Simple Applications

Abstract

Four simple applications of the formulas derived in the book are considered. The first application illustrates Theorem 4.14 from Section 4.8 about the convergence of the Borda and Condorcet counts as the size of the electorate increases. This application is aimed at planning a public opinion poll for ranking several options (like the candidates for election) with no cyclic majorities. Three other applications are based on formulas from Theorems 6.4 and 6.6 from Sections 6.4 and 6.5. One application deals with planing a public opinion poll with expected and guaranteed levels of representativeness. The other application describes how to plan a TV round table with invitees ‘from the street’, where the public opinion on each of several issues will be represented by at least one invitee. The last application discusses man’s ability to make complex decisions by focusing on seven to ten criteria instead of considering all available information. This is explained by the analogy between selections of criteria and representative bodies that make adequate decisions on behalf of the whole society. In particular, it is concluded that complex problems can often be analyzed with small models, and additional extensions bring much less gain than usually hoped for.

Knowing is not enough, we must apply. Willing is not enough, we must do.

Johann Wolfgang von Goethe (1749–1832)