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.
There is a large literature on individual-level signaling in economics, following on the Nobel-prize-winning work of Spence @cite_26 . The general model there is quite different from our population-level signaling model; in the Spence model, (not populations) invest in (in terms of money or effort) signals whose costs correlate with the individual's type. In that model, equilibria can emerge where high-type individuals are more likely to invest in the signal than low-types, which can result in the signal being useful for admissions or hiring.
@cite_26
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1. Introduction, 355. — 2. Hiring as investment under uncertainty, 356. — 3. Applicant signaling, 358. — 4. Informational feedback and the definition of equilibrium, 359. — 5. Properties of informational equilibria: an example, 361. — 6. The informational impact of indices, 368. — Conclusions, 374.