Axiomatizations of quasi-polynomial functions on bounded chains

Two emergent properties in aggregation theory are investigated, namely horizontal maxitivity and comonotonic maxitivity (as well as their dual counterparts) which are commonly defined by means of certain functional equations. We completely describe the function classes axiomatized by each of these properties, up to weak versions of monotonicity in the cases of horizontal maxitivity and minitivity. While studying the classes axiomatized by combinations of these properties, we introduce the concept of quasi-polynomial function which appears as a natural extension of the well-established notion of polynomial function. We give further axiomatizations for this class both in terms of functional equations and natural relaxations of homogeneity and median decomposability. As noteworthy particular cases, we investigate those subclasses of quasi-term functions and quasi-weighted maximum and minimum functions, and provide characterizations accordingly

Probabilistic sophistication and multiple priors.

We show that under fairly mild conditions, a maximin expected utility preference relation is probabilistically sophisticated if and only if it is subjective expected utility.

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

Uniform Labeled Transition Systems for Nondeterministic, Probabilistic, and Stochastic Process Calculi

Labeled transition systems are typically used to represent the behavior of nondeterministic processes, with labeled transitions defining a one-step state to-state reachability relation. This model has been recently made more general by modifying the transition relation in such a way that it associates with any source state and transition label a reachability distribution, i.e., a function mapping each possible target state to a value of some domain that expresses the degree of one-step reachability of that target state. In this extended abstract, we show how the resulting model, called ULTraS from Uniform Labeled Transition System, can be naturally used to give semantics to a fully nondeterministic, a fully probabilistic, and a fully stochastic variant of a CSP-like process language.Comment: In Proceedings PACO 2011, arXiv:1108.145

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