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

TL;DR

This paper introduces a new family of information measures called volume mutual information and develops practical mechanisms for multi-task peer prediction that work with a finite number of tasks, improving upon previous methods.

Contribution

It proposes VMI-Mechanisms based on volume mutual information, extending the DMI-Mechanism to be more practical and approximately optimal with finite tasks.

Findings

VMI-Mechanisms are practical and approximately optimal.

Volume mutual information provides a geometric interpretation of information.

DMI-Mechanism may not be optimal, but VMI-Mechanisms can improve performance.

Abstract

In the setting where we ask participants multiple similar possibly subjective multi-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 feedback without verification. A series of works have successfully designed multi-task peer prediction mechanisms where reporting truthfully is better than any other strategy (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 dominantly truthful but also works for a finite number of tasks (practical). However, the existence of other practical dominantly-truthful multi-task peer prediction mechanisms remains to be an open question. This work answers the above question by providing 1. a new family of information-monotone information measures: volume mutual information (VMI), where DMI is a special case; 2. a new family of practical dominantly-truthful multi-task peer prediction mechanisms, VMI-Mechanisms. To illustrate the importance of VMI-Mechanisms, we also provide a tractable effort incentive optimization goal. We show that DMI-Mechanism may not be not optimal but we can construct a sequence of VMI-Mechanisms that are approximately optimal. The main technical highlight in this paper is a novel geometric information measure, Volume Mutual Information, that is based on a simple idea: we can measure an object A's information amount by the number of objects that is less informative than A. Different densities over the object lead to different information measures. This also gives Determinant Mutual Information a simple geometric interpretation.