Selecting an intra-profile dictator

Preferences are often best aggregated by adopting the preference of one individual, who is then called an “intra-profile dictator” since her preference is decisive under the present preference profile. This paper explores how to select intra-profile dictators. First, we demonstrate that under a continuity requirement, any intra-profile dictatorship extends to a full dictatorship when the preference space has more than one dimension. Consequently, we provide two possibility results that allow for discontinuity. The first is an aggregation rule that selects the greatest element according to a linear (and therefore discontinuous) ranking over the preference space. The second is a rule that selects an order statistic according to a linear (and therefore discontinuous) ordering over the preference space.