Related papers: Convex Choice
We consider cooperative multi-agent consensus optimization problems over both static and time-varying communication networks, where only local communications are allowed. The objective is to minimize the sum of agent-specific possibly…
While there is extensive literature on approximation of convex bodies by inscribed or circumscribed polytopes, much less is known in the case of generally positioned polytopes. Here we give upper and lower bounds for approximation of convex…
Idiosyncratic tendency to choose one alternative over others in the absence of an identified reason, is a common observation in two-alternative forced-choice experiments. It is tempting to account for it as resulting from the (unknown)…
This paper explores the fair allocation of indivisible items in a multidimensional setting, motivated by the need to address fairness in complex environments where agents assess bundles according to multiple criteria. Such multidimensional…
Spaces of convex and concave functions appear naturally in theory and applications. For example, convex regression and log-concave density estimation are important topics in nonparametric statistics. In stochastic portfolio theory, concave…
We model stochastic choices with categorization. The agent preliminarly groups alternatives in homogenous disjoint classes, then randomly chooses one class and randomly picks an item within the selected class. We give a formal definition of…
Modeling the preferences of agents over a set of alternatives is a principal concern in many areas. The dominant approach has been to find a single reward/utility function with the property that alternatives yielding higher rewards are…
A principal must allocate a set of heterogeneous tasks (or objects) among multiple agents. The principal has preferences over the allocation. Each agent has preferences over which tasks they are assigned, which are their private…
We investigate approximately optimal mechanisms in settings where bidders' utility functions are non-linear; specifically, convex, with respect to payments (such settings arise, for instance, in procurement auctions for energy). We provide…
There is a growing need for discrete choice models that account for the complex nature of human choices, escaping traditional behavioral assumptions such as the transitivity of pairwise preferences. Recently, several parametric models of…
We introduce a single-winner perspective on voting on matchings, in which voters have preferences over possible matchings in a graph, and the goal is to select a single collectively desirable matching. Unlike in classical matching problems,…
This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of…
Convex geometries are closure systems satisfying the anti-exchange axiom. Every finite convex geometry can be embedded into a convex geometry of finitely many points in an n-dimensional space equipped with a convex hull operator, by the…
This note presents two results. First, it shows that under mild conditions, a decision problem is quasi-concave if the set of optimal actions is convex under every belief. Second, it shows that if a decision problem is quasi-concave, then…
Neural codes are collections of binary strings motivated by patterns of neural activity. In this paper, we study algorithmic and enumerative aspects of convex neural codes in dimension 1 (i.e. on a line or a circle). We use the theory of…
Many-to-many matching with contracts is studied in the framework of revealed preferences. All preferences are described by choice functions that satisfy natural conditions. Under a no-externality assumption individual preferences can be…
This work contributes to a foundational question in economic theory: how do individual-level cognitive biases interact with collective choice mechanisms? We study a setting where voters hold intrinsic preference rankings over a set of…
Learning to make decisions from observed data in dynamic environments remains a problem of fundamental importance in a number of fields, from artificial intelligence and robotics, to medicine and finance. This paper concerns the problem of…
Biased-coin designs are used in clinical trials to allocate treatments with some randomness while maintaining approximately equal allocation. More recent rules are compared with Efron's [Biometrika 58 (1971) 403-417] biased-coin rule and…
This paper presents a type theory in which it is possible to directly manipulate $n$-dimensional cubes (points, lines, squares, cubes, etc.) based on an interpretation of dependent type theory in a cubical set model. This enables new ways…