Bayesians Commit the Gambler's Fallacy

Area of Science:

• Cognitive Science
• Behavioral Economics
• Probability Theory

Background:

• The gambler's fallacy is commonly viewed as a cognitive bias indicating irrationality.
• This fallacy involves expecting random processes to self-correct, such as predicting a different outcome after a streak.

Purpose of the Study:

• To investigate whether the gambler's fallacy can be explained as a rational response.
• To model Bayesian agents with causal uncertainty and limited memory encountering random data.

Main Methods:

• Simulating Bayesian agents with varying degrees of causal uncertainty.
• Observing agent responses to statistically independent random processes.
• Analyzing agent predictions after different sequences of outcomes.

Main Results:

• Bayesian agents with initial causal uncertainty exhibited the gambler's fallacy.
• Agents ruled out 'streaky' hypotheses faster than 'switchy' ones, leading to asymmetric confidence.
• Limited memory exacerbated the fallacy, persisting even with large amounts of data.

Conclusions:

• The gambler's fallacy can arise from rational Bayesian inference under conditions of uncertainty and limited memory.
• Observed empirical trends in gambler's fallacy studies align with these rational, albeit limited, Bayesian responses.
• This suggests that apparent irrationality may stem from adaptive strategies to incomplete information.