Discriminant Functions and Majority Voting

This paper is based on the notion of discriminatory power of a pattern classifier acting over a feature space. Discriminant functions are normally used to trace out regions of the feature space corresponding to specific pattern classes. Indeterminate cases occur whenever a pattern lies on a class boundary. The number of occurrences of such indeterminacies measures the relative discriminatory power of a family of discriminant functions. In this paper these concepts are applied to majority voting decisions. It is first shown how regular majority voting leads to discriminant functions with insufficient discriminatory power whenever intransitive social ordering occurs. An (improved) family of discriminant functions is proposed to resolve such cases.