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Free-Riding in Multi-Issue Decisions

Martin Lackner, Jan Maly, Oliviero Nardi

TL;DR

This work analyzes free-riding in multi-issue voting under OWA, Thiele, and global-optimization rules, showing that fairness-driven multi-issue decisions are broadly susceptible to manipulation except under fully utilitarian rules. It combines axiomatic, complexity-theoretic, and numerical experiments to demonstrate that while single-issue free-riding is often possible, it carries non-negligible risk and long-term effects are hard to predict. The study reveals NP-hardness results for detecting beneficial free-riding and related recognition tasks, and provides quantitative insight into how parameters (e.g., number of issues, voters, and candidates) influence the prevalence and risk of manipulation. Overall, free-riding is not a simple, risk-free tactic in real-world multi-issue settings, though it becomes more tempting under certain rule families, particularly when governance emphasizes common fairness across issues.

Abstract

Voting in multi-issue domains allows for compromise outcomes that satisfy all voters to some extent, but such fairness considerations open the possibility of a special form of manipulation: free-riding, where voters untruthfully oppose a popular opinion in one issue to receive increased consideration in other issues; we study under which conditions this is possible and show that even weak fairness considerations enable free-riding, and through computational and experimental analysis, we find that while free-riding in multi-issue domains is often possible, it comes at a non-negligible individual risk for voters, making its allure smaller than one could intuitively assume.

Free-Riding in Multi-Issue Decisions

TL;DR

This work analyzes free-riding in multi-issue voting under OWA, Thiele, and global-optimization rules, showing that fairness-driven multi-issue decisions are broadly susceptible to manipulation except under fully utilitarian rules. It combines axiomatic, complexity-theoretic, and numerical experiments to demonstrate that while single-issue free-riding is often possible, it carries non-negligible risk and long-term effects are hard to predict. The study reveals NP-hardness results for detecting beneficial free-riding and related recognition tasks, and provides quantitative insight into how parameters (e.g., number of issues, voters, and candidates) influence the prevalence and risk of manipulation. Overall, free-riding is not a simple, risk-free tactic in real-world multi-issue settings, though it becomes more tempting under certain rule families, particularly when governance emphasizes common fairness across issues.

Abstract

Voting in multi-issue domains allows for compromise outcomes that satisfy all voters to some extent, but such fairness considerations open the possibility of a special form of manipulation: free-riding, where voters untruthfully oppose a popular opinion in one issue to receive increased consideration in other issues; we study under which conditions this is possible and show that even weak fairness considerations enable free-riding, and through computational and experimental analysis, we find that while free-riding in multi-issue domains is often possible, it comes at a non-negligible individual risk for voters, making its allure smaller than one could intuitively assume.
Paper Structure (31 sections, 31 theorems, 34 equations, 8 figures)

This paper contains 31 sections, 31 theorems, 34 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Structure
  3. Related Work
  4. The Model
  5. OWA rules
  6. Thiele rules
  7. Global-Optimization-Based Rules
  8. Free-Riding
  9. Possibility and Risk of Free-Riding
  10. Possibility of Free-Riding
  11. The Risk of Free-Riding
  12. Computational Complexity
  13. Numerical Simulations
  14. Model setup and parameter values
  15. Considered voting rules and forms of free-riding
  16. ...and 16 more sections

Key Result

Proposition 1

The OWA rule defined by $\alpha=(1,\frac{1}{kn}, \frac{1}{k^2n^2}, \dots)$ is equivalent to the leximin rule.

Figures (8)

  • Figure 1: Possibility and risk of single-issue free-riding. The left column of diagrams show sequential Thiele methods, the right sequential OWA methods. The three rows correspond to the square, many groups, and unbalanced distributions.
  • Figure 2: Results for repeated free-riding with the square voter distribution. In contrast to Figure \ref{['fig:exp-single']}, we see a much higher likelihood of successful free-riding with very little risk.
  • Figure 3: Average change in satisfaction from free-riding, comparing different voter distributions as well as single-issue vs. repeated free-riding.
  • Figure 4: Varying the number of voters (our default choice is $n=20$): an increase in the number of voters decreases the effectiveness of free-riding by a single voter.
  • Figure 5: Varying the number of candidates (our default choice is $m=5$): more candidates per issue increase the likelihood of free-riding.
  • ...and 3 more figures

Theorems & Definitions (59)

  • Example 1
  • Example 1
  • Proposition 1
  • proof
  • Example 2
  • Example 3
  • Definition 1
  • Proposition 2
  • Definition 2: Simple elections
  • Theorem 3
  • ...and 49 more