Related papers: Metric Distortion of Small-group Deliberation
The adaptive voter model allows for studying the interplay between homophily, the tendency of like-minded individuals to attract each other, and social influence, the tendency for connected individuals to influence each other. However, it…
Optimization of distortion riskmetrics with distributional uncertainty has wide applications in finance and operations research. Distortion riskmetrics include many commonly applied risk measures and deviation measures, which are not…
Citizens' assemblies are an increasingly influential form of deliberative democracy, where randomly selected people discuss policy questions. The legitimacy of these assemblies hinges on their representation of the broader population, but…
We study a fundamental stochastic selection problem involving $n$ independent random variables, each of which can be queried at some cost. Given a tolerance level $\delta$, the goal is to find a value that is $\delta$-approximately minimum…
We present a new algorithmic framework for grouped variable selection that is based on discrete mathematical optimization. While there exist several appealing approaches based on convex relaxations and nonconvex heuristics, we focus on…
Group testing is the process of pooling arbitrary subsets from a set of $n$ items so as to identify, with a minimal number of tests, a "small" subset of $d$ defective items. In "classical" non-adaptive group testing, it is known that when…
We investigate a dynamical model of opinion formation in which an individual's opinion is influenced by interactions with a group of other agents. We introduce a bias towards one of the opinions in a manner not considered earlier to the…
Social choice theory is the study of preference aggregation across a population, used both in mechanism design for human agents and in the democratic alignment of language models. In this study, we propose the representative social choice…
Given a finite group with a generating subset there is a well-established notion of length for a group element given in terms of its minimal length expression as a product of elements from the generating set. Recently, certain quantities…
Social dynamics determined by voting in a stochastic environment is analyzed for a society composed of two cohesive groups of similar size. Within the model of random walks determined by voting, explicit formulas are derived for the capital…
Public discourse and opinions stem from multiple social groups. Each group has beliefs about a topic (such as vaccination, abortion, gay marriage, etc.), and opinions are exchanged and blended to produce consensus. A particular measure of…
We develop an adaptive-metric framework for norm-minimization-based outer approximation algorithms in bounded convex vector optimization. The key idea is to let the scalarization metric vary across iterations while measuring approximation…
We rigorously quantify the improvement in the sample complexity of variational divergence estimations for group-invariant distributions. In the cases of the Wasserstein-1 metric and the Lipschitz-regularized $\alpha$-divergences, the…
We revisit the selection problem, namely that of computing the $i$th order statistic of $n$ given elements, in particular the classic deterministic algorithm by grouping and partition due to Blum, Floyd, Pratt, Rivest, and Tarjan (1973).…
During deliberation processes, mediators and facilitators typically need to select a small and representative set of opinions later used to produce digestible reports for stakeholders. In online deliberation platforms, algorithmic selection…
Deterministically generating near-uniform point samplings of the motion groups like SO(3), SE(3) and their n-wise products SO(3)^n, SE(3)^n is fundamental to numerous applications in computational and data sciences. The natural measure of…
Under which conditions and with which distortions can we preserve the pairwise-distances of low-complexity vectors, e.g., for structured sets such as the set of sparse vectors or the one of low-rank matrices, when these are mapped in a…
Experimental design is a classical statistics problem and its aim is to estimate an unknown $m$-dimensional vector $\beta$ from linear measurements where a Gaussian noise is introduced in each measurement. For the combinatorial experimental…
Metric learning aims to embed one metric space into another to benefit tasks like classification and clustering. Although a greatly distorted metric space has a high degree of freedom to fit training data, it is prone to overfitting and…
In the long-studied problem of combinatorial group testing, one is asked to detect a set of $k$ defective items out of a population of size $n$, using $m \ll n$ disjunctive measurements. In the non-adaptive setting, the most widely used…