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In the setting where we ask participants multiple similar possibly subjectivemulti-choice questions (e.g. Do you like Bulbasaur? Y/N; do you like Squirtle?Y/N), peer prediction aims to design mechanisms that encourage honest feedbackwithout verification. A series of works have successfully designed multi-taskpeer prediction mechanisms where reporting truthfully is better than any otherstrategy (dominantly truthful), while they require an infinite number of tasks.A recent work proposes the first multi-task peer prediction mechanism,Determinant Mutual Information (DMI)-Mechanism, where not only is dominantlytruthful but also works for a finite number of tasks (practical). However, theexistence of other practical dominantly-truthful multi-task peer predictionmechanisms remains to be an open question. This work answers the above questionby providing 1. a new family of information-monotone information measures:volume mutual information (VMI), where DMI is a special case; 2. a new familyof practical dominantly-truthful multi-task peer prediction mechanisms,VMI-Mechanisms. To illustrate the importance of VMI-Mechanisms, we also providea tractable effort incentive optimization goal. We show that DMI-Mechanism maynot be not optimal but we can construct a sequence of VMI-Mechanisms that areapproximately optimal. The main technical highlight in this paper is a novelgeometric information measure, Volume Mutual Information, that is based on asimple idea: we can measure an object A's information amount by the number ofobjects that is less informative than A. Different densities over the objectlead to different information measures. This also gives Determinant MutualInformation a simple geometric interpretation.

More Dominantly Truthful Multi-task Peer Prediction with a Finite Number of Tasks