Flippable Pairs and Subset Comparisons in Comparative Probability Orderings and Related Simple Games


Autoria(s): Christian, Robin; Slinko, Arkadii; CONDER, Marston
Data(s)

04/02/2008

04/02/2008

01/10/2006

Resumo

We show that every additively representable comparative probability order on n atoms is determined by at least n - 1 binary subset comparisons. We show that there are many orders of this kind, not just the lexicographic order. These results provide answers to two questions of Fishburn et al (2002). We also study the flip relation on the class of all comparative probability orders introduced by Maclagan. We generalise an important theorem of Fishburn, Peke?c and Reeds, by showing that in any minimal set of comparisons that determine a comparative probability order, all comparisons are flippable. By calculating the characteristics of the flip relation for n = 6 we discover that the regions in the corresponding hyperplane arrangement can have no more than 13 faces and that there are 20 regions with 13 faces. All the neighbours of the 20 comparative probability orders which correspond to those regions are representable. Finally we define a class of simple games with complete desirability relation for which its strong desirability relation is acyclic, and show that the flip relation carries all the information about these games. We show that for n = 6 these games are weighted majority games.

Formato

302496 bytes

application/pdf

Identificador

http://hdl.handle.net/1866/2153

Idioma(s)

en

Publicador

Université de Montréal, Département de sciences économiques

Relação

Cahier de recherche #2006-18

Palavras-Chave #Additively representable linear orders #comparative probability #elicitation #subset comparisons #simple game #weighted majority game #desirability relation
Tipo

Article