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The Axiom of Choice (AC for short) is the most (in)famous axiom of the usual foundations of mathematics, ZFC set theory. The (non-)essential use of AC in mathematics has been well-studied and thoroughly classified. Now, fragments of…
Harsanyi (1955) showed that the only way to aggregate individual preferences into a social preference which satisfies certain desirable properties is ``utilitarianism'', whereby the social utility function is a weighted average of…
The problem of finding a (continuous) utility function for a semiorder has been studied since in 1956 R.D. Luce introduced in \emph{Econometrica} the notion. There was almost no results on the continuity of the representation. A similar…
The impossibility theorem in Roth (1982) states that no stable mechanism satisfies strategy-proofness. This paper explores the Machiavellian frontier of stable mechanisms by weakening strategy-proofness. For a fixed mechanism $\varphi$ and…
A primary motivation for reasoning under uncertainty is to derive decisions in the face of inconclusive evidence. However, Shafer's theory of belief functions, which explicitly represents the underconstrained nature of many reasoning…
We investigate a generalisation of the coherent choice functions considered by Seidenfeld et al. (2010), by sticking to the convexity axiom but imposing no Archimedeanity condition. We define our choice functions on vector spaces of…
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…
The undercut procedure was presented by Brams et al. [2] as a procedure for identifying an envy-free allocation when agents have preferences over sets of objects. They assumed that agents have strict preferences over objects and their…
We present a method for using standard techniques from satisfiability checking to automatically verify and discover theorems in an area of economic theory known as ranking sets of objects. The key question in this area, which has important…
This paper studies preference aggregation under risk. In our model, each agent has an incomplete preference relation represented by a set of expected utility functions. The classical Pareto principle is silent on agreement involving…
Arrow's Impossibility Theorem is a seminal result of Social Choice Theory that demonstrates the impossibility of ranked-choice decision-making processes to jointly satisfy a number of intuitive and seemingly desirable constraints. The…
We show that classical density functional theory can be based on the constrained search method [M. Levy, Proc. Natl. Acad. Sci. 76, 6062 (1979)]. From the Gibbs inequality one first derives a variational principle for the grand potential as…
The goal is to show that an edge-reinforced random walk on a graph of bounded degree, with reinforcement weight function $W$ taken from a general class of reciprocally summable reinforcement weight functions, traverses a random attracting…
The rigid relation principle, introduced in this article, asserts that every set admits a rigid binary relation. This follows from the axiom of choice, because well-orders are rigid, but we prove that it is neither equivalent to the axiom…
We present a necessary and sufficient condition for Alt's system to be represented by a continuous utility function. Moreover, we present a necessary and sufficient condition for this utility function to be concave. The latter condition can…
We conclude from Goedel's Theorem VII of his seminal 1931 paper that every recursive function f(x_{1}, x_{2}) is representable in the first-order Peano Arithmetic PA by a formula [F(x_{1}, x_{2}, x_{3})] which is algorithmically verifiable,…
Incorporating graph side information into recommender systems has been widely used to better predict ratings, but relatively few works have focused on theoretical guarantees. Ahn et al. (2018) firstly characterized the optimal sample…
This paper studies delegation in a model of discrete choice. In the delegation problem, an uninformed principal must consult an informed agent to make a decision. Both the agent and principal have preferences over the decided-upon action…
This study proposes a new efficiency requirement, a minimal almost weak Pareto principle, which says that x is socially better than y whenever the only one individual never prefers y to x, and all the others prefers x to y. Then, I show…
Since Leonard Savage's epoch-making "Foundations of Statistics", Subjective Expected Utility Theory has been the presumptive model for decision-making. Savage provided an act-based axiomatization of standard expected utility theory. In this…