# The Price of Local Fairness in Multistage Selection

## TL;DR

This paper explores fairness in multi-stage decision processes, introducing new fairness notions, and quantifies the trade-offs between local fairness constraints and decision accuracy through theoretical and empirical analysis.

## Contribution

It extends fairness concepts to multi-stage settings, proposes a linear programming approach for fair selection, and analyzes the cost of local fairness in such scenarios.

## Key findings

- The price of local fairness is smaller when the sensitive attribute is observed early.
- Globally fair selections tend to be more locally fair when the sensitive attribute is observed later.
- Small trade-offs exist between fairness and precision in multi-stage selection problems.

## Abstract

The rise of algorithmic decision making led to active researches on how to define and guarantee fairness, mostly focusing on one-shot decision making. In several important applications such as hiring, however, decisions are made in multiple stage with additional information at each stage. In such cases, fairness issues remain poorly understood. In this paper we study fairness in $k$-stage selection problems where additional features are observed at every stage. We first introduce two fairness notions, local (per stage) and global (final stage) fairness, that extend the classical fairness notions to the $k$-stage setting. We propose a simple model based on a probabilistic formulation and show that the locally and globally fair selections that maximize precision can be computed via a linear program. We then define the price of local fairness to measure the loss of precision induced by local constraints; and investigate theoretically and empirically this quantity. In particular, our experiments show that the price of local fairness is generally smaller when the sensitive attribute is observed at the first stage; but globally fair selections are more locally fair when the sensitive attribute is observed at the second stage---hence in both cases it is often possible to have a selection that has a small price of local fairness and is close to locally fair.