Recursive Borda Aggregation

Leo Goto and Satoshi Nakada

Papers from arXiv.org

Abstract: 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.

Date: 2026-06, Revised 2026-08
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