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See detailPrudent ranking rules: Theoretical contributions and applications
Lamboray, Claude UL

Doctoral thesis (2007)

The subject of this PhD thesis is about ordinal ranking rules. An ordinal ranking rule is a procedure which combines several initial rankings into a global ranking. Given the difficulty and ambiguity of ... [more ▼]

The subject of this PhD thesis is about ordinal ranking rules. An ordinal ranking rule is a procedure which combines several initial rankings into a global ranking. Given the difficulty and ambiguity of aggregating ordinal data, it is worthwhile studying ranking rules which, depending on the initial data, do not lead to one, but to several global rankings, hence leaving some indeterminateness about the final result. It appears that the concept of a prudent order, initially introduced by Arrow and Raynaud, is a possible answer from such a perspective. In this approach, pairwise majority margins are computed which count for any two alternatives the number of initial rankings that prefer the first over the second alternative. A prudent order is then defined as a linear order which maximizes the smallest pairwise majority margin. It was our main objective in this thesis to gain a better understanding of the family of prudent ranking rules. According to our definition, a prudent ranking rule is a rule which outputs only prudent orders. To achieve this goal, we pursued different strategies: i) axiomatic characterizations which highlight the distinctive features of a ranking rule, ii) comparison of the properties or results of prudent ranking rules to those of other ranking rules, and iii) empirical simulations allowing for more quantitative conclusions. The thesis is divided into 3 parts. Part I contains an introduction to the ordinal ranking problem. Our main theoretical contributions can be found in Part II. Finally, Part III illustrates the use of prudent ranking rules in two fields of applications. [less ▲]

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