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Abstract

Bookstein's deduction that any distribution function reducing to G(x + y) = G(y) or H(x x y) = H(x) x H(y) will be resilient to aggregation ambiguity is applied to performance odds. The Rasch model application to three measurable compositions result. TEAMs work as unions of perfect agreement doing best with easy problems. PACKs work as collections of perfect DISagreements doing best with intermediate and hard problems. CHAINs work as connections of IMperfect agreements doing better than TEAMs with hard problems. Four problem/solution necessities for inference are reviewed: uncertainty met by probability, distortion met by additivity, confusion met by separability and ambiguity met by divisibility. Connotations, properties and applications of TEAM, PACK and CHAIN groups are ventured.

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