We identify and explore differential access to population-level signaling (also known as information design) as a source of unequal access to opportunity. A population-level signaler has potentially noisy observations of a binary type for each member of a population and, based on this, produces a signal about each member. A decision-maker infers types from signals and accepts those individuals whose type is high in expectation. We assume the signaler of the disadvantaged population reveals her observations to the decision-maker, whereas the signaler of the advantaged population forms signals strategically. We study the expected utility of the populations as measured by the fraction of accepted members, as well as the false positive rates (FPR) and false negative rates (FNR). We first show the intuitive results that for a fixed environment, the advantaged population has higher expected utility, higher FPR, and lower FNR, than the disadvantaged one (despite having identical population quality), and that more accurate observations improve the expected utility of the advantaged population while harming that of the disadvantaged one. We next explore the introduction of a publicly-observable signal, such as a test score, as a potential intervention. Our main finding is that this natural intervention, intended to reduce the inequality between the populations' utilities, may actually exacerbate it in settings where observations and test scores are noisy.
Closer to our setting, Ostrovsky and Schwarz @cite_28 study a model in which schools provide noisy information about their students to potential employers. Their focus is on understanding properties of the equilibria of the system; they do not fully characterize the equilibria, they do not consider the role of signaling in compounding inequity, and they do not investigate the impact of interventions like our standardized test. Unlike us, they do not consider the case where the schools have imperfect observations of the students' types. Such work falls into a broader literature on optimal information structures (e.g., @cite_15 ).
@cite_28 @cite_15
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In the traffic assignment problem, first proposed by Wardrop in 1952, commuters select the shortest available path to travel from their origins to their destinations. We study a generalization of this problem in which competitors, who may control a nonnegligible fraction of the total flow, ship goods across a network. This type of games, usually referred to as atomic games, readily applies to situations in which the competing freight companies have market power. Other applications include intelligent transportation systems, competition among telecommunication network service providers, and scheduling with flexible machines. Our goal is to determine to what extent these systems can benefit from some form of coordination or regulation. We measure the quality of the outcome of the game without centralized control by computing the worst-case inefficiency of Nash equilibria. The main conclusion is that although self-interested competitors will not achieve a fully efficient solution from the system's point of view, the loss is not too severe. We show how to compute several bounds for the worst-case inefficiency that depend on the characteristics of cost functions and on the market structure in the game. In addition, building upon the work of Catoni and Pallotino, we show examples in which market aggregation (or collusion) adversely impacts the aggregated competitors, even though their market power increases. For example, Nash equilibria of atomic network games may be less efficient than the corresponding Wardrop equilibria. When competitors are completely symmetric, we provide a characterization of the Nash equilibrium using a potential function, and prove that this counterintuitive phenomenon does not arise. Finally, we study a pricing mechanism that elicits more coordination from the players by reducing the worst-case inefficiency of Nash equilibria. This paper develops a model of strategic communication, in which a better-informed Sender (S) sends a possibly noisy signal to a Receiver (R), who then takes an action that determines the welfare of both. We characterize the set of Bayesian Nash equilibria under standard assumptions, and show that equilibrium signaling always takes a strikingly simple form, in which S partitions the support of the (scalar) variable that represents his private information and introduces noise into his signal by reporting, in effect, only which element of the partition his observation actually lies in. We show under further assumptions that before S observes his private information, the equilibrium whose partition has the greatest number of elements is Pareto-superior to all other equilibria, and that if agents coordinate on this equilibrium, R's equilibrium expected utility rises when agents' preferences become more similar. Since R bases his choice of action on rational expectations, this establishes a sense in which equilibrium signaling is more informative when agents' preferences are more similar. Summary In this paper we propose, survey and compare some classes of probability densities that may be used to represent partial prior information, to model either prior ignorance or Bayesian sensitivity analysis. We distinguish two types of models appropriate for two different situations: near ignorance models which are suitable in problems where there is little prior information, and neighbourhood models, which can be used to 'robustify' a strict Bayesian analysis in problems where there is substantial prior information about location. We argue that, especially for the first situation, a reasonable class of prior densities is not the same as a class of reasonable prior densities. We discuss various desiderata for a 'reasonable' class, including coherence and sensible dependence of inferences on sample size. The translation invariant models studied here are classes of conjugate priors, classes of double exponential densities and a neighbourhood of the uniform prior. Of the neighbourhood models we examine examples of E-contamination neighbourhoods (previously studied by Huber, Berger and Berliner) and intervals of measures (DeRobertis and Hartigan). We illustrate the models in the simple problem of constructing credible intervals for an unknown normal mean. Of the models studied in detail, a translation-invariant class of double exponential priors is favoured for modelling little prior information, and a type of interval of measures seems most suitable for robust Bayesian analysis. In this paper, we study the problem of learning in the presence of classification noise in the probabilistic learning model of Valiant and its variants. In order to identify the class of “robust” learning algorithms in the most general way, we formalize a new but related model of learning from statistical queries . Intuitively, in this model a learning algorithm is forbidden to examine individual examples of the unknown target function, but is given acess to an oracle providing estimates of probabilities over the sample space of random examples. One of our main results shows that any class of functions learnable from statistical queries is in fact learnable with classification noise in Valiant's model, with a noise rate approaching the information-theoretic barrier of 1 2. We then demonstrate the generality of the statistical query model, showing that practically every class learnable in Valiant's model and its variants can also be learned in the new model (and thus can be learned in the presence of noise). A notable exception to this statement is the class of parity functions, which we prove is not learnable from statistical queries, and for which no noise-tolerant algorithm is known.