Related papers: On the Arrow property
Geoffrion's theorem is a fundamental result from mathematical programming assessing the quality of Lagrangian relaxation, a standard technique to get bounds for integer programs. An often implicit condition is that the set of feasible…
We examine multi-task benchmarks in machine learning through the lens of social choice theory. We draw an analogy between benchmarks and electoral systems, where models are candidates and tasks are voters. This suggests a distinction…
A class of rational functions characterized by some wonderful properties is studied. The properties that identify this class include simple algebra (their inverses can be expressed in radicals), simple topology (the total space of the…
We consider different choice procedures such as scoring rules, rules, using majority relation, value function and tournament matrix, which are used in social and multi-criteria choice problems. We focus on the study of the properties that…
We consider a setting in which agents are allocated land plots and they have additive preferences over which plot they get and who their neighbor is. Strategyproofness, Pareto optimality, and individual rationality are three fundamental…
Preference cycles are prevalent in problems of decision-making, and are contradictory when preferences are assumed to be transitive. This contradiction underlies Condorcet's Paradox, a pioneering result of Social Choice Theory, wherein…
We consider a model where an agent is must choose between alternatives that each provide only an imprecise description of the world (e.g. linguistic expressions). The set of alternatives is closed under logical conjunction and disjunction,…
We provide a necessary and sufficient condition for rationalizable implementation of social choice functions, i.e., we offer a complete answer regarding what social choice functions can be rationalizably implemented.
Coordination is a desirable feature in many multi-agent systems such as robotic and socioeconomic networks. We consider a task allocation problem as a binary networked coordination game over an undirected regular graph. Each agent in the…
Impartial selection problems are concerned with the selection of one or more agents from a set based on mutual nominations from within the set. To avoid strategic nominations of the agents, the axiom of impartiality requires that the…
We study unirational algebraic varieties and the fields of rational functions on them. We show that after adding a finite number of variables some of these fields admit an infinitely transitive model. The latter is an algebraic variety with…
In most contemporary approaches to decision making, a decision problem is described by a sets of states and set of outcomes, and a rich set of acts, which are functions from states to outcomes over which the decision maker (DM) has…
In this paper we demonstrate that the class of basic feasible functionals has recursion theoretic properties which naturally generalize the corresponding properties of the class of feasible functions. We also improve the Kapron - Cook…
Bounded rationality, that is, decision-making and planning under resource limitations, is widely regarded as an important open problem in artificial intelligence, reinforcement learning, computational neuroscience and economics. This paper…
Sorting algorithms are fundamental to computer science, and their correctness criteria are well understood as rearranging elements of a list according to a specified total order on the underlying set of elements. As mathematical functions,…
The inner alignment problem, which asserts whether an arbitrary artificial intelligence (AI) model satisfices a non-trivial alignment function of its outputs given its inputs, is undecidable. This is rigorously proved by Rice's theorem,…
When given a class of functions and a finite collection of sets, one might be interested whether the class in question contains any function whose domain is a subset of the union of the sets of the given collection and whose restrictions to…
Every m by n matrix A with rank r has exactly r independent rows and r independent columns. The fact has become the most fundamental theorem in linear algebra such that we may favor it in an unconscious way. The sole aim of this paper is to…
We show that if a Laurent series $f\in\mathbb{C}((t))$ satisfies a particular kind of linear iterative equation, then $f$ is either a rational function or it is differentially transcendental over $\mathbb{C}(t)$. This condition is more…
We develop a model to study the role of rationality in economics and biology. The model's agents differ continuously in their ability to make rational choices. The agents' objective is to ensure their individual survival over time or,…