  We introduce the concept of a multi-principal assistance game (MPAG), and
circumvent an obstacle in social choice theory, Gibbard's theorem, by using a
sufficiently collegial preference inference mechanism. In an MPAG, a single
agent assists N human principals who may have widely different preferences.
MPAGs generalize assistance games, also known as cooperative inverse
reinforcement learning games. We analyze in particular a generalization of
apprenticeship learning in which the humans first perform some work to obtain
utility and demonstrate their preferences, and then the robot acts to further
maximize the sum of human payoffs. We show in this setting that if the game is
sufficiently collegial, i.e. if the humans are responsible for obtaining a
sufficient fraction of the rewards through their own actions, then their
preferences are straightforwardly revealed through their work. This revelation
mechanism is non-dictatorial, does not limit the possible outcomes to two
alternatives, and is dominant-strategy incentive-compatible.
