arXiv subjects

Satoshi Nakada

Publications and source records attributed to Satoshi Nakada.

10 recordsLinked to original sources

arXiv2026

Scoring Rules as Least-Squares Estimators

Kawada (2018) proved that every scoring rule is equivalent to the corresponding cosine similarity rule. The original proof relies on a direct analysis of the cosine similarity optimization problem. In this note, we present an alternative, simpler proof based on a basic least-squares characterization. Our argument shows that the arithmetic mean of the score vectors is the unique minimizer of the total squared Euclidean distance and that the cosine similarity formulation is an immediate consequence of this optimization property. This result provides a transparent geometric interpretation of scoring rules and clarifies why the cosine similarity rule necessarily coincides with the corresponding scoring rule.

econ.TH↗

arXiv2026

Note on an Axiomatization of the Baldwin Rule

Goto and Nakada (2026) showed that the Baldwin rule can be characterized using Neutrality, Bottom Consistency, Faithfulness, Cancellation and Bottom Independence. While their proof relies on the technique of linear algebra and graph theory, in this note, we provide a simpler proof using purely combinatorial arguments based on permutations and amplified preference profiles, thereby providing a more transparent proof of the characterization.

econ.TH↗

arXiv2026

Peak-Robust Voting Rules

This paper proposes new robustness criteria for social choice correspondences under single-peaked preferences, inspired by the concepts of robustness in statistical estimation, where robust estimators are designed to be resilient to both model misspecification and outliers. Motivated by robustness to model assumptions, we introduce peak-robustness: a voting rule is peak-robust if it never selects an alternative that is a majority loser relative to some unchosen alternative for any preference profile sharing the same peak profile. To capture robustness to outliers, we propose tail-invariance, which requires that variations in the tails of the peak distribution do not affect the collective decision. Our main result shows that the median voting rule is the unique efficient rule satisfying these robustness criteria. When peak-robustness is weakened, we characterize the broader class of quantile rules. Taken together, these results provide a robustness-based axiomatic foundation for median and quantile voting rules, independent of the traditional strategy-proofness approach.

econ.TH↗

arXiv2026

Recursive Borda Aggregation

We study a new class of voting rules, recursive Borda rules, in which the Borda criterion is applied recursively through successive elimination decisions rather than in a single step. Our first result provides an axiomatic foundation for a regular subclass of recursive Borda rules. We show that recursive reformulations of Young's (1974) axioms characterize a regular subclass of recursive Borda rules. Our second result establishes an exact connection between recursive Borda rules and the Condorcet criterion. We characterize precisely when a recursive Borda rule satisfies Condorcet Consistency. As a consequence, every regular recursive Borda rule satisfies Condorcet Consistency, and Condorcet Consistency identifies a sharp upper bound on admissible elimination regions. Within this class, the Baldwin rule, the strict Nanson rule, and the Nanson rule emerge as the three canonical procedures, and we provide unified axiomatic characterizations of all three. Taken together, our results extend Young's axiomatic theory of the Borda rule from one-shot positional aggregation to recursive aggregation and derive Condorcet Consistency rather than postulating it as an independent axiom.

econ.TH↗

arXiv2026

A New Method for Finding the Schulze Winner Set

We propose a new voting algorithm based on the pairwise majority-comparison matrix derived from voters' preference profiles. We show that this algorithm induces exactly the winner set of the Schulze rule (Schulze, 1997). Our algorithm successively eliminates weaker candidates in terms of all-pairs comparisons, thereby reflecting a dual spirit to Condorcet's original idea of splitting preference cycles (de Condorcet, 1785). We further show that the direct sum of the survival sets obtained at each elimination round coincides with the Schwartz set (Schwartz, 1972). These two equivalence results provide a formal mathematical foundation for the ``folklore'' relationship between the Schulze winner set and the Schwartz set, as well as a new Condorcetian interpretation of the Schulze winner set.

econ.TH↗

arXiv2025

Characterizing the ELS Values with Fixed-Population Invariance Axioms

We study efficient, linear, and symmetric (ELS) values, a central family of allocation rules for cooperative games with transferable-utility (TU-games) that includes the Shapley value, the CIS value, and the ENSC value. We first show that every ELS value can be written as the Shapley value of a suitably transformed TU-game. We then introduce three types of invariance axioms for fixed player populations. The first type consists of composition axioms, and the second type is active-player consistency. Each of these two types yields a characterization of a subclass of the ELS values that contains the family of least-square values. Finally, the third type is nullified-game consistency: we define three such axioms, and each axiom yields a characterization of one of the Shapley, CIS, and ENSC values.

econ.TH↗

arXiv2025

Characterizations of Proportional Division Value in TU-Games via Fixed-Population Consistency

We study the proportional division value in TU-games, which distributes the grand coalition worth in proportion to the players' stand-alone worths. Focusing on fixed-population consistency, we characterize the proportional division value through three types of axioms: axioms concerning transformations of the grand coalition worth, composition axioms, and nullified-game consistency. The first type captures how payoffs respond when the grand coalition worth changes. The composition axioms require that the outcome be the same whether a game is solved directly or through a two-step procedure based on a reference allocation and an associated adjustment of the game. Nullified-game consistency requires that, when some players' payoffs are fixed, the solution for the remaining players in the adjusted game coincides with their original payoffs. Together with efficiency and/or fairness-related conditions where appropriate, these axioms characterize the proportional division value.

econ.TH↗

arXiv2025

The Coarse Nash Bargaining Solutions

This paper studies the axiomatic bargaining problem and proposes a new class of bargaining solutions, called coarse Nash solutions. These solutions assign to each problem a set of outcomes coarser than that chosen by the classical Nash solution (Nash, 1950). Our main result shows that these solutions can be characterized by new rationality axioms for choice correspondences, which are modifications of Nash's independence of irrelevant alternatives (or more precisely, Arrow's (1959) choice axiom), when combined with standard axioms.

econ.TH↗

arXiv2025

A Characterization of Egalitarian and Proportional Sharing Principles: An Efficient Extension Operator Approach

Some well-known solutions for cooperative games with transferable utility (TU-games), such as the Banzhaf value, the Myerson value, and the Aumann-Dreze value, fail to satisfy efficiency. Despite their desirable normative properties, this inefficiency motivates the search for a systematic method to restore efficiency while preserving their underlying normative structure. This paper proposes an efficient extension operator as a general approach to restore efficiency by extending any underlying solution to an efficient one. We consider novel axioms for those operators and characterize the egalitarian surplus sharing method and the proportional sharing method in a unified manner. As applications, we demonstrate the generality of our method by developing an efficient-fair extension of solutions for TU games with communication networks, as well as a variant for TU games with coalition structures.

econ.TH↗

arXiv2025

Robust Voting under Uncertainty

This paper proposes normative criteria for voting rules under uncertainty about individual preferences. The criteria emphasize the importance of responsiveness, i.e., the probability that the social outcome coincides with the realized individual preferences. Given a convex set of probability distributions of preferences, denoted by $P$, a voting rule is said to be $P$-robust if, for each probability distribution in $P$, at least one individual's responsiveness exceeds one-half. Our main result establishes that a voting rule is $P$-robust if and only if there exists a nonnegative weight vector such that the weighted average of individual responsiveness is strictly greater than one-half under every extreme point of $P$. In particular, if the set $P$ includes all degenerate distributions, a $P$-robust rule is a weighted majority rule without ties.

econ.TH↗