Monocultures may lead to
Braess's like paradoxes in which introducing a "better option" (such as a more accurate algorithm) leads to suboptimal monocultural convergence - a monoculture whose correlated nature results in degraded overall quality of the decisions. Since monocultures form in areas of high-stakes decisions such as credit scoring and automated hiring, it is important to achieve optimal decision making. This scenario can be studied through the lens of
mechanism design, in which agents are choosing between a set of algorithms, some of which return correlated outputs. The overall impact of the decision making is measured by
social welfare.
Suboptimal monocultures convergence in automated hiring This section demonstrates the concern of suboptimal monoculture convergence using automated hiring as a case study. Hiring is the process of ranking a group of candidates and hiring the top-valued. In recent years
automated hiring (automatically ranking candidates based on their interaction with an AI powered system) became popular. As shown by
Kleinberg, under some assumptions, suboptimal automated hiring monocultures naturally form, namely, choosing the correlated algorithm is a
dominant strategy, thus converging to monoculture that leads suboptimal social welfare.
Framework In this scenario we will consider two firms and a group S of n candidate with hidden utilities of x_i. For hiring process - each firm will produce a noisy-ranking of the candidates, then each firm (in a random order) hires the first available candidate in their ranking. Each firm can choose to use either an independent human rankers or use a common algorithmic ranking. The ranking algorithm \mathcal{F}_\theta is modeled as a noisy distribution above
permutations of S parametrized by an accuracy parameter \theta > 0. In order for \mathcal{F}_\theta to make sense it should satisfy these conditions: •
Differentiability: The probability of each permutation \pi is continues and differentiable in \theta •
Asymptotic optimality: For the true ranking \pi^*: \lim_{\theta\to\infin} Pr[\pi^*] = 1 •
Monotonicity: The expected utility of the top-ranked candidate gets better as \theta increases, even if any subset of S is removed. These conditions state that a firm should always prefer higher values of \theta, even if it is not first in the selection order. Both the algorithmic and human ranking methods are of the form of \mathcal{F}_\theta and differ by the accuracy parameters \theta_A, \theta_H. The algorithmic ranking output is corotated - it always outputs the same permutation. In contrast, a human ranked premutation is drawn from \mathcal{F}_{\theta_H} independently for each of firms. For s_1, s_2 \in \{A, H\} strategies of the first and second firm, Social welfare W_{s_1,s_2} is defied as the sum of utilities of the hired candidates.
Conditions to suboptimal convergence The Braess's like paradox in this framework is suboptimal monocultures converges. That is, using the algorithmic ranking is dominant strategy thus converging toward monoculture yet it yields suboptimal welfare W_{A,A} (welfare in a world without algorithmic ranking is higher). The main theorem proved by Kleinberg of this model is that for any \theta_H and any noisy ranking family \mathcal{F}_\theta that satisfy these conditions: •
Preference for the first position: For all \theta>0 if \pi,\sigma \sim \mathcal{F}_\theta then \mathbb{E}[\pi_1-\pi_2|\pi_1\ne\sigma_1]>0. •
Preference for weaker competition: For all \theta_1 > \theta_2, \sigma \sim \mathcal{F}_{\theta_1} and\ \pi, \tau \sim \mathcal{F}_{\theta_2}: \mathbb{E}[\pi_1^{(-\sigma_1)}] . there exists a \theta_A>\theta_H such that both firms prefer using the sherd algorithmic ranking even though the social welfare is higher when both use the human evaluators. In other words - regardless of the accuracy of the human rankers there exists a more accurate algorithm whose introduction leads to suboptimal monoculture convergence. The implications of this theorem is that under these conditions, firms will choose to use the algorithmic ranking even though that the correlated nature of algorithmic monocultures degrades total social welfare. Even though algorithmic rankings are more accurate. The first condition on \mathcal{F}_\theta (Preference for the first position) is equivalent to a preference of firms to have independent ranking (in our setting - non algorithmic). This means that a firm should prefers independent ranking methods given all else is equal. The intuition behind preference for weaker competition is that when a candidate is removed (hired by a different firm), the best remaining candidate is better in expectation when the removed candidate is chosen based on a less accurate ranking. Thus, a firm should always prefer that its competitors would be less accurate. These conditions are met for \mathcal{F}_\theta that is the
Mallows Model distributions and some types of
random utility models (Gaussian or Laplacian noise). == See also ==