The bridge tournament problem and calibration designs for comparing pairs of objects

Abstract

The classical tournament problem caiJs for arranging v individuals into teams of /) players so that a player is teamed the same number of times with each of the other players and also that each player is pitted equally often against each of the other players. The play of the tuurnament results in the determination of difference in performance of the various pairings of the groups. In the special case when p = 2 each team consists of two players and the desigris are called bridge tournament designs. In high precisiun calibration one can measure only the difference between two nominally equal groups S(l that if u objects are to be inte rcompared in groups of fJ objects, then the solutions tu the tour nament proble m provide schedules for the gl'lluping. These designs are useful in weighing a nd any othe r measul'emcnts where the objects tu be measured can be combined intu gl'llups without loss of precision or accuracy ill the comparisons. Tilis paper presents general methuds fill' constructing of bridge lournament designs, i.e., for Lht' case whcn p = 2, fur all /1 ~ 50. Key Wurds: Calibration, calibration designs. combinatorial analysis, difference sets, experiment designs', incomplete block designs, tourname nts, weighing designs.