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 are 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, a major issue
hinders the practical usage of those mechanisms: they 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 new mechanism,
Determinant based Mutual Information Mechanism (DMI-Mechanism), that is
dominantly truthful when the number of tasks is at least 2C and the number of
participants is at least 2. C is the number of choices for each question (C=2
for binary-choice questions). In addition to incentivizing honest reports,
DMI-Mechanism can also be transferred into an information evaluation rule that
identifies high-quality information without verification when there are at
least 3 participants. To the best of our knowledge, DMI-Mechanism is the first
dominantly truthful mechanism that works for a finite number of tasks, not to
say a small constant number of tasks.

本文提出了一种新的机制，基于行列式互信息机制 (DMI-Mechanism)，可以在只有有限数量 (至少为 2) 的任务情况下实现直接的诚实报告和互信息计算，并且可以作为信息精度评估规则。