Dominantly Truthful Peer Prediction Mechanisms with a Finite Number of Tasks

Abstract

In the setting where participants are asked multiple similar possibly subjective multi-choice questions (e.g. Do you like Panda Express? Y/N; do you like Chick-fil-A? Y/N), a series of peer prediction mechanisms have been designed to incentivize honest reports and some of them achieve dominantly truthfulness: truth-telling is a dominant strategy and strictly dominate other “non-permutation strategy” with some mild conditions. However, those mechanisms require the participants to perform an infinite number of tasks. When the participants perform a finite number of tasks, these mechanisms only achieve approximated dominant truthfulness. The existence of a dominantly truthful multi-task peer prediction mechanism that only requires a finite number of tasks remains to be an open question that may have a negative result, even with full prior knowledge. This paper answers this open question by proposing a family of mechanisms, VMI-Mechanisms, that are dominantly truthful with a finite number of tasks. A special case of this family, DMI-Mechanism, only requires ≥ 2 C tasks where C is the number of choices for each question ( C = 2 for binary-choice questions). The implementation of these mechanisms does not require any prior knowledge (detail-free) and only requires ≥ 2 participants. To the best of our knowledge, any mechanism of the family is the first dominantly truthful peer prediction mechanism that works for a finite number of tasks. The core of these new mechanisms is a new family of information-monotone information measures: volume mutual information (VMI). VMI is based on a simple geometric information measure design method, the volume method. The volume method measures the informativeness of an object by “counting” the number of objects that are less informative than it. In other words, the more objects that the object of interest dominates, the more informative it is considered to be. Finally, in the setting where agents need to invest efforts to obtain their private signals, we show how to select the mechanism to optimally incentivize efforts among a proper set of VMI-Mechanisms.