Across nine main studies (N = 7,024) and nine supplemental studies (N = 3,279), we find that people make systematically different choices when choosing between individuals and choosing between equivalent policies that affect individuals. In college admissions and workplace hiring contexts, we randomly assigned participants to select one of two individuals or choose one of two selection policies. People were significantly more likely to choose a policy that would favor a disadvantaged candidate over a candidate with objectively higher achievements than they were to favor a specific disadvantaged candidate over a specific candidate with objectively higher achievements. We document these divergent choices among admissions officers, working professionals, and lay people, using both within-subject and between-subject designs, and across a range of stimuli and decision contexts. We find evidence that these choices diverge because thinking about policies causes people to rely more on their values and less on the objective attributes of the options presented, which overall, leads more people to favor disadvantaged candidates in selection contexts. This research documents a new type of preference reversal in important, real-world decision contexts, and has practical and theoretical implications for understanding why our choices so frequently violate our espoused policies.