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Aggregating Incomplete Rankings

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Yasunori Okumura

Theoretical Economics · Submitted 26 Feb 2024

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Thus, we identify the necessary and sufficient conditions on evaluability profiles to ensure the existence of the functions satisfying four different combinations of properties.

how it is stated · asserted 1.00 read the record →

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arXiv ID2402.16309 (version 4)
Pith IDLI3RXUQ2, Pith's permanent record of this paper and its review
CitationYasunori Okumura. "Aggregating Incomplete Rankings." arXiv:2402.16309 (2024). https://pith.science/paper/LI3RXUQ2
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,485 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.51 · human participants 0.19 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.21 · compares with prior results 0.23 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; .

This study considers the method to derive a ranking of alternatives by aggregating the rankings submitted by several individuals who may not evaluate all of them. The collection of subsets of alternatives that individuals (can) evaluate is referred to as an evaluability profile. For a given evaluability profile, we define an aggregating ranking function whose inputs are the rankings of individuals on the alternatives they evaluate. We investigate the properties of aggregating ranking functions, which are modifications of those introduced in previous studies. Whether an aggregating ranking function satisfying a combination of properties exists depends on the evaluability profile. Thus, we identify the necessary and sufficient conditions on evaluability profiles to ensure the existence of the functions satisfying four different combinations of properties. Furthermore, to examine how frequently possible or impossible evaluability profiles occur, we derive the proportion of each type in specific cases.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 This study considers the method to derive a ranking of alternatives by aggregating the rankings submitted by several individuals who may not evaluate all of them. contribution 0.78 0.51 0.04 asserted 0.80
s1 The collection of subsets of alternatives that individuals (can) evaluate is referred to as an evaluability profile. background 0.56 0.17 0.02 asserted 0.99
s2 For a given evaluability profile, we define an aggregating ranking function whose inputs are the rankings of individuals on the alternatives they evaluate. method 0.69 0.88 0.04 asserted 0.99
s3 We investigate the properties of aggregating ranking functions, which are modifications of those introduced in previous studies. contribution 0.73 0.57 0.04 asserted 0.94
s4 Whether an aggregating ranking function satisfying a combination of properties exists depends on the evaluability profile. result 0.93 0.65 0.20 asserted 0.99
s5 Thus, we identify the necessary and sufficient conditions on evaluability profiles to ensure the existence of the functions satisfying four different combinations of properties. result 0.65 0.95 0.71 asserted 1.00
s6 Furthermore, to examine how frequently possible or impossible evaluability profiles occur, we derive the proportion of each type in specific cases. result 0.54 0.95 0.08 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 1.00.

What was examined, and what was not

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  • arXiv listing abstract v4
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

This study considers the method to derive a ranking of alternatives by aggregating the rankings submitted by several individuals who may not evaluate all of them. The collection of subsets of alternatives that individuals (can) evaluate is referred to as an evaluability profile. For a given evaluability profile, we define an aggregating ranking function whose inputs are the rankings of individuals on the alternatives they evaluate. We investigate the properties of aggregating ranking functions, which are modifications of those introduced in previous studies. Whether an aggregating ranking function satisfying a combination of properties exists depends on the evaluability profile. Thus, we identify the necessary and sufficient conditions on evaluability profiles to ensure the existence of the functions satisfying four different combinations of properties. Furthermore, to examine how frequently possible or impossible evaluability profiles occur, we derive the proportion of each type in specific cases.

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