On the minimum violations ranking of a tournament

Article Abstract:

The process of rank ordering a set of players or objects is studied in terms of a set of pairwise comparisons generated from a tournament. The criterion is based on having as few cases as possible in which one player is ranked above another when the second was actually defeated by the first in the tournament. This is called a violation, with the goal being to find the minimum violations ranking (MVR). The idea of a distance on the set of tournaments is described to set the MVR problem in the proper perspective, and a set of natural axioms is given that all distance measures should follow. The MVR problem is shown to be equivalent to the minimum distance problem. This, in turn, can be shown in many forms, particularly as a problem of finding the minimum feedback edge set in a graph and as a mixed integer generalized network problem.

Analysis, Mathematical models, Tournaments, Sports tournaments, Order picking systems, Order picking

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Ordinal ranking with intensity of preference

Article Abstract:

Ordinal ranking models request respondents to assign a set of preferences to a group of objects or activities, without indicating the intensity of the rankings assigned. Such ordinal ranking procedures generally occur in group or committee work, and examples are investigated which involve the ranking of candidates for elective office openings. The innovative ordinal model developed allows respondents to specify the intensity of their preferences, as well as the ranking of all preferences. Consensus assessments using this model are also explained.

Decision-making, Group, Group decision making

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A data development model for aggregating preference rankings

Article Abstract:

A model for aggregating votes from a ballot in a preferential election is presented. The model uses a composite index to provide all candidates with a fair evaluation of their overall standing. The composite index model eliminates two problems: solving a problem for each decision-making unit, and having several units tied for first place. Only one problem needs to be solved to identify the winner of the election.

Management science, Usage, Evaluation, Data envelopment analysis, Set theory

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