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Ranking and selection from paired-comparison data (with discussion). (English) Zbl 0767.62021
The frontiers of modern statistical inference procedures, II, Proc. Discuss. 2nd Int. Conf., IPASRAS-II, Sydney/Aust. 1987, Am. Sci. Press Ser. Math. Manage. Sci. 28, 3-24 (1992).

Summary: [For the entire collection see Zbl 0759.00005.]

Subset selection and indifference zone approaches to the selection of the best object in a balanced paired-comparison experiment are reviewed. Weak and strong curtailment are introduced in this context. It is shown that the probability of correctly selecting the best object is the same under strong curtailment as for the completed experiment if the Bradley-Terry preference model holds.

For unbalanced paired-comparison data, with at most one comparison per pair, it is proposed to rank the objects on the basis of the following scoring system expressed in the language of tournaments: The score of a player $A$ is the total number of (a) wins of players defeated by $A$ minus losses of players to whom $A$ lost, plus (b) $A$’s wins minus $A$’s losses. A tied match counts as half a win plus half a loss. More general experiments can be treated similarly.

##### MSC:
 62F07 Statistical ranking and selection procedures