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Goals, Constraints, and Transparently Fair Assignments: A Field Study of Randomization Design in the UEFA Champions League

Boczon, Marta and Wilson, Alistair (2022) Goals, Constraints, and Transparently Fair Assignments: A Field Study of Randomization Design in the UEFA Champions League. Management Science. (In Press)

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We analyze the design of a randomization procedure in a field setting with high stakes and substantial public interest: matching sports teams in the UEFA Champions League. While striving for fairness in the chosen lottery -giving teams similar distributions over potential partners - the designers seek to balance two conflicting forces: (i) imposing a series of combinatorially complex constraints on the feasible matches; (ii) designing an easy-to-understand and credible randomization. We document the tournament's solution, which focuses on sequences of uniform draws over each element in the final match, assisted by a computer to form the support for each draw. We first show that the constraints' effects within this procedure are substantial, with shifts in expected prizes of up to a million euro and large distortions in match likelihoods of otherwise comparable team pairs. However, examining all possible counterfactual lotteries over the feasible assignments, we show that the generated inequalities are for the most part unavoidable, that the tournament design is close to a constrained-best. In two extensions we outline how substantially fairer randomizations are possible when the constraints are weakened, and how the developed procedure can be adopted to more-general settings.


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Item Type: Article
Status: In Press
CreatorsEmailPitt UsernameORCID
Wilson, Alistairalistair.wilson@pitt.edualistair0000-0001-8118-2376
Date: February 2022
Date Type: Acceptance
Journal or Publication Title: Management Science
Schools and Programs: Dietrich School of Arts and Sciences > Economics
Refereed: Yes
Article Type: Research Article
Date Deposited: 23 Feb 2022 22:16
Last Modified: 23 Feb 2022 22:16


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