Least-Unpopularity-Factor Matching

One of the most common administrative tasks that organizations perform is the assignment of people to positions based on the people’s preferences. A computer program that chooses an assignment automatically would be useful, but what assignment rule should it follow? I proposed the rule of least-unpopularity-factor matching, which is difficult to subvert and always designates a “best” assignment—but I proved that there is no practical way to actually compute that assignment for large numbers of people and positions. The result eliminates one possibility in the search for a rule suitable for an automatic assignment program but suggests where a suitable rule might be found.