Open research questions in Game Theory and Voting Systems
240 gap statements mined from Game Theory and Voting Systems papers in our 4.5M-paper local library, which holds 1,689 papers on the topic — drawn mostly from each paper's own stated research gap, future-work, challenge and limitation notes, and its abstract. The ones listed below are a selection still marked open; each names the study that raised it, with a DOI link where the paper has one.
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What the literature leaves open
The lack of direct work on optimizing CG using DP for better results. The need for a method that optimizes CG solutions via DP and GP.
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.
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 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 lack of stability in online assignment games due to sub-optimal matchings. The need for a framework to study the stability performances of randomized algorithms.
Whether this latter case admits an efficient algorithm remains an open question. Our findings resolve open questions in equitable division and extend the existential guarantees to much richer valuation models, under the reasonable assumption that agents agree on the sign of their value for the grand bundle.
The lack of instance-dependent proportionality notions in approval-based multiwinner voting. The need for a dynamic extension of JR and EJR that minimizes the quota requirements using the parameter α. The limited understanding of the computational aspects of the instance-dependent quota.
The lack of understanding of the approximability of control problems. The need for algorithms that can efficiently solve electoral control problems.
The paper identifies the lack of mechanisms that incentivize truthful reporting while minimizing verification as a research gap. The paper also identifies the need for mechanisms that can handle noisy verification as a research gap.
The study is based on a simulation and may not reflect real-world elections. The number of candidates and voters is limited. The study only considers four voter preference models.
Schulze and Ranked Pairs Under Stress: A Computational Comparison of Two Condorcet Voting Methods · 2026 · DOIThe underlying drivers and implications of optimisation in NICE technology appraisals are poorly understood. There is a need to understand the impact of optimised decisions on patient outcomes.
The paper suggests future research directions, including empirical evaluations of the algorithms and applications to various domains. The paper notes that the algorithms can be improved by reducing the time complexity. The paper suggests that the framework can be applied to other cooperative game theory models.
The existing algorithms require accurate numeric welfare values as input to compute an optimal partition. The paper identifies the need for algorithms that can compute an exact optimum despite the presence of anticipation errors. The paper notes that the existing algorithms do not address the problem of organizing agents into possibly overlapping coalitions to maximize social welfare.
Our exposition was limited to simple, connected, undirected, unweighted graphs, but while none of these limitations is conceptual, any extension comes with a considerable number of cases to deal with and would present a distraction from the main content.
Building on ideas from McDermid and Manlove, we resolve the open problem of Rodríguez and Manlove by showing that it is NP-hard to find a coalition-stable assignment for $\mbox{HRS}$.
Hospitals/Residents with Inseparable Couples: Finding a Coalition-Stable Assignment Is NP-Hard · 2026Future research could explore the implications of the paper's findings for policy debates. Future research could investigate the application of the extended framework to other areas of social choice theory.
The paper highlights the need for further research on the rationality of Sen's impossibility theorem.
We therefore believe the most fruitful direction is strengthening the Ω(𝑘 2) lower bound.
Ranking Opinions with Few States in Population Protocols · 2026Although the computation of equilibria in general bimatrix games is known to be PPAD-complete, there are some interesting special cases for which the complexity remains open. For example, it is known that win-lose games, where all payoffs are 0 or 1, are hard. Separately, it is also known that sparse bimatrix games, where the number of non-zero entries in each row and column is constant, are also hard.
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.
Conventional risk-limiting audits require a software-independent accounting of ballot batch sizes - Establishing a sufficiently accurate manifest often requires handling every ballot and can be the dominant cost of conducting…
Sublinear Risk-Limiting Audits from Direct Ballot Selection and Statistical Ballot Manifests · 2026Further study of the stability performances of randomized algorithms in online assignment games. Exploration of other measures of instability and their connections to the optimality ratio.
Evaluating the rules on real-world data, such as the Polkadot dataset. Exploring the application of the dynamic extensions to other settings, such as apportionment. Investigating the use of other methods, such as approximation algorithms, to compute the optimal α-value.
Further study of the approximability of electoral control problems. Development of algorithms for electoral control problems. Analysis of the performance of algorithms in electoral control problems.
Most-cited papers in Game Theory and Voting Systems
- Rank-Order Tournaments as Optimum Labor Contracts · Journal of Political Economy · 1981 · 3,934 citations
- The Competitive Exclusion Principle · Science · 1960 · 2,673 citations
- A Method for Evaluating the Distribution of Power in a Committee System · American Political Science Review · 1954 · 1,493 citations
- The outranking approach and the foundations of electre methods · Theory and Decision · 1991 · 1,203 citations
- Whom or What Does the Representative Individual Represent? · The Journal of Economic Perspectives · 1992 · 1,057 citations
- Information Aggregation, Rationality, and the Condorcet Jury Theorem · American Political Science Review · 1996 · 731 citations
- The Optimal Allocation of Prizes in Contests · American Economic Review · 2001 · 690 citations
- Machiavelli and the Gale-Shapley Algorithm · American Mathematical Monthly · 1981 · 668 citations
- The Price of Fairness · Operations Research · 2011 · 572 citations
- Algorithm for optimal winner determination in combinatorial auctions · Artificial Intelligence · 2002 · 525 citations
Most recent work
- The survival of the weakest in a biased donation game · Applied Mathematics and Computation · 2026
- Interval extensions of the Owen value in a cooperative game with a coalition structure and augmenting system · Annals of Operations Research · 2026
- 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 Clustering Approach for NSGA ‐ II in Political Redistricting · Networks · 2026
- Do people make their votes count? An experimental study on voter errors and electoral systems · Public Choice · 2026
- Blackwell-Monotone Updating Rules · Journal of Political Economy · 2026
- Structural and Algorithmic Results for Stable Cycles and Partitions in the Roommates Problem · ACM Transactions on Economics and Computation · 2026
- Party Competition with Costly Voting · Journal of Artificial Societies and Social Simulation · 2026
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