Fairness in the Multi-Secretary Problem

TL;DR

This paper explores fairness in online multi-secretary and multi-winner election problems by proposing mechanisms that combine online algorithms with social choice rules, supported by theoretical and experimental analysis.

Contribution

It introduces new mechanisms that integrate online decision-making techniques with social choice fairness principles, addressing limitations of existing proportionality notions.

Findings

Proposed mechanisms achieve improved fairness in online settings.

Theoretical analysis demonstrates the effectiveness of the mechanisms.

Experimental results validate the practical performance of the proposed methods.

Abstract

This paper bridges two perspectives: it studies the multi-secretary problem through the fairness lens of social choice, and examines multi-winner elections from the viewpoint of online decision making. After identifying the limitations of the prominent proportionality notion of Extended Justified Representation (EJR) in the online domain, the work proposes a set of mechanisms that merge techniques from online algorithms with rules from social choice -- such as the Method of Equal Shares and the Nash Rule -- and supports them through both theoretical analysis and extensive experimental evaluation.