So You Think You're a Bayesian? The Natural Mode of Probabilistic Reasoning
Related to: The Conjunction Fallacy, Conjunction Controversy The heuristics and biases research program in psychology has discovered many different ways that humans fail to reason correctly under uncertainty. In experiment after experiment, they show that we use heuristics to approximate probabilities rather than making the appropriate calculation, and that these heuristics are systematically biased. However, a tweak in the experiment protocols seems to remove the biases altogether and shed doubt on whether we are actually using heuristics. Instead, it appears that the errors are simply an artifact of how our brains internally store information about uncertainty. Theoretical considerations support this view. EDIT: The view presented here is controversial in the heuristics and biases literature; see Unnamed's comment on this post below. EDIT 2: The author no longer holds the views presented in this post. See this comment. A common example of the failure of humans to reason correctly under uncertainty is the conjunction fallacy. Consider the following question: > Linda is 31 years old, single, outspoken and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in antinuclear demonstrations. > > What is the probability that Linda is: > > (a) a bank teller > > (b) a bank teller and active in the feminist movement In a replication by Gigerenzer, 91% of subjects rank (b) as more probable than (a), saying that it is more likely that Linda is active in the feminist movement AND a bank teller than that Linda is simply a bank teller (1993). The conjunction rule of probability states that the probability of two things being true is less than or equal to the probability of one of those things being true. Formally, P(A & B) ≤ P(A). So this experiment shows that people violate the conjunction rule, and thus fail to reason correctly under uncertainty. The representative heuri
Since utility functions are only unique up to affine transformation, I don't know what to make of this comment. Do you have some sort of canonical representation in mind or something?