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A necessary 4-cycle condition for dice representability of reciprocal relations

Content Provider	Springer Nature Link
Author	De Meyer, H. De Baets, B. De Loof, K.
Copyright Year	2012
Abstract	The comparison of independent random variables can be modeled by a set of dice and a reciprocal relation expressing the winning probability of one dice over another. It is well known that dice transitivity is a necessary 3-cycle condition for a reciprocal relation to be dice representable, i.e. to be the winning probability relation of a set of dice. Although this 3-cycle condition is sufficient for a rational-valued reciprocal relation on a set of three elements to be dice representable, it has been shown that this is no longer the case for sets consisting of four or more elements. In this contribution, we provide a necessary 4-cycle condition for dice representability of reciprocal relations. Moreover, we show that our condition is sufficient in the sense that a given rational-weighted 4-cycle and reciprocally weighted inverse cycle, both fulfilling the 4-cycle condition, can be extended to a winning probability graph representing a dice-representable reciprocal relation on four elements.
Ending Page	170
Page Count	20
Starting Page	151
File Format	PDF
ISSN	16194500
e-ISSN	16142411
Journal	4OR
Issue Number	2
Volume Number	11
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2012-10-05
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Dice transitivity Applications Industrial and Production Engineering Winning probability relation Graph theory (including graph drawing) Optimization Reciprocal relation Operations Research/Decision Theory Directed graphs (digraphs), tournaments Independent random variables Paths and cycles Game-theoretic models Dice representability
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Management Science and Operations Research Management Information Systems Computational Theory and Mathematics

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