Axiomatic theories of choice introduce preference as a primitive relation, which is interpreted through specific empirical procedures such as choice or pricing. Models of rational choice assume a principle of procedure invariance, which requires strategically equivalent methods of elicitation to yield the same preference order. Thus, if the decision maker prefers A to B, then the cash equivalent, or minimum selling price, of A should exceed that of B. However, there is a substantial body of evidence showing that the price ordering of risky prospects is systematically different from the choice ordering, contrary to standard theories of choice.

The effect of elicitation method on preference between gambles was first observed by Slovic and Lichtenstein (1968) who found that both buying and selling prices of gambles were primarily determined by the payoffs, whereas choices between gambles (and ratings of their attractiveness) were primarily influenced by the probabilities of winning and losing. Slovic and Lichtenstein reasoned that, if the method used to elicit preferences affected the weighting of the gambles' components, it should be possible to construct pairs of gambles such that the same individual would choose one member of the pair but set a higher price for the other. Lichtenstein and Slovic (1971, 1973) demonstrated such reversals in a series of studies, one of which was conducted on the floor of the Four Queens Casino in Las Vegas with experienced gamblers playing for real money.

The preference-reversal phenomenon involves a pair of gambles of comparable expected value.