Condorcet’s theory of voting

Condcrcet ' s criterion states that an alternative that defeats every other by a simple majority is the socially optimal choice. Condorcet argued that if the object of voting is to determine the "best " decision for society but voters sometimes make mistakes in their judgments, then the majority alternative (if it exists) is statistical-ly most likely to be the best choice. Strictly speaking, this claim is not true; in some situations Borda's rule gives a sharper estimate of the best alternative. Nevertheless, Condorcet did propose a novel and statistically correct rule for finding the most likely ranking of the alternatives. This procedure, which is sometimes known as "Kemeny's rule, " is the unique social welfare function that satisfies a variant of independence of irrelevant alternatives together with several other standard properties. [Our aim is] to inquire by mere reasoning, what own prevails, this proves only that I have degree of confidence the judgment of assemblies made a mistake, and that what I believed deserves, whether large or small, subject to a high or low plurality, split into several different to be the general will was not so " (1962, bodies or gathered into one only, composed of 153)