An agent with star-shaped preferences has a unique ideal point (optimum), where he is maximally satisfied.
However, knowing the optimum of an agent is insufficient for deciding which of two non-optimal distributions they prefer.
Hence, the set of all these points is a star domain with respect to the optimum p. It is not clear whether the converse holds too.
[clarification needed] Landsberger and Meilijson[3] define star-shaped utility functions.
They use this definition to explain the fact that people purchase both insurance and lotteries.
Border and Jordan[1] characterize the strategyproof mechanisms for agents with quadratic preferences - a special case of star-shaped preferences (see median voting rule).
Lindner, Nehring and Puppe[4] and Goel, Krishnaswami, Sakshuwong and Aitamurto[5] study agents with metric-based preferences with the