Academic journal article Memory & Cognition

# The Effects of Payout and Probability Magnitude on the Allais Paradox

Academic journal article Memory & Cognition

# The Effects of Payout and Probability Magnitude on the Allais Paradox

## Article excerpt

The Allais paradox decision bias was first offered as a challenge to the expected utility theory over 60 years ago. Although the Allais paradox is a standard challenge for normative theories of risky choice, its causes are not well understood. The present experiment uses two manipulations of the Allais paradox to investigate the commonly proposed probability-weighting explanation of the paradox. Reducing the magnitude of the outcomes did not affect the size of the Allais paradox, contradicting previous literature and supporting the probability weighting hypothesis. Reducing the probability of the nonzero outcomes to eliminate certainty reduced, but did not eliminate, the Allais paradox, a result inconsistent with probability weighting and other theories of the Allais paradox. The results suggest that the certainty effect alone cannot explain the Allais paradox.

The goal of most decisions is to find the option that leads to the best possible outcome, but the outcomes of decisions are often not known in advance. One proposed axiom of rational choice under conditions of uncertainty is the independence axiom, which states that any outcome common to two sets of options should not influence the choice between the two options (Savage, 1954).

Although highly intuitive, the independence axiom is the subject of a famous challenge proposed by Allais in 1953. When presented with the pairs of gambles shown in Table 1, decision makers tend to choose the safe common consequence (CC)-high gamble and the risky CC-low gamble: They prefer a 100% chance of \$1 million to the 3-outcome risky gamble, but prefer the 10% chance of \$5 million to the 11% chance of \$1 million (Allais, 1953).

To see why these preferences violate the independence axiom, suppose these gambles are to be resolved by drawing a ball from an urn with 100 balls numbered 1 to 100, as shown in Table 2. When making a choice between the first pair of gambles, the only question should be your preferences when drawing Balls 1-11. Because winning \$1 million on a draw of Ball 12-100 is common to both options-a common consequence-haw you feel about it is irrelevant to the decision. Moreover, changing the common consequence from \$1 million to \$0 (as in the second pair of gambles) should not change the decision, since the outcome of drawing Balls 1-11 has not changed (Savage, 1954).

This violation of the independence axiom is commonly known as the Allais paradox, a robust and widely demonstrated phenomenon (e.g., Birnbaum, 2004; Camerer, 1989; Conlisk, 1989; Kahneman & Tversky, 1979; Slovic & Tversky, 1974; Wu & Gonzalez, 1996).