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Group Decision and Negotiation

Erschienen in:

01.09.2015

Pairwise Dichotomous Cohesiveness Measures

verfasst von: J. C. R. Alcantud, R. de Andrés Calle, J. M. Cascón

Erschienen in: Group Decision and Negotiation | Ausgabe 5/2015

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Abstract

In a framework where experts or agents express their opinions in a dichotomous way, we analyze the cohesiveness of their opinions on a fixed set of issues in a population. A parametric family of related measures are introduced and axiomatically characterized. They are ordinally equivalent when the population is fixed, and some further properties are proved. In order to argue that this restricted dichotomous situation is nevertheless versatile, the paper ends with several empirical illustrations based on real forecasts (for the 2012 American presidential election) and elections (with real data from referenda in two countries and from elections in several scientific societies).

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We appeal to the standard model where each person either qualifies or disqualifies each member of the collective. Ju (2013) refers to a more general domain condition that allows neutral opinions.

A partition of a set \(S\) is a collection of pairwise disjoint non-empty subsets of \(S\) whose union is \(S\).

This is the adapted version of the axiom with the same name in Alcalde and Vorsatz (2013) in the analysis of coherence in societies with linear orders.

Section 5.4 below refers to this case in more detail.

Source: http://elections.nytimes.com/2012/results/president/exit-polls.

Source: http://www.realclearpolitics.com/polls/.

Source: http://uselectionatlas.org/PRED/.

Source: http://www.electionprojection.com/2012elections/president12.php.

Source: http://edition.cnn.com/ELECTION/2012/.

Source: http://elections.huffingtonpost.com/pollster.

We do not intend to draw conclusions from these figures. It is known that the adequacy of AV for the choice of committees and of single candidates is different. For sophisticated voters as the members of these societies are, the expression of their opinions can easily be influenced by the type of election.

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Alcantud JCR, Muñoz-Torrecillas MJ (2013) On the measurement of sociopolitical consensus in direct democracies: proposal of indexes. MPRA Paper No 47268

Alcantud JCR, de Andrés Calle R, Cascón JM (2013) On measures of cohesiveness under dichotomous opinions: some characterizations of approval consensus measures. Inf Sci 240:45–55

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Titel: Pairwise Dichotomous Cohesiveness Measures
verfasst von: J. C. R. Alcantud
R. de Andrés Calle
J. M. Cascón
Publikationsdatum: 01.09.2015
Verlag: Springer Netherlands
Erschienen in: Group Decision and Negotiation / Ausgabe 5/2015
Print ISSN: 0926-2644
Elektronische ISSN: 1572-9907
DOI: https://doi.org/10.1007/s10726-014-9415-5

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