Related papers: Statistical Bounds on Equity
Two prominent objectives in social choice are utilitarian - maximizing the sum of agents' utilities, and leximin - maximizing the smallest agent's utility, then the second-smallest, etc. Utilitarianism is typically computationally easier to…
Altruistic behaviour is disadvantageous for the individual while is advantageous for its group. If the target of the selection is the individual, one would expect the selection process to lead to populations formed by wholly homogeneous…
Most decision theories, including expected utility theory, rank dependent utility theory and cumulative prospect theory, assume that investors are only interested in the distribution of returns and not in the states of the economy in which…
The optimal (`equilibrium') macroscopic properties of an economy with $N$ industries endowed with different technologies, $P$ commodities and one consumer are derived in the limit $N\to\infty$ with $n=N/P$ fixed using the replica method.…
We study the problem of fairly allocating indivisible items to agents with different entitlements, which captures, for example, the distribution of ministries among political parties in a coalition government. Our focus is on picking…
We study economies where consumers interact independently with many monopolists. When consumer valuations over goods are correlated, correlation can distort the induced distribution of consumer surplus (information rents). We identify which…
We develop an axiomatic framework to evaluate income distributions from the perspective of an opportunity-egalitarian social planner. Building on a formal link with the literature on decision theory under ambiguity, we characterize a class…
This paper examines a government's strategic resource allocation choices when facing an opposing group whose military power is uncertain. We investigate how this uncertainty affects the government's decision to divide resources in a way…
The well-known Condorcet's Jury theorem posits that the majority rule selects the best alternative among two available options with probability one, as the population size increases to infinity. We study this result under an asymmetric…
The study of fairness in intelligent decision systems has mostly ignored long-term influence on the underlying population. Yet fairness considerations (e.g. affirmative action) have often the implicit goal of achieving balance among groups…
We propose a simple yet effective solution to tackle the often-competing goals of fairness and utility in classification tasks. While fairness ensures that the model's predictions are unbiased and do not discriminate against any particular…
The Shapley-Folkman theorem shows that Minkowski averages of uniformly bounded sets tend to be convex when the number of terms in the sum becomes much larger than the ambient dimension. In optimization, Aubin and Ekeland [1976] show that…
The random utility model (RUM, McFadden and Richter, 1990) has been the standard tool to describe the behavior of a population of decision makers. RUM assumes that decision makers behave as if they maximize a rational preference over a…
We study the fair allocation of indivisible items under relevance constraints, where each agent has a set of relevant items and can only receive items that are relevant to them. While the relevance constraint has been studied in recent…
Aggregating risks from multiple sources can be complex and demanding, and decision makers usually adopt heuristics to simplify the evaluation process. This paper axiomatizes two closed related and yet different heuristics, narrow bracketing…
Random partition models are widely used in Bayesian methods for various clustering tasks, such as mixture models, topic models, and community detection problems. While the number of clusters induced by random partition models has been…
Suppose we are given the conditional probability of one variable given some other variables.Normally the full joint distribution over the conditioning variablesis required to determine the probability of the conditioned variable.Under what…
Let us consider $k ~(\ge 2)$ independent populations $\Pi_1, \ldots,\Pi_k$, where $\Pi_i$ follows exponential distribution with hazard rate ${\sigma_i},$ ($i = 1,\ldots,k$). Suppose $Y_{i1},\ldots, Y_{in}$ be a random sample of size $n$…
Various measures can be used to estimate bias or unfairness in a predictor. Previous work has already established that some of these measures are incompatible with each other. Here we show that, when groups differ in prevalence of the…
Let $\mathbf{X}_1,...,\mathbf{X}_n$ be a random sample from a $p$-dimensional population distribution. Assume that $c_1n^{\alpha}\leq p\leq c_2n^{\alpha}$ for some positive constants $c_1,c_2$ and $\alpha$. In this paper we introduce a new…