Properties of ladder tournaments

Ladder tournaments use work trials to screen workers for positions in organizations. Despite being common in many industries, their properties remain poorly understood, especially in organizations characterized by complex complementarities and externalities in their production process. In this study, we formalize the ranking rule generated by a ladder tournament and derive measures of relative performance that can be used to compare workers when their true inputs cannot be observed. We show that this rule is reflexive but not generally transitive, unless the organization has fewer than three layers of hierarchy or is complete. It follows that complete organizations have an embedded merit-based hierarchical structure. We also study the relationship between a worker's tournament rank and his utility or usefulness as measured by the frequency with which he plays a pivotal role. We show that a worker's likelihood of being pivotal is a weakly increasing function of his rank. This finding implies that in complete organizations, ladder tournaments discriminate more effectively between workers than do mechanisms based on pivotability or marginal productivity.