Addressing Bias in Online Selection with Limited Budget of Comparisons

TL;DR

This study explores how the allocated budget enhances the success probability of online selection algorithms as a multicolor secretary problem, allowing comparisons between candidates from distinct groups at a fixed cost.

Abstract

Consider a hiring process with candidates coming from different universities. It is easy to order candidates with the same background, yet it can be challenging to compare them otherwise. The latter case requires additional costly assessments, leading to a potentially high total cost for the hiring organization. Given an assigned budget, what would be an optimal strategy to select the most qualified candidate? We model the above problem as a multicolor secretary problem, allowing comparisons between candidates from distinct groups at a fixed cost. Our study explores how the allocated budget enhances the success probability of online selection algorithms.

Figures (8)

• Figure 1: Schematic description of a DT algorithm in the case of 3 groups
• Figure 2: Acceptance region of $\mathcal{A}_*$
• Figure 3: Single threshold algorithm: optimal threshold and corresponding success probability
• Figure 4: Single threshold: success probability for $2$ groups, with $N = 500$ and $\lambda \in [0,1]$
• Figure 5: Convergence to the asymptotic success probability, with $\lambda_k = 1/K$ for all $k \in [K]$

Theorems & Definitions (41)

• Remark 2.1
• Lemma 3.1
• Theorem 3.2
• Corollary 3.2.1
• Lemma 4.1
• Lemma 4.2
• Theorem 4.3
• Corollary 4.3.1
• Lemma A.1: jamieson2014lil
• proof