An Upper Bound for the Expected Difference between Order Statistics

Lopez, Manuel; Marengo, James E.

doi:10.4169/math.mag.84.5.365

Cited by 22 publications

(2 citation statements)

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“…In this section, we will make several approximations, growing tight with large n, that we treat formally in the full version. Our analysis makes use of results from [15,16,19]. This section is intended to demonstrate the techniques needed to understand the condition (2).…”

Section: The Case Where K =mentioning

confidence: 99%

Selection Problems in the Presence of Implicit Bias

2023

The Societal Impacts of Algorithmic Decision-Making

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Over the past two decades, the notion of implicit bias has come to serve as an important component in our understanding of bias and discrimination in activities such as hiring, promotion, and school admissions. Research on implicit bias posits that when people evaluate others -for example, in a hiring context -their unconscious biases about membership in particular demographic groups can have an effect on their decision-making, even when they have no deliberate intention to discriminate against members of these groups. A growing body of experimental work has demonstrated the effect that implicit bias can have in producing adverse outcomes.Here we propose a theoretical model for studying the effects of implicit bias on selection decisions, and a way of analyzing possible procedural remedies for implicit bias within this model. A canonical situation represented by our model is a hiring setting, in which recruiters are trying to evaluate the future potential of job applicants, but their estimates of potential are skewed by an unconscious bias against members of one group. In this model, we show that measures such as the Rooney Rule, a requirement that at least one member of an underrepresented group be selected, can not only improve the representation of the affected group, but also lead to higher payoffs in absolute terms for the organization performing the recruiting. However, identifying the conditions under which such measures can lead to improved payoffs involves subtle tradeoffs between the extent of the bias and the underlying distribution of applicant characteristics, leading to novel theoretical questions about order statistics in the presence of probabilistic side information.

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Section: The Case Where K =mentioning

confidence: 99%

Selection Problems in the Presence of Implicit Bias

2023

The Societal Impacts of Algorithmic Decision-Making

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“…Thus, E Y(n:n) − Y (n−1:n) |M = m = E Z (m:m) − Z (m−1:m). Using an analysis similar to that of[16],E Z (m:m) − Z (m−1:m) = F Z,(m:m) (x)) − (1 − F Z,(m−1:m) (x)) dx = Z,(m−1:m) − F Z,(m:m) (x) dx = Z (x) m−1 (1 − F Z (x)) dx ≥ Z (x) m−1 (1 − F Z (x)) dxChoose η ∈ (0, 1 − F (T )) and η ∈ (η, 1 − F (T )). Let r = F −1 Z (F (T ) + η) and r = F −1…”

mentioning

confidence: 99%

Selection Problems in the Presence of Implicit Bias

Kleinberg,

Raghavan

2018

Preprint

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Over the past two decades, the notion of implicit bias has come to serve as an important component in our understanding of discrimination in activities such as hiring, promotion, and school admissions. Research on implicit bias posits that when people evaluate others -for example, in a hiring context -their unconscious biases about membership in particular groups can have an effect on their decision-making, even when they have no deliberate intention to discriminate against members of these groups. A growing body of experimental work has pointed to the effect that implicit bias can have in producing adverse outcomes.Here we propose a theoretical model for studying the effects of implicit bias on selection decisions, and a way of analyzing possible procedural remedies for implicit bias within this model. A canonical situation represented by our model is a hiring setting: a recruiting committee is trying to choose a set of finalists to interview among the applicants for a job, evaluating these applicants based on their future potential, but their estimates of potential are skewed by implicit bias against members of one group. In this model, we show that measures such as the Rooney Rule, a requirement that at least one of the finalists be chosen from the affected group, can not only improve the representation of this affected group, but also lead to higher payoffs in absolute terms for the organization performing the recruiting. However, identifying the conditions under which such measures can lead to improved payoffs involves subtle trade-offs between the extent of the bias and the underlying distribution of applicant characteristics, leading to novel theoretical questions about order statistics in the presence of probabilistic side information.

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