voting mechanism design

This paper addresses proportional representation in multi-round sequential decision-making: ensuring that any α%-consensus voter group receives representation in approximately α% of rounds under sequential approval voting. It systematically adapts proportional representation axioms—previously defined for multi-winner elections—to the sequential setting, introducing three novel rule families: online (Sequential Phragmén), semi-online (Method of Equal Shares), and offline (Proportional Approval Voting), each satisfying distinct strength levels of proportionality axioms. Leveraging load-balancing, resource-allocation, and global-optimization mechanisms, the rules are evaluated on synthetic data, U.S. election data, and Moral Machine ethical preference data. Results demonstrate that, compared to conventional global aggregation methods, the proposed rules significantly improve equality in utility distribution across demographic groups. This confirms proportional aggregation as a critical pathway toward fair sequential decision-making.

This paper investigates mechanism design for private-good allocation under arbitrary feasibility constraints, focusing on the joint satisfaction of strategy-proofness and Pareto efficiency. Methodologically, it introduces the notion of “local dictatorship” to characterize two-agent mechanisms, establishes a succinct necessary and sufficient condition for group strategy-proofness, and unifies the analysis of classic problems—including house allocation, roommate matching, and social choice—via marginal mechanism decomposition and compositional constraint modeling. Key contributions include: (i) the first complete characterization of strategy-proof and Pareto-efficient mechanisms for two agents; (ii) a proof that all compatible mechanisms for the roommate problem must be generalized sequential dictatorships; (iii) a simplified, reconstructed proof framework for the Gibbard–Satterthwaite theorem; and (iv) the identification and formalization of a novel class of robust matching mechanisms.

This paper studies collective aggregation of individual budget distributions in multi-dimensional budget allocation, focusing on mechanism design within the star-shaped preference domain. Method: We introduce a novel star-shaped utility function based on share ratios and analyze mechanisms—including the Nash product maximization mechanism and the uniform phantom mechanism—under various distance metrics (e.g., ℓ₁, ℓ₂). Contribution/Results: We establish the first mechanism achieving simultaneous Pareto efficiency, group strategyproofness, and core fairness in multi-option settings. We characterize the Nash product maximization mechanism as both group strategyproof and core fair. For two alternatives, we prove the uniform phantom mechanism is the unique rule satisfying all three properties; however, under ℓ₁ or ℓ₂ distances, no mechanism can satisfy all three in settings with three or more alternatives. Finally, we construct a computationally tractable mechanism that ensures both fairness and efficiency, offering a new paradigm for budget aggregation that balances theoretical rigor with practical implementability.

This paper investigates how preference restrictions—such as single-peakedness, single-crossingness, and Euclidean preferences—mitigate fundamental computational challenges in computational social choice. Addressing key bottlenecks—including the hardness of domain identification and NP-hardness of winner determination—this work provides the first unified computational framework for modeling and analyzing both classical and emerging preference domains. Leveraging graph-theoretic, poset-based, and combinatorial structures, it introduces a general domain-identification framework and designs polynomial-time algorithms for domain recognition and winner computation under otherwise intractable voting rules (e.g., Kemeny and Young). These advances substantially circumvent Arrow-type impossibility results, enhancing structural regularity and computational tractability in preference aggregation. The results improve the computability, interpretability, and practical applicability of real-world electoral systems and multi-agent decision-making frameworks.

This paper addresses the fundamental challenge of acquiring and processing full preference profiles in large-scale collective decision-making—e.g., jury trials, indirect elections, and AI alignment—where eliciting preferences from all individuals is infeasible. Method: It pioneers a statistical learning formulation of social choice, introduces a formal axiomatic framework for representativeness, and employs combinatorial analysis to prove an Arrow-type impossibility theorem for representative samples. The approach integrates computational social science, statistical learning theory, mechanism design, and axiomatic modeling. Contribution/Results: The work establishes the first social choice framework with provable generalization error guarantees, thereby relaxing the classical assumption of complete preference knowledge. It provides a statistically grounded, justification-sensitive foundation for democratic representativeness and bridges social choice theory, machine learning, and AI alignment through a unified theoretical lens.

This study investigates the construction of stochastic social choice rules that simultaneously satisfy consistency and strategyproofness within the conditional expected utility (CEU) framework. Through axiomatic analysis and mechanism design, and by precisely characterizing two preference domains—CEUC and CEUCEP—the paper fully delineates the structure of feasible rules. It shows that on the CEUC domain, only random dictatorship rules are admissible. In contrast, on the CEUCEP domain, when there are three alternatives and at least four agents, non-dictatorial rules become viable: specifically, convex combinations of novel stochastic duopolistic rules and coalition-weighted rules exist, thereby transcending the limitations inherent in traditional random dictatorship.

This study addresses the fair allocation of indivisible goods under binary valuations, aiming to characterize the unique rule that simultaneously satisfies multiple fairness and strategic axioms. Through an axiomatic analysis combining mechanism design and welfare economics, the paper establishes that the Maximum Nash Welfare (MNW) rule—equivalent to both the leximin and strictly concave additive welfare rules—is the only allocation mechanism satisfying envy-freeness up to one good (EF1), strategyproofness, neutrality, minimal completeness, and the independence of inessential demands (IDU) for any number of agents. For the two-agent case, an alternative set of axioms yielding the same characterization is also provided. This work presents the first uniqueness result for fair allocation rules under binary valuations, offering a foundational theoretical framework and design principles for mechanism designers.

This work addresses the synthesis of social norms in strategic multi-agent environments by modeling it as a Bayesian single-parameter multi-unit procurement auction grounded in Alternating-time Temporal Logic (ATL). The authors introduce a representation lemma that compresses valuations satisfying alternating bisimulation into a characteristic set of ATL formulas, and reduce payment determination to allocation determination. This reduction enables, for the first time, the transformation of an FP^NP-complete allocation problem into an integer linear program (ILP). The resulting PO-ASL mechanism is theoretically guaranteed to be incentive-compatible, individually rational, and profit-maximizing in expectation, while remaining efficiently implementable using standard ILP solvers.

This study investigates whether unanimous social choice functions can be implemented via obviously strategy-proof mechanisms within the social choice framework introduced by Bahel and Sprumont. Drawing on mechanism design theory and the notion of obvious strategy-proofness, the paper provides the first complete characterization of the class of unanimous social choice functions that admit such implementation. The central result establishes that a unanimous social choice function is implementable in an obviously strategy-proof manner if and only if it corresponds to a dictatorial rule. This finding not only delineates the precise boundary of feasible mechanisms under stringent incentive compatibility requirements but also underscores the unique role of dictatorship in ensuring robust truth-telling incentives.