Publication Date:
2012-10-08
Description:
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. Content Type Journal Article Category Research Paper Pages 1-20 DOI 10.1007/s10288-012-0214-z Authors K. De Loof, Department of Mathematical Modelling, Statistics and Bioinformatics, Ghent University, Coupure links 653, 9000 Gent, Belgium B. De Baets, Department of Mathematical Modelling, Statistics and Bioinformatics, Ghent University, Coupure links 653, 9000 Gent, Belgium H. De Meyer, Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 S9, 9000 Gent, Belgium Journal 4OR: A Quarterly Journal of Operations Research Online ISSN 1614-2411 Print ISSN 1619-4500
Print ISSN:
1619-4500
Electronic ISSN:
1614-2411
Topics:
Mathematics
Permalink
