The authors consider situations in which shares of n firms are held by the same n firms as well as by individual investors. The problem is to determine the actual control of the firms by the individual investors. In part 1, the authors develop the mathematical model, and explain the basic notions of clutter and of effective reduction. In part 2 they introduce the idea of a consistent reduction, prove existence of such, and show the relation between consistent and effective reductions. In part 3 the authors introduce multilinear extensions and show how these can be used to calculate the effective and consistent reductions. Several examples are worked out in detail.
