mathematically grounded tools.
A theory result. No direct application yet.
Authors
Kit Scriven, Nitin Kohli
Abstract
Social choice literature on multiwinner elections tends to focus on characterizing two distinct tasks: majoritarian representation and proportional representation. However, many real world systems can be viewed as operating between these two extremes, such as majority jackpot systems used in several countries throughout history. Towards the goal of better understanding these systems from a social choice perspective, we introduce two frameworks that encompass existing desiderata for majoritarian and proportional settings: coalitions, which encompasses properties such as fixed majority and solid coalitions; and stability, which encompasses various generalizations of Condorcet's criterion for single-winner elections, such as Gehrlein stability and local stability, among others. We develop theory and tools that characterize the mathematical and computational aspects of both frameworks across a wide array of preference structures (such as the unrestricted domain over candidates and the restricted domain of party lists). Building on this foundation, we shed new light on majority jackpot electoral systems, which to date have received limited mathematical analysis in the social choice literature.