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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This paper explores information disclosure in matching markets, e.g., the informativeness of transcripts given out by universities. We show that the same, "benchmark," amount of information is disclosed in essentially all equilibria. We then demonstrate that if universities disclose the benchmark amount of information, students and employers will not find it profitable to contract early; if they disclose more, unraveling will occur. A sender randomly draws a “prospect” characterized by its profitability to the sender and its relevance to a receiver. The receiver observes only a signal provided by the sender and accepts the prospect if his Bayesian inference about the prospect’s relevance exceeds his opportunity cost. The sender’s profits are typically maximized by partial information disclosure, whereby the receiver is induced to accept less relevant but more profitable prospects (“switches”) by pooling them with more relevant but less profitable ones (“baits”). Extensions include maximizing a weighted sum of sender profits and receiver surplus and allowing the sender to use monetary incentives.