Independence Axiom

Assume X, Y, and Z are lotteries. Denote "X is preferred to Y" as X≻Y, and indifference between them by X∼Y. One version of the probability axioms are then given by the following, the last of which is the independence axiom:

1. Completeness:  forall X,Y either X≻Y,Y≻X or X∼Y.

2. Transitivity: X≻Y,Y≻Z==>X≻Z.

3. Continuity:  forall X≻Y≻Z, exists a unique p such that pX+(1-p)Z∼Y.

4. Independence: if X≻Y, then pX+(1-p)Z≻pY+(1-p)Z for all Z and p in (0,1).

See also

Allais Paradox, Probability Axioms, Saint Petersburg Paradox

This entry contributed by Ed Pegg, Jr. (author's link)

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Kulish, M. "The Independence Axiom: A Survey." May 2002.

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Independence Axiom

Cite this as:

Pegg, Ed Jr. "Independence Axiom." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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