Unraveling Fairness Notions: A Comprehensive Analysis of Implications and Paradoxes

In this paper, we explore the complex concept of fairness in allocation, where multiple agents with unequal entitlements are involved. We delve into various definitions and interpretations of fairness, which often lead to inconsistencies and misunderstandings within the research community. To address these issues, we present a comprehensive analysis of six fairness notions commonly used in the literature, including share-based notions, individual fairness, and global fairness.
Our analysis reveals that while some fairness notions are individually monotone, meaning they always prioritize the interests of one agent over another, others violate this property. This is where paradoxes come into play, as an agent may find it advantageous to distribute some of their entitlement to other agents, leading to a situation known as an inversion.
To better understand these concepts, let’s consider an analogy: imagine a group of friends sharing a pie equally among themselves. While each friend may feel that they deserve a fair share of the pie, there may be situations where some friends have more claims to certain slices than others. In this scenario, fairness notions such as share-based allocations can help ensure that each friend receives at least their share value, while individual fairness and global fairness notions prioritize different aspects of fairness, such as ensuring that no agent is disadvantaged relative to others or that the overall allocation is fair regardless of the entitlements of individual agents.
Our paper aims to clarify these complex concepts by providing a detailed analysis of each fairness notion, highlighting their strengths and weaknesses, and demonstrating how they can be applied in various scenarios. By understanding these nuances, researchers and practitioners can make more informed decisions when designing fair allocation systems that prioritize the interests of all agents involved.