Closed adaptive sequential paired-comparison selection procedures

Abstract

Closed adaptive sequential procedures were introduced by Bechhofer and Kulkarni (1982) as a new method for selecting the best of t ( 2) Bernoulli populations. We modify this approach to obtain two procedures for selecting the best of t objects in a curtailed Round Robin-type paired-comparison experiment. Objects are paired sequentially and the experiment is stopped as soon as one object has achieved a number of preferences that no other object can equal (weak curtailment) or surpass (strong curtailment) if the tournament were run to completion. Ties for first place are broken at random, Weak curtailment clearly selects the same object as the complete Round Robin, with generally substantially fewer comparisons. Strong curtailment effects a further appreciable reduction in the average number of comparisons needed. It is shown that the probabilities of selecting a particular object are the same for weak and strong curtailment if the Bradley-Terry model holds, but generally not otherwise. Some comparisons are...