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We propose a new perspective on representation learning in reinforcement learning based on geometric properties of the space of value functions. We leverage this perspective to provide formal evidence regarding the usefulness of value…
We study how electoral rules shape polarization dynamics when voters and candidates both adapt to repeated election outcomes. We introduce two geometric primitives for comparing rules under this feedback: the \emph{winner radius} $R_t =…
Existence of an increasing quasi-concave value function consistent with given preference information is an important issue in various fields including Economics, Multiple Criteria Decision Making, and Applied Mathematics. In this paper, we…
The controversies around the 2020 US presidential elections certainly casts serious concerns on the efficiency of the current voting system in representing the people's will. Is the naive Plurality voting suitable in an extremely polarized…
The median voter theorem has long been the default model of voter behavior and candidate choice. While contemporary work on the distribution of political opinion has emphasized polarization and an increasing gap between the "left" and the…
We study vote delegation with "well-behaving" and "misbehaving" agents and compare it with conventional voting. Typical examples for vote delegation are validation or governance tasks on blockchains. There is a majority of well-behaving…
In crowd counting datasets, each person is annotated by a point, which is usually the center of the head. And the task is to estimate the total count in a crowd scene. Most of the state-of-the-art methods are based on density map…
The convolution of a function with an isotropic Gaussian appears in many contexts such as differential equations, computer vision, signal processing, and numerical optimization. Although this convolution does not always have a closed form…
Voting can abstractly model any decision-making scenario and as such it has been extensively studied over the decades. Recently, the related literature has focused on quantifying the impact of utilizing only limited information in the…
In the coevolving voter model, each voter has one of two diametrically opposite opinions, and a voter encountering a neighbor with the opposite opinion may either adopt it or rewire the connection to another randomly chosen voter sharing…
In computational social choice, the distortion of a voting rule quantifies the degree to which the rule overcomes limited preference information to select a socially desirable outcome. This concept has been investigated extensively, but…
Political and social identities structure how people evaluate political information, a finding decades deep in political science and routinely discarded by computational tools that often produce single scores that treat a piece of text, an…
This paper introduces a definition of ideological polarization of an electorate around a particular central point. By being flexible about the location or width of the center, this measure enables the researcher to analyze polarization…
Probabilistic risk aversion, defined through quasi-convexity in probabilistic mixtures, is a common useful property in decision analysis. We study a general class of non-monotone mappings, called the generalized rank-dependent functions,…
The voter model and the Axelrod model are two of the main stochastic processes that describe the spread of opinions on networks. The former includes social influence, the tendency of individuals to become more similar when they interact,…
We consider the problems of \emph{learning} and \emph{testing} real-valued convex functions over Gaussian space. Despite the extensive study of function convexity across mathematics, statistics, and computer science, its learnability and…
We study the dynamics of opinion formation in a heterogeneous voter model on a complete graph, in which each agent is endowed with an integer fitness parameter $k \ge 0$, in addition to its $+$ or $-$ opinion state. The evolution of the…
Aggregating preferences under incomplete or constrained feedback is a fundamental problem in social choice and related domains. While prior work has established strong impossibility results for pairwise comparisons, this paper extends the…
We investigate the coarsening dynamics of a simplified version of the persistent voter model in which an agent can become a zealot -- i.e. resistent to change opinion -- at each step, based on interactions with its nearest neighbors. We…
In this paper we propose a general class of covariate-adjusted response-adaptive (CARA) designs based on a new functional urn model. We prove strong consistency concerning the functional urn proportion and the proportion of subjects…