Scholarlink

<p>We present an axiomatic study of various solutions to the social ranking problem, where a solution links any ranking of coalitions of players to a binary relation between individual players. We focus on solutions that align with the desirability relation, asserting that player <i>i</i> is more desirable than player <i>j</i> if any coalition including <i>i</i> but not <i>j</i> ranks higher than the corresponding coalition formed by replacing <i>i</i> with <i>j</i>. Unlike previous characterizations, our study highlights the central role of the desirability property as a foundational axiom in the characterization of five solutions from the related literature: <i>Ceteris Paribus</i> majority, lexicographic excellence and its dual, <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="355_2025_1590_Article_IEq1.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="28" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^{(1)}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msup> </math></EquationSource> </InlineEquation> solution and its dual. Our main results reveal additional similarities among these five solutions and emphasize the essential features that should be considered when selecting the most appropriate solution for a given scenario. A practical application involving a bicameral legislature is also presented.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Desirability and social ranking

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年4月2日

查看全文
  • Michele Aleandri,
  • Felix Fritz,
  • Stefano Moretti

摘要

We present an axiomatic study of various solutions to the social ranking problem, where a solution links any ranking of coalitions of players to a binary relation between individual players. We focus on solutions that align with the desirability relation, asserting that player i is more desirable than player j if any coalition including i but not j ranks higher than the corresponding coalition formed by replacing i with j. Unlike previous characterizations, our study highlights the central role of the desirability property as a foundational axiom in the characterization of five solutions from the related literature: Ceteris Paribus majority, lexicographic excellence and its dual, \(L^{(1)}\) L ( 1 ) solution and its dual. Our main results reveal additional similarities among these five solutions and emphasize the essential features that should be considered when selecting the most appropriate solution for a given scenario. A practical application involving a bicameral legislature is also presented.