Temporal Fairness in Decision Making Problems

TL;DR

This work introduces temporal fairness, a paradigm that embeds fairness considerations across time into decision-making optimization. Building from OP, it defines FOP and progressively incorporates historical fairness (HFOP), discounted historical fairness (DHFOP), and multi-step planning with future forecasts (MSDHFOP) to balance short-term quality with long-term equity. The framework is instantiated across four domains (CAP, VRP, TAP, NSP) and evaluated qualitatively, demonstrating that including historical and future information can improve fairness with modest computational overhead. The findings suggest practical paths for deploying temporally aware fairness in centralized optimization, and point to future work on multi-metric and multi-future fairness formulations.

Abstract

In this work we consider a new interpretation of fairness in decision making problems. Building upon existing fairness formulations, we focus on how to reason over fairness from a temporal perspective, taking into account the fairness of a history of past decisions. After introducing the concept of temporal fairness, we propose three approaches that incorporate temporal fairness in decision making problems formulated as optimization problems. We present a qualitative evaluation of our approach in four different domains and compare the solutions against a baseline approach that does not consider the temporal aspect of fairness.

Figures (6)

• Figure 1: Depicts a university course assignment, in which courses are to be assigned to lecturers with different levels of expertise in different areas. The lecturer in gray is on sabbatical leave.
• Figure 2: Depicts a concrete scenario of a university course assignment. Figure \ref{['subfig:unfair previous plans']} depicts the scenario in which $l_1$ was assigned a higher lecturing load over the past 4 semesters. Figure \ref{['subfig:fairness debt fair plan']} and \ref{['subfig:fairness debt unfair plan']} depict the cumulative lecturing load of $l_1$ (blue) and $l_2$ (red) with possible solutions to the current allocation problem (dashed gray). \ref{['subfig:fairness debt fair plan']} depicts the case where at timestep $t$ a fair allocation is made with both lecturers given the same load ($1.5$ courses each). \ref{['subfig:fairness debt unfair plan']} depicts the case where an unfair allocation is made and $l_2$ is assigned all the lecturing load (3 courses).
• Figure 3: Compares the fairness of the solutions computed using a fop (red) and hfop (blue) in a simple scenario with no quality metric $Q$. Each solution is evaluated with both the relative max-min fairness metric $F^\text{rmm}$, and its historical variant $F_H^\text{rmm}$, shown respectively in dashed and solid lines. The $x$ axis is in log scale.
• Figure 4: Depicts the discounted historical relative max-min fairness metric $F_{H,\gamma}^\text{rmm}$ in the setting where from time step $t=0$ onwards we schedule perfectly balanced loads. The smaller the discount factor $\gamma$, the faster the historical fairness is compensated.
• Figure 5: The quality $Q$, fairness $F^\text{qmmg}$, and historical fairness $F_H^\text{qmmg}$ of the solutions computed by $\textsc{hfop}\xspace$ under different values of $\beta$, in the course assignment domain.

Theorems & Definitions (7)

• Definition 1
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• Definition 7