When Should a Principal Delegate to an Agent in Selection Processes?

TL;DR

The paper analyzes when a principal should delegate selection decisions to an agent in high-stakes settings with noisy signals. It develops a principled principal–agent model with two-dimensional applicant quality (ability $s$ and fit $f$) and a scalar trade-off $t=\alpha f+(1-\alpha)s$, deriving closed-form expressions for expected utility under delegation and no delegation, and extends the analysis to multi-group fairness under mean biases or variance disparities in signals. Key findings show that delegation can improve efficiency and applicant quality in certain regimes (notably with high selectivity thresholds and specific $\alpha$ values), but fairness outcomes depend critically on the type of disparity; additive mean bias can be corrected when known, whereas variance disparities can lead to exclusion or group-blind outcomes. The results provide nuanced guidance for designing delegated versus non-delegated selection processes in hiring and admissions, highlighting that choices should depend on signal quality, fairness goals, and the expected alignment between principal and agent objectives. Overall, the work illuminates how delegation shapes efficiency and fairness in selection under informational frictions and contributes to responsible-AI and algorithmic delegation debates in high-stakes settings.

Abstract

Decision-makers in high-stakes selection processes often face a fundamental choice: whether to make decisions themselves or to delegate authority to another entity whose incentives may only be partially aligned with their own. Such delegation arises naturally in settings like graduate admissions, hiring, or promotion, where a principal (e.g. a professor or worker) either reviews applicants personally or decisions are delegated to an agent (e.g. a committee or boss) that evaluates applicants efficiently, but according to a potentially misaligned objective. We study this trade-off in a stylized selection model with noisy signals. The principal incurs a cost for selecting applicants, but can evaluate applicants based on their fit with a project, team, workplace, etc. In contrast, the agent evaluates applicants solely on the basis of a signal that correlates with the principal's metric, but this comes at no cost to the principal. Our goal is to characterize when delegation is beneficial versus when decision-making should remain with the principal. We compare these regimes along three dimensions: (i) the principal's utility, (ii) the quality of the selected applicants according to the principal's metric, and (iii) the fairness of selection outcomes under disparate signal qualities.

Figures (6)

• Figure 1: We plot the expected fraction of hires (normalized by demographic ratios) from group $A$ (solid lines) and group $B$ (dashed lines) respectively as a function of the agent's selection threshold $\tau_1$ for different levels of bias $\beta$ on the mean of group $B$'s observed score distribution ($\tilde{s}$) and different levels of population skew ($\Lambda_A$). As $\tau_1$ increases, the gap between the groups grows uniformly indicating that the disadvantaged group suffers as the selection process becomes more selective (from blue outwards to red). The same trend is observed in the magnitude of bias ($\beta$). However, as the prevalence of the majority group in the population ($\Lambda_A$) increases, the leading group has little scope for gaining additional advantage, so the extent of disparities actually diminishes.
• Figure 2: We plot the expected fraction of hires (normalized by demographic ratios) from group $A$ (solid lines) and group $B$ (dashed lines) respectively as a function of the agent's selection threshold $\tau_1$ ($> 0$) for different levels of the ratio $r = \sigma_{\tilde{s}, B}/\sigma_{\tilde{s}, A}$ and different levels of population skew ($\Lambda_A$). The ratio $r$ captures how much more noisy group $B$'s signals are with respect to group $A$. In this case, group $B$ becomes increasingly more favored for selection and unfairness grows in favor of group $B$ as $r$ and $\tau_1$ increase.
• Figure 3: The principal's net expected utility per hired applicant $v(\tilde{\tau}^*)$ is non-monotonic in $\alpha$ when the principal does not delegate. Parameter combinations for sub-figures: (a) $\sigma_e = 2$, $c_{rev} = 0.1$. (b) $\sigma_s = 1.5$, $\sigma_f = 1$. (c) $\sigma_s = 1.5$, $\sigma_f = 1$, $\sigma_{ef} = \sigma_{es} = 0.5$, $c_{rev} = 0.1$.
• Figure 4: We plot $\Delta_{quality}$ and $\Delta_{utility}$ as a function of $\alpha$ for different levels of agent's threshold $\tau_1$. Positive values of $\Delta$ indicate that the principal prefers delegation. Parameter combination: $c_{rev} = 0.1$, $\sigma_f = 1$, $\sigma_s = 2$, $\sigma_{\tilde{f}} = 1.12$, $\sigma_{\tilde{s}} = 2.06$. We provide a more comprehensive graphical representation of regimes where delegation is beneficial in Appendix \ref{['app:extra_fig']}.
• Figure 5: We plot the expected quality of a selected applicant (when the agent uses a selection threshold of $\tau_1$) as a function of the variance $\sigma_{\tilde{s}}$ of the noisy signal $\tilde{s}$. As $\sigma_{\tilde{s}}$ increases, the expected quality decays monotonically for all $\alpha$.

Theorems & Definitions (28)

• Lemma 3.1
• Corollary 3.2
• Corollary 3.3
• Lemma 3.4
• Theorem 3.5
• Corollary 3.6
• Theorem 4.1
• Corollary 4.2
• Lemma 4.3
• Claim 4.4