Related papers: Great Expectations. Part II: Generalized Expected …
The purpose of this paper is to investigate the generalized formulation of weighted optimal guidance laws with impact angle constraint. From the generalized formulation, we explicitly find the feasible set of weighting functions that lead…
We initiate a novel direction in randomized social choice by proposing a new definition of agent utility for randomized outcomes. Each agent has a preference over all outcomes and a {\em quantile} parameter. Given a {\em lottery} over the…
In the present article we use the quantum formalism to describe the effects of risk and ambiguity in decision theory. The main idea is that the probabilities in the classic theory of expected utility are estimated probabilities, and thus do…
Budget aggregation is a process in which citizens vote by declaring their individual ideal budget allocation, and a pre-determined rule aggregates all votes into a single outcome. Recent theoretical work has proposed various aggregation…
This paper introduces a space of variable lotteries and proves a constructive version of the expected utility theorem. The word ``constructive'' is used here in two senses. First, as in constructive mathematics, the logic underlying proofs…
Self-adaptation can be realized in various ways. Rule-based approaches prescribe the adaptation to be executed if the system or environment satisfy certain conditions and result in scalable solutions, however, with often only satisfying…
The goal of this note is to provide a geometric setting in which generalized arithmetic means are best predictors in an appropriate metric. This characterization provides a geometric interpretation to the concept of certainty equivalent.…
In problems involving the allocation of a single non-disposable commodity, we study rules defined on a general domain of preferences requiring only that each preference exhibit a unique global maximum. Our focus is on rules that satisfy a…
Quantum Decision Theory, advanced earlier by the authors, and illustrated for lotteries with gains, is generalized to the games containing lotteries with gains as well as losses. The mathematical structure of the approach is based on the…
This paper studies how violations of structural assumptions like expected utility and exponential discounting can be connected to basic rationality violations, even though these assumptions are typically regarded as independent building…
Prediction is a complex notion, and different predictors (such as people, computer programs, and probabilistic theories) can pursue very different goals. In this paper I will review some popular kinds of prediction and argue that the theory…
It is well known that ex ante social preferences and expected utility are not always compatible. In this note, we introduce a novel framework that naturally separates social preferences from selfish preferences to answer the following…
This paper introduces a class of objects called decision rules that map infinite sequences of alternatives to a decision space. These objects can be used to model situations where a decision maker encounters alternatives in a sequence such…
It has been argued by Shepard that there is a robust psychological law that relates the distance between a pair of items in psychological space and the probability that they will be confused with each other. Specifically, the probability of…
Decision theorists propose a normative theory of rational choice. Traditionally, they assume that they should provide some constant and invariant principles as criteria for rational decisions, and indirectly, for agents. They seek a…
Scoring rules for eliciting expert predictions of random variables are usually developed assuming that experts derive utility only from the quality of their predictions (e.g., score awarded by the rule, or payoff in a prediction market). We…
Universal scaling laws of fluctuations (the $\Delta$-scaling laws) can be derived for equilibrium and off-equilibrium systems when combined with the finite-size scaling analysis. In any system in which the second-order critical behavior can…
In this essay, I wish to share a novel perspective based on the principle of universalization in arriving at the relativistic and quantum world from the classical world. I also delve on some insightful discussion on going ``beyond''.
We investigate the application of classification techniques to utility elicitation. In a decision problem, two sets of parameters must generally be elicited: the probabilities and the utilities. While the prior and conditional probabilities…
The mathematical study of voting, social choice theory, has traditionally only been applicable to choices among a few predetermined alternatives, but not to open-ended decisions such as collectively selecting a textual statement. We…