Open research questions in Game Theory and Voting Systems
72 unresolved questions extracted from the limitations and future-work sections of 1,368 Game Theory and Voting Systems papers in our library. Each links back to the study that raised it.
What the literature leaves open
Further theoretical analysis of individual DP is needed. The paper suggests removing or relaxing the assumption that the number of comparisons L contributed by each individual is fixed and known. The paper highlights the need for a comprehensive comparison between edge DP and individual DP.
The paper identifies a gap in existing work on differential privacy and ranking from pairwise comparisons. The paper highlights the need for developing differentially private algorithms for ranking from pairwise comparisons. The paper notes that existing work on edge DP does not consider the more realistic setting with multiple item comparisons.
The complexity of electoral control problems. The lack of understanding of the approximability of control problems. The need for algorithms that can efficiently solve electoral control problems.
The problem of computing a Nash equilibrium is known to be intractable in general. The common-payoff property does not simplify the problem. The paper needs to show that the problem is CLS-complete.
The complexity of voting systems. The difficulty of evaluating the performance of different voting methods. The need for a new metric to measure the robustness of winners.
Schulze and Ranked Pairs Under Stress: A Computational Comparison of Two Condorcet Voting Methods · 2026 · DOIThe challenge of characterizing approximate forms of utilitarian aggregation for finitely many vN-M utilities. The challenge of showing that small violations of the Pareto principles lead to aggregation rules that remain approximately utilitarian.
The presence of forbidden and forced arcs. The need for an efficient algorithm to find an allocation in the strong core or decide that it is empty. The need to accommodate partial order preferences.
Scope is limited to crash-failure models. Network model assumes reliable point-to-point channels. Implementation complexity assessments are subjective.
The gap between theoretical complexity and practical performance. Limited analysis of Byzantine fault tolerance. Lack of systematic evaluation of message loss scenarios.
The visualization of different allocations needs to be somewhat robust to the scale of the graph. The defense budget must be satisfied.
To study allocations that are "nearly in the strong core". To find allocations for which a few agents cover all blocking cycles.
Our work resolves an open question of theirs by showing that $1/e$ cannot be achieved even in the cardinal case of the $1$-$B$ knapsack secretary problem.
Knapsack Secretary is not $1/e$-Competitive · 2026While the RAT-degree has been analyzed in settings such as single-winner elections, its implications for multi-winner voting remain unexplored.
The Degree of Strategy-Proofness for Risk-Averse Committee Selection · 2026Future research could explore the implications of the paper's results for the design of electoral systems. Future research could also examine the effects of other factors, such as voter preferences and election rules, on equilibrium expected turnout and the probability of winning.
The paper identifies a gap in existing explanations of voting. Prior work has concluded that the probability of a given voter being decisive is miniscule, but this paper claims that substantial voter turnout can occur even in a totally instrumental, outcome-oriented polity.
Further studies could investigate the role of the EDA constraint in children's acquisition of vocabulary. Further studies could also investigate the implications of the EDA constraint for educational materials and tasks.
Prior work has not fully explained the young child's deficient performance on comparison tasks. The EDA constraint may fill this gap.
The need to correct the misconceptions about the Lane et al. algorithm. The need to demonstrate the accuracy of the Lane et al. algorithm.
No sensitivity analysis is provided regarding parameter variations, such as changes in weights, unit costs, or coalition structures, and their impact on the optimal allocation.
The study focuses on a single case application (JAMB CBT centers in Nigeria); generalization to other cooperative game scenarios and supply chain contexts remains unexplored.
To generalize the results to other types of tournaments. To study the properties of the voting profiles that admit any candidate as the winner. To apply the results to real-world knockout tournaments.
The paper identifies a critical drawback of knockout tournaments: the winner heavily depends on the initial order of the candidates. The paper identifies a need for a voting profile that admits any candidate as the winner.
The computational complexity of determining whether a given random matching is ex-post stable has remained unresolved. The problem has been studied in the context of school choice, housing assignment, and resident matching.
Future research can focus on extending the results to games with unconstrained or upper-bounded coalition sizes. The authors suggest studying the stability of hedonic games with more complex size constraints.
Single-Deviation Stability in Additively Separable Hedonic Games with Constrained Coalition Sizes · 2026 · DOIThere is a gap in the literature regarding the computational complexity of the associated existence problem. The paper identifies the need for a full picture of the existence of stable outcomes with respect to given size parameters.
Single-Deviation Stability in Additively Separable Hedonic Games with Constrained Coalition Sizes · 2026 · DOI
Most-cited papers in Game Theory and Voting Systems
- A Bargaining Model of Collective Choice · American Political Science Review · 2000 · 268 citations
- Fair division of indivisible goods: Recent progress and open questions · Artificial Intelligence · 2023 · 77 citations
- Escaping the Impossibility of Fairness: From Formal to Substantive Algorithmic Fairness · Philosophy & Technology · 2022 · 50 citations
- Imposing Contiguity Constraints in Political Districting Models · Operations Research · 2021 · 47 citations
- Sufficiency and the Threshold Question · The Journal of Ethics · 2020 · 47 citations
- A Recursive Partitioning Method for the Prediction of Preference Rankings Based Upon Kemeny Distances · Psychometrika · 2016 · 34 citations
- Insurance, Big Data and Changing Conceptions of Fairness · European Journal of Sociology · 2020 · 32 citations
- From fair predictions to just decisions? Conceptualizing algorithmic fairness and distributive justice in the context of data-driven decision-making · Frontiers in Sociology · 2022 · 22 citations
- Fair division of mixed divisible and indivisible goods · Artificial Intelligence · 2021 · 22 citations
- A measure of distance between judgment sets · Social Choice and Welfare · 2011 · 19 citations
Most recent work
- Optimal Differentially Private Ranking from Pairwise Comparisons · Journal of the American Statistical Association · 2026
- We can do so much better than binary decisions and error rates: why don’t we? · Law Probability and Risk · 2026
- Opening up new possibilities for algorithmic fairness · Philosophy & Technology · 2026
- A GP SOLUTION TO COOPERATIVE GAME-DYNAMIC PROGRAMMING OPTIMIZATION · Advances and Applications in Discrete Mathematics · 2026
- Combinatorics and Optimization of Weighted Voting · Mathematics Magazine · 2026
- Voting profiles admitting all candidates as knockout winners · Discrete Applied Mathematics · 2026
- Optimising the decision threshold in a weighted voting system: the case of the IMF’s Board of Governors · Economics of Governance · 2026
- Wishocracy: Solving the Democratic Principal-Agent Problem Through Pairwise Preference Aggregation · Zenodo (CERN European Organization for Nuclear Research) · 2026
- Ex-post Stability under Two-Sided Matching: Complexity and Characterization · Algorithmica · 2026
- Preference-Approval Structures and Opportunity Sets · Group Decision and Negotiation · 2026
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