Arpeggio Paradox See Audition Hearing Theories Of

ARROW'S PARADOX/IMPOSSIBILITY THEOREM. The American economist Kenneth J. Arrow (1921- ) formulated this theorem showing that no social-choice (e.g., a voting system) function can guarantee to aggregate the individual preferences of a social group into a collective preference ranking so as to satisfy the following four "criteria of fairness": an ordering is always produced; universally-shared preferences are reflected; the outcome does not depend on preferences for ir relevant options; and each individual can influence the outcome (i.e., "non-dictator-ship"). Thus, Arrow's impossibility theorem refers to the modeling of any democratic process where one would like a fixed procedure for "aggregating" the preferences of a group of individuals into an overall ordering; and Arrow's result shows that this is not possible, in general, for a group larger than two individuals if the procedure is required to fulfill these four "criteria of fairness." The proof of Arrow's paradox rests on the profile of individual preferences invoking "Condorcet's paradox of intransitive preferences" - named after the French philosopher and mathematician Marie Antoine Condorcet (1743-1794) who enunciated it in 1785 - which deals with the complexity of voting and choices, by which a final choice is made by the rejection of all other alternatives in a series of paired contests; Condorcet noted that majority voting is the best voting rule/system when only two people can vote. Arrow's paradox shows that any social-choice function that satisfies the first three "criteria of fairness" necessarily violates the fourth criterion and, as a consequence, results in a "dictatorial" situation or outcome. See also DECISION-MAKING THEORIES; EXCHANGE AND SOCIAL EXCHANGE THEORY. REFERENCE

Arrow, K. J. (1951). Alternative approaches to the theory of choice in risk-taking situations. Econometrica, 19, 417426.

ARTIFICIAL INTELLIGENCE. See CELLULAR AUTOMATON MODEL.

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Conquering Fear In The 21th Century

The Ultimate Guide To Overcoming Fear And Getting Breakthroughs. Fear is without doubt among the strongest and most influential emotional responses we have, and it may act as both a protective and destructive force depending upon the situation.

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