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Dividing the Spoils: Can AI Make Team Assignments Fair?

"Explore how fair division algorithms, particularly those enhanced with AI, are changing the way teams are formed, ensuring equity and satisfaction for all involved."


Imagine you're a league organizer tasked with forming balanced and satisfied teams from a pool of diverse players. It's a challenge that goes beyond simply assigning individuals to groups. It requires a delicate balancing act to ensure fairness and satisfaction for everyone involved. Traditionally, this process might rely on manual selection, prone to biases and inefficiencies.

Fair division, a field of economics and computer science, tackles the problem of dividing resources or tasks among individuals or groups in a way that minimizes conflict and maximizes satisfaction. Recently, researchers have been exploring how to apply fair division algorithms to team assignments, considering the preferences of both the teams and the individuals involved.

A new study delves into the complexities of fair division in team formation, introducing algorithms that aim to guarantee envy-freeness and stability. These algorithms not only seek to distribute talent equitably but also take into account the personal preferences of the participants, ensuring a more harmonious and productive team environment.

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A Word With Two Lives: Gathering and Justice

The word "fair" carries two distinct meanings relevant to this discussion: a temporary public gathering for entertainment and commerce, and, as Merriam-Webster puts it, being free from favor toward either side with a proper balance of conflicting interests. The Washington State Fair exemplifies the first sense, having begun in Puyallup in 1900, celebrated 125 years in 2025, and welcomed over one million guests across a 20-day run to become the largest single attended event in the state. Wikipedia likewise notes that fairs are typically temporary gatherings with scheduled times lasting from an afternoon to several weeks. That scale is a useful reminder of how many distinct preferences and competing claims can converge on a single shared resource, so when AI is asked to divide the spoils of such a gathering, the second meaning of fair becomes the operative challenge.

No Universal Yardstick

There is no single accepted method for defining or measuring fairness in team assignments, and approaches vary widely by context. Common strategies lean on formal ideals such as proportional representation, envy-freeness, or equality of opportunity, but translating those ideals into a real roster involves choices about how to weigh individual preferences. Because these definitions can conflict, an outcome that satisfies one standard can fail another, and reasonable observers may disagree about which result is genuinely fair. In practice, the field is characterized by trade-offs and context-dependent judgment rather than a settled, universal method.

A Long Line of Public Gatherings

The Cambridge Dictionary traces "fair" to a public event, usually held outside, where goods and sometimes farm animals are shown and sold and where food and entertainment are often present. This long-standing sense of the fair as a market and celebration long predates any question of algorithmic allocation. It serves as a reminder that dividing resources—goods, spaces, or places at a gathering—has always involved deciding who gets what. Formal, automated methods for making those decisions equitable are, by comparison, far more recent.

The Two-Sided Preference Problem: Why It Matters

Diverse sports team formed with AI, equations in background.

Traditional fair division algorithms often focus on one-sided preferences, meaning they only consider the desires of one party involved. In team assignments, this might mean only considering the team's preferences for players, without regard for the players' own preferences for which team they'd like to join. This oversight can lead to suboptimal outcomes and dissatisfaction.

The new research addresses this limitation by incorporating two-sided preferences, where both the teams and the individuals have a say in the assignment process. This approach acknowledges that individuals might have reasons to prefer certain teams, such as familiarity with the coach, proximity to their home, or the team's overall culture. By considering these preferences, the algorithm aims to create assignments that are not only fair but also mutually beneficial.

  • Envy-Freeness: Ensures that no team envies another, meaning they wouldn't prefer another team's set of members over their own.
  • Swap Stability: Prevents situations where two individuals would both be better off swapping teams, maintaining overall satisfaction.
  • Individual Stability: Guarantees that no individual would prefer to leave their assigned team for another, promoting team cohesion and commitment.
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An Evolving Research Front

Research on algorithmic fairness in group decision-making is still young and moving quickly, so findings are frequently preliminary rather than settled. Much of the current work explores new metrics, estimation methods, and ways of incorporating user feedback into assignment systems. The field is not yet at a stage where consensus results can be stated with confidence. Readers should treat specific claims here as emerging work that is likely to be refined, challenged, or superseded as the research matures.

Fairness in Practice Is Messy

Critics of automated assignment systems point out that mathematical fairness does not automatically produce outcomes people perceive as fair. Systems can fail when the underlying data reflects existing bias, when one fairness criterion is prioritized at the expense of others, or when users do not trust the process behind the decision. There are also documented cases in adjacent decision-making domains where algorithms reinforced rather than corrected inequities. These failures underline that fairness cannot be treated purely as an optimization problem divorced from human judgment and organizational context.

Competing Ideas of Fairness

Different fairness conceptions lead to materially different assignments, so comparing approaches requires specifying the standard first. Proportionality, envy-freeness, equality of outcomes, and equality of opportunity can each be defended on their own terms, yet they frequently disagree about which team composition is best. A method that looks fair under one lens can look arbitrary under another. Because no ranking of these criteria is universally accepted, comparative analysis in this area tends to be conditional rather than absolute.

The study focuses on guaranteeing envy-freeness up to one participant (EF1), which means that any envy can be eliminated by removing just one member from the envied team. This condition, combined with swap stability and individual stability, ensures a robust and equitable allocation that minimizes dissatisfaction and promotes team harmony.

The Future of Fair Team Formation

As AI continues to evolve, fair division algorithms hold immense potential for revolutionizing team formation across various domains. By incorporating two-sided preferences and prioritizing stability, these algorithms can create more equitable and satisfying team environments, leading to improved performance and overall morale. Embracing these innovative approaches promises a future where team assignments are not only fair but also contribute to the success and well-being of all involved.

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Where the Conversation Stands

Putting the available material together, the central tension is between fairness as a technical property and fairness as a lived experience. Technical definitions give designers something concrete to optimize, but they cannot resolve competing values on their own. Broadly, commentators suggest that defensible systems will need to make their fairness criteria explicit and subject them to stakeholder input. Any synthesis at this stage should therefore be read as provisional, reflecting a field still defining its own terms.

Open Questions Ahead

The next frontier for AI-assisted assignment likely lies in making fairness standards more transparent, adaptive, and responsive to individual preferences. Future systems may incorporate richer preference data and explain their allocation logic in ways users can scrutinize. There is also open ground in defining fair procedures, not just fair results, since the legitimacy of a decision may depend on how it was reached. These directions are more plausible projections than confirmed outcomes, and their feasibility remains uncertain.

Fairness Beyond a Single Assignment

Team assignments do not happen in isolation; they sit within organizations, institutions, and communities where fairness concerns accumulate across many repeated decisions. A single assignment can look equitable while the broader pattern across many assignments remains skewed. Systemic challenges include data quality, power imbalances in who defines the criteria, and the difficulty of auditing outcomes over time. Addressing those larger patterns is likely to matter as much as perfecting any individual allocation algorithm.

The Human Stakes of Fairness

Dictionary.com defines fair as the treating of all sides alike, justly and equitably, such as a fair compromise, while The Free Dictionary observes that of fairness-related terms, "fair" is the most general and that "just" stresses conformity with what is legally or ethically right or proper. For people on the receiving end of AI-made assignments, these distinctions matter: perceived fairness depends on whether outcomes feel like treating all sides alike and whether they square with ethical or legal norms. An algorithm may optimize a mathematical definition of fairness while missing the human sense of being heard or understood. Ultimately, any assignment system is measured by the people it affects and whether they judge its verdicts to be fair.

About this Article -

Written with AI assistance from published research, and reviewed by the Mystum team. See our About page for more information.

This article is based on research published under:

DOI-LINK: 10.1016/j.geb.2024.07.008,

Title: Fair Division With Two-Sided Preferences

Subject: cs.gt econ.th

Authors: Ayumi Igarashi, Yasushi Kawase, Warut Suksompong, Hanna Sumita

Published: 12-06-2022

Everything You Need To Know

1

What is fair division, and how is it applied to team assignments?

Fair division is a field in economics and computer science focused on dividing resources or tasks fairly among individuals or groups. When applied to team assignments, it uses algorithms to create teams that minimize conflict and maximize satisfaction among participants. Researchers are employing these algorithms to consider preferences of both teams and individuals, ensuring equitable distribution of talent and a harmonious team environment. The goal is to move beyond manual selection, which is prone to bias, and achieve more objective and efficient team formations.

2

How do two-sided preference algorithms improve team assignments compared to traditional methods?

Traditional algorithms often rely on one-sided preferences, typically focusing on team desires without considering individual preferences. This can lead to suboptimal outcomes and dissatisfaction. Two-sided preference algorithms, however, incorporate the preferences of both teams and individuals. This means the algorithm considers factors like a player's preference for a team based on the coach, location, or team culture. By considering these two-sided preferences, the algorithm aims to create assignments that are not only fair but also mutually beneficial, leading to better team cohesion and overall satisfaction.

3

What are the key principles of fairness used in the algorithms mentioned, and what do they mean?

The study emphasizes three key principles: * **Envy-Freeness:** Ensures that no team envies another, meaning they wouldn't prefer to have another team's members over their own. * **Swap Stability:** Prevents situations where two individuals would both be better off swapping teams, which preserves overall satisfaction. * **Individual Stability:** Guarantees that no individual would prefer to leave their assigned team for another, thus promoting team cohesion and commitment. The research focuses on 'envy-freeness up to one participant (EF1)' which means any envy can be eliminated by removing just one member from the envied team, which contributes to a more robust and equitable allocation.

4

How does considering individual preferences impact team dynamics and morale?

Incorporating individual preferences significantly impacts team dynamics and morale. When individuals are assigned to teams based on their preferences (like team culture, proximity, or coach familiarity), they are more likely to feel valued and satisfied. This leads to better team cohesion, increased commitment, and improved overall morale. When individuals are placed on teams where they want to be, it creates a more positive and productive team environment, where members are more likely to collaborate effectively and contribute to the team's success.

5

What are the future implications of AI-driven fair division algorithms for team formation?

The future of team formation, as envisioned by AI-driven fair division algorithms, promises a revolution across various domains. By leveraging two-sided preferences and prioritizing stability, these algorithms have the potential to create more equitable and satisfying team environments. This leads to improved team performance, higher morale, and a more positive overall experience for all involved. As AI continues to evolve, these algorithms can be refined and adapted to complex scenarios, ensuring that team assignments are not just fair but also contribute to the success and well-being of every participant.

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