This article considers what justification can be found for selecting randomly and in what circumstances it applies, including that of selecting patients to be treated by a scarce medical procedure. The author demonstrates that balancing the merits of fairness, common good, equal rights, and equal chance as they apply in various situations frequently leads to the conclusion that random selection may not be the most appropriate mode of selection. Broome acknowledges that, in the end, we may be forced to conclude that the only merit of random selection is the political one of guarding against partiality and oppression.