Abstract

In the application of economic theory to actual analysis, we are often bewildered how to use theory because the framework normally supposes the existence of all cases, which is not actually realised. Here, I introduce an easy way to significantly reduce cases to examine while maintaining the theoretical conclusion. When all cases are deployed, there are three approaches to examine the relationship among chosen elements: vertical, horizontal and random, for which set expansion and contraction properties, k-set feasibility or basic binariness, and revealed preference are generally used, respectively. We concentrate on first two approaches and significantly weaken the approaches to cascaded choice structure and specific k-set feasibility, respectively. Finally, we show how our approach reduces the number of cases to examine in the framework of collective choice theory. The reader will see how effective and easy to handle this approach is in the application of theory.

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