A note on selecting maximals in finite spaces

Given a choice problem, the maximization rule may select many alternatives. In such cases, it is common practice to interpret that the final choice will end up being made by some random procedure, assigning to any maximal alternative the same probability of being chosen. However, there may be reasons based on the same original preferences for which it is suitable to select certain maximal alternatives over others. This paper introduces two choice criteria induced by the original preferences such that maximizing with respect to each of them may give a finer selection of alternatives than maximizing with respect to the original preferences. Those criteria are built by means of several preference relations induced by the original preferences, namely, two (weak) dominance relations, two indirect preference relations and the dominance relations defined with the help of those indirect preferences. It is remarkable that as the original preferences approach being complete and transitive, those criteria become both simpler and closer to such preferences. In particular, they coincide with the original preferences when these are complete and transitive, in which case they provide the same solution as those preference

An Ordinal View of Independence with Application to Plausible Reasoning

An ordinal view of independence is studied in the framework of possibility theory. We investigate three possible definitions of dependence, of increasing strength. One of them is the counterpart to the multiplication law in probability theory, and the two others are based on the notion of conditional possibility. These two have enough expressive power to support the whole possibility theory, and a complete axiomatization is provided for the strongest one. Moreover we show that weak independence is well-suited to the problems of belief change and plausible reasoning, especially to address the problem of blocking of property inheritance in exception-tolerant taxonomic reasoning.Comment: Appears in Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (UAI1994

Is risk aversion irrational? Examining the “fallacy” of large numbers

A moderately risk averse person may turn down a 50/50 gamble that either results in her winning $200 or losing$100. Such behaviour seems rational if, for instance, the pain of losing $100 is felt more strongly than the joy of winning$200. The aim of this paper is to examine an influential argument that some have interpreted as showing that such moderate risk aversion is irrational. After presenting an axiomatic argument that I take to be the strongest case for the claim that moderate risk aversion is irrational, I show that it essentially depends on an assumption that those who think that risk aversion can be rational should be skeptical of. Hence, I conclude that risk aversion need not be irrational

Empirical Tests of Intransitivity Predicted by Models of Risky Choice

Recently proposed models of risky choice imply systematic violations of transitivity of preference. Five studies explored whether people show patterns of intransitivity predicted by four descriptive models. To distinguish ?true? violations from those produced by ?error,? a model was fit in which each choice can have a different error rate and each person can have a different pattern of true preferences that need not be transitive. Error rate for a choice is estimated from preference reversals between repeated presentations of the same choice. Results of five studies showed that very few people repeated intransitive patterns. We can retain the hypothesis that transitivity best describes the data of the vast majority of participants. --decision making,errors,gambling effect,reference points,regret,transitivity

Heuristic Voting as Ordinal Dominance Strategies

Decision making under uncertainty is a key component of many AI settings, and in particular of voting scenarios where strategic agents are trying to reach a joint decision. The common approach to handle uncertainty is by maximizing expected utility, which requires a cardinal utility function as well as detailed probabilistic information. However, often such probabilities are not easy to estimate or apply. To this end, we present a framework that allows "shades of gray" of likelihood without probabilities. Specifically, we create a hierarchy of sets of world states based on a prospective poll, with inner sets contain more likely outcomes. This hierarchy of likelihoods allows us to define what we term ordinally-dominated strategies. We use this approach to justify various known voting heuristics as bounded-rational strategies.Comment: This is the full version of paper #6080 accepted to AAAI'1

Population Ethics under Risk

Population axiology concerns how to evaluate populations in terms of their moral goodness, that is, how to order populations by the relations “is better than” and “is as good as”. The task has been to find an adequate theory about the moral value of states of affairs where the number of people, the quality of their lives, and their identities may vary. So far, this field has largely ignored issues about uncertainty and the conditions that have been discussed mostly pertain to the ranking of risk-free outcomes. Most public policy choices, however, are decisions under uncertainty, including policy choices that affect the size of a population. Here, we shall address the question of how to rank population prospects—that is, alternatives that contain uncertainty as to which population they will bring about—by the relations “is better than” and “is as good as”. We start by illustrating how well-known population axiologies can be extended to population prospect axiologies. And we show that new problems arise when extending population axiologies to prospects. In particular, traditional population axiologies lead to prospect-versions of the problems that they praised for avoiding in the risk-free settings. Finally, we identify an intuitive adequacy condition that, we contend, should be satisfied by any population prospect axiology, and show how given this condition, the impossibility theorems in population axiology can be extended to (non-trivial) impossibility theorems for population prospect axiology