Technical Note—A Note on the One Against Many Battle

This paper treats a sequencing problem that appears in the one-against-many engagement, considered originally by Friedman. We define an extremal order to be an order that satisfies Friedman's necessary condition. The number of extremal orders could be greater than one. If this occurs, then it may happen that Friedman's procedure gives a nonoptimal order as we illustrate by a numerical example. We derive a necessary condition that applies to unique extremal orders and a sufficient condition for an order to be optimal.