Related papers: Convex Choice
An agent's preferences depend on an ordered parameter or type. We characterize the set of utility functions with single-crossing differences (SCD) in convex environments. These include preferences over lotteries, both in expected utility…
A principal wishes to transact business with a multidimensional distribution of agents whose preferences are known only in the aggregate. Assuming a twist (= generalized Spence-Mirrlees single-crossing) hypothesis and that agents can choose…
Euclidean preferences are a widely studied preference model, in which decision makers and alternatives are embedded in d-dimensional Euclidean space. Decision makers prefer those alternatives closer to them. This model, also known as…
In the design of incentive compatible mechanisms, a common approach is to enforce incentive compatibility as constraints in programs that optimize over feasible mechanisms. Such constraints are often imposed on sparsified representations of…
Analysis of high-dimensional data is currently a popular field of research, thanks to many applications e.g. in genetics (DNA data in genomewide association studies), spectrometry or web analysis. At the same time, the type of problems that…
We consider monotone mean-variance (MMV) portfolio selection problems with a conic convex constraint under diffusion models, and their counterpart problems under mean-variance (MV) preferences. We obtain the precommitted optimal strategies…
Social choice becomes easier on restricted preference domains such as single-peaked, single-crossing, and Euclidean preferences. Many impossibility theorems disappear, the structure makes it easier to reason about preferences, and…
A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…
In several matching markets, in order to achieve diversity, agents' priorities are allowed to vary across an institution's available seats, and the institution is let to choose agents in a lexicographic fashion based on a predetermined…
We study some methods of subgradient projections for solving a convex feasibility problem with general (not necessarily hyperplanes or half-spaces) convex sets in the inconsistent case and propose a strategy that controls the relaxation…
A preference profile with m alternatives and n voters is 2-dimensional Euclidean if both the alternatives and the voters can be placed into a 2-dimensional space such that for each pair of alternatives, every voter prefers the one which has…
Variational analysis presents a unified theory encompassing in particular both smoothness and convexity. In a Euclidean space, convex sets and smooth manifolds both have straightforward local geometry. However, in the most basic hybrid case…
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…
We characterize one-dimensional Euclidean preference profiles with a small number of alternatives and voters. In particular, we show the following. 1. Every preference profile with up to two voters is one-dimensional Euclidean if and only…
Convex clustering has recently garnered increasing interest due to its attractive theoretical and computational properties, but its merits become limited in the face of high-dimensional data. In such settings, pairwise affinity terms that…
Autonomously learning diverse behaviors without an extrinsic reward signal has been a problem of interest in reinforcement learning. However, the nature of learning in such mechanisms is unconstrained, often resulting in the accumulation of…
In decision-making problems under uncertainty, probabilistic constraints are a valuable tool to express safety of decisions. They result from taking the probability measure of a given set of random inequalities depending on the decision…
The paper suggests a new --- to the best of the author's knowledge --- characterization of decisions which are optimal in the multi-objective optimization problem with respect to a definite proper preference cone, a Euclidean cone with a…
I study symmetric competitions in which each player chooses an arbitrary distribution over a one-dimensional performance index, subject to a convex cost. I establish existence of a symmetric equilibrium, document various properties it must…
Social decision schemes (SDSs) map the ordinal preferences of individual voters over multiple alternatives to a probability distribution over the alternatives. In order to study the axiomatic properties of SDSs, we lift preferences over…