Can Social Decision Schemes Ever Truly Be Fair? The Incentive Problem

Samir D’Costa in Politics & Policy June 2025 • 4 min read.

"Exploring the Challenges of Designing Impartial Systems in a World of Self-Interest"

Imagine a world where every group decision is perfectly fair, reflecting the true desires of its members. This is the promise of social decision schemes (SDSs), which map individual preferences to collective outcomes. However, the path to such fairness is fraught with challenges. Can we design systems that are both efficient and immune to manipulation? This question has occupied researchers for decades, leading to surprising and often disheartening results.

At the heart of the problem lies the issue of incentives. In multi-agent systems, mechanisms must encourage participation and honesty. But what happens when individuals can strategically misrepresent their preferences to achieve a more favorable result? This is where the concept of "strategyproofness" comes in, a crucial property for any SDS aiming for genuine fairness.

This article explores the complexities of designing incentive-compatible SDSs. We will delve into the world of "pairwise comparison preferences," where voters compare alternatives head-to-head, and uncover the inherent limitations in achieving seemingly desirable properties like efficiency, strategyproofness, and participation.

The Impossibility Theorems: When Fairness Meets Reality

Conflicting priorities in social decision-making, symbolized by people pulling scales.

The pursuit of fair SDSs has led to a series of "impossibility theorems," which demonstrate that certain combinations of desirable properties are fundamentally incompatible. These theorems, like Gibbard-Satterthwaite, reveal deep tensions between strategyproofness and other elementary requirements. For example, a strategyproof voting rule often ends up being dictatorial, where one person's preference dictates the outcome, or imposing, where the rule favors a specific outcome regardless of voter input.

One way to navigate these challenges is to introduce randomization. Instead of selecting a single winner, an SDS can return a lottery, a probability distribution over the alternatives. This opens up new possibilities for achieving fairness and efficiency, but it also raises a new question: How do voters compare lotteries? Researchers often use the concept of "stochastic dominance (SD)," where a lottery is preferred if it yields a higher expected utility for every possible utility representation.

Pairwise Comparison (PC) Preferences: Voters prefer the lottery that is more likely to return a preferred outcome.
PC-Strategyproofness: No voter can benefit by misrepresenting their preferences, based on pairwise comparisons.
PC-Efficiency: A lottery is efficient if no other lottery is preferred by all voters and strictly preferred by at least one voter.

The research article at hand dives deep into these issues by focusing on pairwise comparison (PC) preferences. This framework offers a different way to lift preferences over alternatives to preferences over lotteries, and it leads to some striking results. The authors settle several open questions by demonstrating that Condorcet-consistent SDSs cannot be PC-strategyproof. Furthermore, they show that anonymous and neutral SDSs cannot simultaneously satisfy PC-efficiency and PC-strategyproofness or strict PC-participation.

Navigating the Landscape of Impossibility: Where Do We Go From Here?

The impossibility theorems paint a sobering picture of social decision-making. Achieving perfect fairness, efficiency, and incentive compatibility seems like an unattainable goal. However, these results also provide valuable insights for designing better systems. By understanding the trade-offs and limitations, we can strive for SDSs that are "good enough," balancing competing priorities and minimizing the potential for manipulation. The ongoing research in this area continues to explore new avenues, seeking innovative mechanisms and preference aggregation methods that bring us closer to the ideal of truly fair and representative decision-making.

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This article is based on research published under:

DOI-LINK: 10.1016/j.geb.2023.08.009,

Title: Incentives In Social Decision Schemes With Pairwise Comparison Preferences

Subject: cs.gt econ.th

Authors: Felix Brandt, Patrick Lederer, Warut Suksompong

Published: 26-04-2022

Everything You Need To Know

What are Social Decision Schemes (SDSs), and what is their primary goal?

Social Decision Schemes (SDSs) are systems designed to translate individual preferences into collective choices. The primary goal of SDSs is to achieve fairness by accurately reflecting the desires of the group members in the final outcome. However, the design of such systems is complicated by the need to balance fairness with other properties such as efficiency and strategyproofness, as well as the inherent challenges of motivating honest participation in multi-agent systems.

What is strategyproofness in the context of SDSs, and why is it important for achieving fairness?

Strategyproofness is a crucial property of SDSs. A system is strategyproof if individuals cannot benefit by strategically misrepresenting their preferences to achieve a more favorable result. This is important for fairness because it ensures that the outcome is based on genuine preferences rather than manipulative behavior. Without strategyproofness, individuals might misreport their preferences, leading to outcomes that do not accurately reflect the collective will and thus undermine the fairness of the SDS.

What are impossibility theorems, and how do they impact the design of fair SDSs?

Impossibility theorems demonstrate that certain combinations of desirable properties in SDSs are fundamentally incompatible. The Gibbard-Satterthwaite theorem, for example, reveals tensions between strategyproofness and other requirements. These theorems show that it is impossible to create a voting rule that is always strategyproof, efficient, and non-dictatorial. These results provide insights for designing better systems, forcing designers to acknowledge trade-offs and limitations. To create SDSs that are "good enough", balancing competing priorities and minimizing the potential for manipulation is essential.

How does the concept of "pairwise comparison preferences" (PC Preferences) influence the design of SDSs?

Pairwise Comparison (PC) Preferences provide a framework for voters to compare alternatives head-to-head. This framework offers a different way to lift preferences over alternatives to preferences over lotteries. This approach facilitates the development of voting rules that can deal with uncertainty and provide fairer outcomes. Research shows that Condorcet-consistent SDSs cannot be PC-strategyproof. Also, anonymous and neutral SDSs cannot simultaneously satisfy PC-efficiency and PC-strategyproofness or strict PC-participation.

What is the role of randomization and stochastic dominance (SD) in addressing the challenges of designing fair SDSs?

Randomization is introduced in SDSs by returning a lottery, which is a probability distribution over the alternatives, instead of a single winner. This opens up new possibilities for achieving fairness and efficiency. When lotteries are considered, voters must have a method to compare them. Stochastic dominance (SD) is a tool used to determine if one lottery is preferred to another. SD allows voters to compare lotteries based on expected utility, where a lottery is preferred if it yields a higher expected utility for every possible utility representation. This approach helps to create fairer and more efficient SDSs in the presence of uncertainty.