scholarly journals Axioms for defeat in democratic elections

2021 ◽  
Vol 33 (4) ◽  
pp. 475-524
Author(s):  
Wesley H. Holliday ◽  
Eric Pacuit
Keyword(s):  
Recent Work ◽  
Impossibility Theorem ◽  
Arrow’S Impossibility Theorem ◽  
Impossibility Results ◽  
Independence Of Irrelevant Alternatives ◽  
Arrow's Impossibility Theorem ◽  
Voting Procedures ◽  
Democratic Election ◽  
Definition Of ◽  
Democratic Elections

We propose six axioms concerning when one candidate should defeat another in a democratic election involving two or more candidates. Five of the axioms are widely satisfied by known voting procedures. The sixth axiom is a weakening of Kenneth Arrow’s famous condition of the Independence of Irrelevant Alternatives (IIA). We call this weakening Coherent IIA. We prove that the five axioms plus Coherent IIA single out a method of determining defeats studied in our recent work: Split Cycle. In particular, Split Cycle provides the most resolute definition of defeat among any satisfying the six axioms for democratic defeat. In addition, we analyze how Split Cycle escapes Arrow’s impossibility theorem and related impossibility results.

scholarly journals Schrödinger’s Ballot: Quantum Information and the Violation of Arrow’s Impossibility Theorem

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 1083
Author(s):  
Xin Sun ◽  
Feifei He ◽  
Mirek Sopek ◽  
Meiyun Guo
Keyword(s):  
Quantum Information ◽  
Impossibility Theorem ◽  
Arrow’S Impossibility Theorem ◽  
Detailed Proof ◽  
Quantum Analogue ◽  
Independence Of Irrelevant Alternatives ◽  
Arrow's Impossibility Theorem ◽  
Definition Of

We study Arrow’s Impossibility Theorem in the quantum setting. Our work is based on the work of Bao and Halpern, in which it is proved that the quantum analogue of Arrow’s Impossibility Theorem is not valid. However, we feel unsatisfied about the proof presented in Bao and Halpern’s work. Moreover, the definition of Quantum Independence of Irrelevant Alternatives (QIIA) in Bao and Halpern’s work seems not appropriate to us. We give a better definition of QIIA, which properly captures the idea of the independence of irrelevant alternatives, and a detailed proof of the violation of Arrow’s Impossibility Theorem in the quantum setting with the modified definition.

Define success for yourself, given Arrow’s Impossibility Theorem

2020 ◽  
pp. 27-33
Author(s):  
Susan D'Agostino
Keyword(s):  
Borda Count ◽  
Impossibility Theorem ◽  
Mathematics Students ◽  
Arrow’S Impossibility Theorem ◽  
Run Off ◽  
Arrow's Impossibility Theorem ◽  
Voting System ◽  
Definition Of Success ◽  
The Many ◽  
Definition Of

“Define success for yourself, given Arrow’s Impossibility Theorem” explains different voting methods, including plurality voting, run-off voting, sequential run-off, Borda count, and dictatorship, and explains how Kenneth Arrow’s Impossibility Theorem proves that, in an election with three or more candidates, the only fair voting system is a dictatorship. That is, every voting method other than a dictatorship has a known problem with fairness. Mathematics students and enthusiasts are encouraged to consider the many “candidates” for defining “success” in mathematical and life pursuits before letting their vote be the only vote in electing a personal definition of success. This way, Arrow’s Impossibility Theorem assures a fair outcome. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.

ARROW-TYPE RESULTS UNDER INTUITIONISTIC FUZZY PREFERENCES

2013 ◽  
Vol 09 (01) ◽  
pp. 97-123 ◽  
Author(s):  
GILBERT NJANPONG NANA ◽  
LOUIS AIME FONO
Keyword(s):  
Positive Result ◽  
Social Preferences ◽  
Impossibility Theorem ◽  
Arrow’S Impossibility Theorem ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Preferences ◽  
Arrow's Impossibility Theorem ◽  
Fuzzy Preference

Fono et al.11 characterized, for an intuitionistic fuzzy t-norm [Formula: see text], two properties of a given regular intuitionistic fuzzy strict component of a (T,S)-transitive intuitionistic fuzzy preference. In this paper, we examine these characterizations in the particular case where [Formula: see text]. We then use these (general and particular) results to obtain some intuitionistic fuzzy versions of Arrow's impossibility theorem. Therefore, by weakening a requirement to social preferences, we deduce a positive result, that is, we display an example of a non-dictatorial Intuitionistic Fuzzy Agregation Rule (IFAR) and, we establish an intuitionistic fuzzy version of Gibbard's oligarchy theorem.

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