On January 30th, Ken Binmore (UCL) is invited in the seminar Managing Severe Uncertainty organised by the London School of Economics (from 2.30 to 4.30 pm, LAK.2.06, 2nd floor of the Lakatos Building, Portugal Street). The title of his presentation will be “Rational Decisions in Large Worlds”.
Abstract: Savage denied that Bayesian decision theory applies in large worlds. A minimal extension of Bayesian decision theory to a large-world context assigns upper and lower probabilities to ambiguous or uncertain events—those to which a single probability cannot be assigned. The orthodox Hurwicz criterion evaluates an ambiguous or uncertain event as a weighted arithmetic mean of its upper and lower probability. The ambiguity or uncertainty aversion reported in experiments on the Ellsberg paradox is then explained by assigning a larger weight to the lower probability of winning than to the upper probability. This paper reviews a possible framework for assessing both the arithmetic Hurwicz criterion and a geometric variant. It then argues that only the case of equal weights satisfies appropriate consistency requirements—a result that accords with our own experiments on the Ellsberg paradox. However, the geometric Hurwicz criterion allows another and more severe interpretation of uncertainty aversion that persists even in the case of equal weights.