The number of preference orderings: a recursive approach

摘要

1. Introduction In modern society, voting is ubiquitous: it determines the outcomes of elections, the rankings of sports teams in many leagues, and the winners of the Oscars. Vast sums of money, not to mention questions of war and peace, turn on the voting systems used in these and other contests. Thus, the formulation of voting systems is a prime example of a mathematical problem that also has substantial real-world implications.