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Randomization is often hailed as a fair and useful procedure to distribute government benefits in contexts of oversubscription, with the added benefit of allowing assessments of the impact of government programs. However, little is known about whether those affected by randomization also perceive it as a legitimate. Employing a three-pronged multi-method approach, we show that program beneficiaries and the general public do not share the scholars’ enthusiasm for random assignment. Our quasi-experimental analysis of 3,000 applicants for social housing lotteries in Brazil reveals tepid support for randomization, and this support is higher among winners than among non-winners. In-depth interviews suggest that applicants believe lotteries miss the “most deserving” beneficiaries. Finally, our general population survey experiment corroborates that lotteries are not perceived as fair or efficient when compared to other methods. While an ethically desirable and useful method for selecting beneficiaries, randomization fails to legitimatize government programs.