Decomposition behavior in aggregated data sets

Abstract

Abstract. One kind of aggregation of nonparametric data sets involves combining two (or more) sets with the same structure, but with no interweaving of values. For instance, one could have prices of the same product at different stores on different days, but before and after a significant sales tax hike. In this paper, looking at the case of three 'candidates', we give a precise computation of how decomposition of the underlying voting data of these sets is related to the decomposition of the original set. Among other things, this proves it is possible to obtain data sets with arbitrarily large Basic components relative to their size. A second result gives congruence and other criteria for possible values of the sizes of the various components, and we exhibit pure Basic data sets (discovered using the computer program Sage) which exemplify those criteria.