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A geometric examination of Kemeny's rule

Donald G. Saari, Vincent R. Merlin
2000 Social Choice and Welfare  
By using geometry, a fairly complete analysis of Kemeny's rule (KR) is obtained.  ...  Le Breton for his conversations about Kemeny's rule. ordering.) An attractive aspect of Kemeny's Rule (KR) is Kemeny's claim that his societal ranking is the"closest" to the wishes of the voters.  ...  Kemeny distance and KR Kemeny's choice of a distance makes precise the sense that, say, a 1 1 a 2 1 a 3 is closer to a 2 1 a 1 1 a 3 than to a 2 1 a 3 1 a 1 .  ... 
doi:10.1007/s003550050171 fatcat:rqc2arwk6jgcpah6mctviimbqu

Page 5189 of Mathematical Reviews Vol. , Issue 2001G [page]

2001 Mathematical Reviews  
Ivar Petersen (ES-AOS-A; Tallinn) 20012:91046 91B12 Saari, Donald G. (1-NW; Evanston, IL); Merlin, Vincent R. (F-CAEN-CR; Caen) A geometric examination of Kemeny’s rule. (English summary) Soc.  ...  Using a geometric method developed by D. Saari, the authors an- alyze Kemeny’s rule. The results reveal some interesting properties of the rule.  ... 

Robust Multidimensional Welfare Comparisons: One Vector of Weights, One Vote

Stergios Athanassoglou
2013 Social Science Research Network  
With this voting construct in mind, a rule for aggregating the preferences of many plausible choices of weights, suitably weighted by the importance attached to them, is proposed.  ...  An axiomatic characterization of the rule is provided, and its computational implementation is developed.  ...  Kemeny's Rule In an important paper, Kemeny [20] introduced a rule which I will refer to as Kemeny's rule. 5 Given a set of individual rankings, Kemeny's rule produces a ranking (referred to as "Kemeny-optimal  ... 
doi:10.2139/ssrn.2264748 fatcat:3quqouwv2rhfnevtmuva33o5ku

A probabilistic evaluation framework for preference aggregation reflecting group homogeneity

C. Jansen, G. Schollmeyer, T. Augustin
2018 Mathematical Social Sciences  
Finally, we investigate our framework by comparing aggregation rules in a simulation study.  ...  Groups differ in the homogeneity of their members' preferences.  ...  Kemeny's rule: 15 Given a profile R := (R 1 , . . . , R n ) ∈ R n , the idea of Kemeny's rule is to choose that consensus order Q ∈ R that minimizes the sum of the distances d(R i , Q) to the individual  ... 
doi:10.1016/j.mathsocsci.2018.09.001 fatcat:iwwtgfuqonfztcyesggmhtrwme

Assent-maximizing social choice

Katherine A. Baldiga, Jerry R. Green
2011 Social Choice and Welfare  
Our methods generalize the well-known Kemeny Rule. In the Kemeny Rule it is known a priori that the subset of feasible alternatives will be a pair.  ...  We define a family of social choice rules that depend on the population's preferences and on the probability distribution over the sets of feasible alternatives that the society will face.  ...  Their group theoretic structure is an alternative to examining the geometric structure of the equivalence classes for scoring rules as studied by Saari (1994).  ... 
doi:10.1007/s00355-011-0614-6 fatcat:yiwz7yyqbbdxfd5tmxofftdwuy

Random walks on weighted networks: Exploring local and non-local navigation strategies [article]

A.P. Riascos, José L. Mateos
2019 arXiv   pre-print
We present a general approach to analyzing these strategies by defining the dynamics as a discrete time Markovian process with probabilities of transition expressed in terms of a symmetric matrix of weights  ...  Our results allow to study and compare on the same basis the global dynamics of different types of random walk strategies.  ...  from its simple rules.  ... 
arXiv:1901.05609v1 fatcat:e55uny3ysra6zh7angojba6go4

Explaining All Three-Alternative Voting Outcomes

Donald G. Saari
1999 Journal of Economic Theory  
., runoffs, Kemeny's rule, and Copeland's method). It is shown how to identify, interpret, and construct all profiles supporting each paradox.  ...  Among new conclusions, it is shown why a standard for the field, the Condorcet winner, is seriously flawed.  ...  This charge applies to agendas, the Copeland Method, Kemeny's rule, and many others.  ... 
doi:10.1006/jeth.1999.2541 fatcat:ophbd7tymvefjdkyp7si5o5ohi

Lewis Carroll, Voting, and the Taxicab Metric

Thomas C. Ratliff
2010 The College Mathematics Journal  
For a wonderful account of the way in which these events shaped Dogson's work in elections, see Duncan Black's discussion in Theory of Committees and Elections [2] .  ...  By his third pamphlet, A Method of Taking Votes on More Than Two Issues [3], Dodgson displays an amazing insight into many of the fundamental issues that have shaped modern social choice theory.  ...  rule [7] .  ... 
doi:10.4169/074683410x510308 fatcat:2nydrj2xnzf3jeu6fbhm5bnvie

Automated Rating of Financial and Economic Condition of Companies

Aleksandr Mikhaylovich Batkovskiy, Elena Georgievna Semenova, Valerij Yaroslavovich Trofimets, Elena Nikolaevna Trofimets, Alena Vladimirovna Fomina
2015 Mediterranean Journal of Social Sciences  
relevant set of criteria into a single integral criterion.  ...  The suggested solution may be used as a prototype of a commercial automated system, which allows the customer to specify requirements in respect of the created system, and which allows the developer to  ...  The hierarchical analysis method suggested by Saaty is a closed logical construction, which allows to analyze diverse serious problems with simple rules (Saaty, 1989) .  ... 
doi:10.5901/mjss.2015.v6n5s4p297 fatcat:k2te2f5esjdx5jsymmyyhzyjza

Page 2628 of Mathematical Reviews Vol. , Issue Subject Index [page]

Mathematical Reviews  
(English summary) 2001¢:91063 — Mathematical structure of voting paradoxes. II. Positional voting. (English summary) 2001e:91064 — (with Merlin, Vincent R.) A geometric examination of Kemeny’s rule.  ...  A comparison of Dodgson's method and Kemeny’s rule. (English summary) 2001m:91050 Regenwetter, Michel see Doignon, Jean-Paul et al., (2001d:91001) Saari, Donald G.  ... 

Living with a New Mathematical Species [chapter]

Lynn Arthur Steen
1988 A Computer Science Reader  
our roots is a natural consequence of increasing mathematical maturity.  ...  The history of mathematics can be viewed as a counterpoint between the finite and the infinite, between the discrete and the continuous.  ...  What is not yet so common is to examine critically the effect of applying to mathematics pedagogy computer systems that are only capable of following rules or matching templates.  ... 
doi:10.1007/978-1-4419-8726-6_9 fatcat:lkkkrqwzbnbu5fno3byzuqz2gq

Living with a new mathematical species

Lynn Arthur Steen
1986 The Mathematical intelligencer  
our roots is a natural consequence of increasing mathematical maturity.  ...  The history of mathematics can be viewed as a counterpoint between the finite and the infinite, between the discrete and the continuous.  ...  What is not yet so common is to examine critically the effect of applying to mathematics pedagogy computer systems that are only capable of following rules or matching templates.  ... 
doi:10.1007/bf03026833 fatcat:df5oecnxkzeutkatppttrwagqq

Voting with rubber bands, weights, and strings

Davide P. Cervone, Ronghua Dai, Daniel Gnoutcheff, Grant Lanterman, Andrew Mackenzie, Ari Morse, Nikhil Srivastava, William S. Zwicker
2012 Mathematical Social Sciences  
Rubber band voting machines We'll consider voting rules for which A is a finite set of alternatives, and a ballot consists of a strict ranking (linear ordering) of A's members.  ...  We introduce some new voting rules based on a spatial version of the median in R k known as the mediancentre, or Fermat-Weber point.  ...  Then it selects the ranking σ identified with the permutahedron vertex b closest to M . 5 Kemeny's rule and approval voting Moreover, the interpretation applies to quite a broad class of voting rules  ... 
doi:10.1016/j.mathsocsci.2011.08.003 fatcat:d4xegosvvzbzdez6d77l6x4agm

Democracy and Social Choice: A Response to Saari

Mathias Risse
2003 Social Science Research Network  
of Kemeny's Rule," Social Choice and Welfare 17 (2000) : 403-438.  ...  Again, such insights are friendly amendments, not objections. 16 16 Saari has presented the argument discussed here in several publications, in particular in Saari and Vincent Merlin, "A Geometric Examination  ... 
doi:10.2139/ssrn.413161 fatcat:e4c5bxwbujeiroooks7syei2cu

Information Operations Recognition: from Nonlinear Analysis to Decision-making [article]

Aleksandr G. Dodonov, Dmitry V. Lande, Vitaliy V. Tsyganok, Oleh V. Andriichuk, Sergii V. Kadenko, Anastasia N. Graivoronskaya
2019 arXiv   pre-print
The book is addressed to a broad circle of specialists from information technology and security domains.  ...  The book provides a detailed description of mathematical principles of information operations recognition, based on mathematical statistics, nonlinear dynamics, complex networks theory, information and  ...  Condorcet rule, Markov chains, and Kemeny's method allow us to avoid such explicit transitions from ranks to ratios. Existing methods: a brief overview Condorcet rule.  ... 
arXiv:1901.10876v2 fatcat:la2d5dgya5ft7nuispo7es3adq
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