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arxiv: 2404.17413 · v6 · pith:HRIX4V67new · submitted 2024-04-26 · 💻 cs.GT · econ.TH

Voting with Partial Orders: The Plurality and Anti-Plurality Classes

Ulle Endriss , Federico Fioravanti This is my paper

Pith reviewed 2026-05-24 02:23 UTC · model grok-4.3

classification 💻 cs.GT econ.TH
keywords voting theorypartial ordersplurality ruleanti-pluralityaxiomatic characterizationsocial choicepreference aggregation
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The pith

Plurality and anti-plurality voting rules extend to partial orders through axiomatic characterizations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper takes the standard plurality rule, which selects alternatives appearing most often in first position of linear orders, and the anti-plurality rule, which selects alternatives appearing least often in last position, and defines extensions that apply when preferences are partial orders. It supplies axiomatic characterizations for these extended rules. A reader would care because partial orders capture common cases of incomplete or incomparable preferences, and the characterizations aim to keep the extensions faithful to the original rules' behavior on complete rankings.

Core claim

The plurality and anti-plurality rules for linear orders extend to partial orders in ways that can be characterized axiomatically, preserving key properties of the original rules.

What carries the argument

The plurality class and anti-plurality class of voting rules defined via axioms on partial orders.

Load-bearing premise

Natural extensions of plurality and anti-plurality to partial orders admit clean axiomatic characterizations that remain faithful to the original rules.

What would settle it

An example partial-order profile where every rule satisfying the stated axioms either fails to match plurality or anti-plurality on the linear-order subcase or produces an outcome that violates an intuitive extension of the original counting logic.

read the original abstract

In the theory of voting, the Plurality rule for preferences that come in the form of linear orders selects the alternatives most frequently appearing in the first position of those orders, while the Anti-Plurality rule selects the alternatives least often occurring in the final position. We explore extensions of these rules to preferences that are partial orders, offering axiomatic characterisations for them.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The paper extends the plurality rule (selecting alternatives most often ranked first) and anti-plurality rule (selecting alternatives least often ranked last) from linear orders to partial orders, and supplies axiomatic characterizations of the resulting classes of rules on partial orders.

Significance. If the characterizations are faithful to the linear-order case and internally consistent, the work would provide a useful axiomatic foundation for voting with incomplete preferences, a setting that arises in many applications. The explicit focus on both plurality and anti-plurality classes is a clear contribution to the literature on social choice with partial orders.

major comments (1)
  1. The abstract states that the extensions are 'natural' and the characterizations are 'axiomatic,' yet no definition of the extended rules or statement of the characterizing axioms appears in the supplied abstract. The central claim therefore cannot be assessed for faithfulness to the linear-order case or for the absence of ad-hoc parameters without the body of the paper.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their review. The single major comment concerns the brevity of the abstract. We address it point-by-point below and will revise the abstract accordingly.

read point-by-point responses

  1. Referee: The abstract states that the extensions are 'natural' and the characterizations are 'axiomatic,' yet no definition of the extended rules or statement of the characterizing axioms appears in the supplied abstract. The central claim therefore cannot be assessed for faithfulness to the linear-order case or for the absence of ad-hoc parameters without the body of the paper.

    Authors: We agree that the abstract, as written, is concise and does not contain explicit definitions of the extended plurality and anti-plurality rules on partial orders or the statements of the characterizing axioms. These appear in the body (the extensions are introduced via the natural lifting of the linear-order definitions in Section 3, and the axioms are stated and used in the characterizations of Sections 4 and 5). Abstracts are conventionally limited in length, which is why the details were omitted. To address the concern, we will revise the abstract to include a brief indication of the key axioms (e.g., reinforcement, neutrality, and the relevant consistency properties) and to note that the extensions preserve the linear-order behavior without introducing ad-hoc parameters. This revision will make the central claims more assessable from the abstract alone while remaining within typical length limits. revision: yes

Circularity Check

0 steps flagged

No significant circularity in axiomatic extensions

full rationale

The paper defines extensions of plurality and anti-plurality to partial orders and supplies axiomatic characterizations for those extensions. No equations, definitions, or citations in the provided material reduce the claimed characterizations to self-referential inputs, fitted parameters presented as predictions, or load-bearing self-citations whose content is itself unverified. The derivation proceeds by independent definition of the extended rules followed by standard axiomatic verification, which is self-contained against external benchmarks and does not exhibit any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no explicit free parameters, background axioms, or invented entities; ledger left empty pending full text.

pith-pipeline@v0.9.0 · 5577 in / 918 out tokens · 17175 ms · 2026-05-24T02:23:58.111366+00:00 · methodology

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Reference graph

Works this paper leans on

33 extracted references · 33 canonical work pages

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