124,754 research outputs found
Maximin Safety: When Failing to Lose is Preferable to Trying to Win
We present a new decision rule, \emph{maximin safety}, that seeks to maintain
a large margin from the worst outcome, in much the same way minimax regret
seeks to minimize distance from the best. We argue that maximin safety is
valuable both descriptively and normatively. Descriptively, maximin safety
explains the well-known \emph{decoy effect}, in which the introduction of a
dominated option changes preferences among the other options. Normatively, we
provide an axiomatization that characterizes preferences induced by maximin
safety, and show that maximin safety shares much of the same behavioral basis
with minimax regret.Comment: 14 page
Bayesian Decision Theory and Stochastic Independence
As stochastic independence is essential to the mathematical development of probability theory, it seems that any foundational work on probability should be able to account for this property. Bayesian decision theory appears to be wanting in this respect. Savage’s postulates on preferences under uncertainty entail a subjective expected utility representation, and this asserts only the existence and uniqueness of a subjective probability measure, regardless of its properties. What is missing is a preference condition corresponding to stochastic independence. To fill this significant gap, the article axiomatizes Bayesian decision theory afresh and proves several representation theorems in this novel framework
Bayesian Decision Theory and Stochastic Independence
Stochastic independence has a complex status in probability theory. It is not part of the definition of a probability measure, but it is nonetheless an essential property for the mathematical development of this theory. Bayesian decision theorists such as Savage can be criticized for being silent about stochastic independence. From their current preference axioms, they can derive no more than the definitional properties of a probability measure. In a new framework of twofold uncertainty, we introduce preference axioms that entail not only these definitional properties, but also the stochastic independence of the two sources of uncertainty. This goes some way towards filling a curious lacuna in Bayesian decision theory
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