How to Mix the Membership of Groups: A Solution to Free Riding, Leadership Training, and Early Dominance

Abstract

The rationale for mixing the membership of groups is presented and the result of mixing is defined for three levels of quality: minimal, complete, and perfect. Two systematic mixing methods, transposition and laddered rotation, are explored. Four findings on the number of complete- and perfect-quality mixes that are possible under specified conditions are explained. Steps for manually implementing transposition and laddered rotation are given, and equations for implementing them computationally are supplied. A table is presented showing the number of complete- and perfect-quality mixes that can be obtained with number of groups ranging from 2 to 7 and group sizes of the same range.