Person:

Mandal, Debmalya

We study the social choice problem where a group of n voters report their preferences over alternatives and a voting rule is used to select an alternative. We show that when the preferences of voters are positively correlated according to the Kendall-Tau distance, the probability that any scoring rule is not ex post incentive compatible (EPIC) goes to zero exponentially fast with the number of voters, improving over the previously known rate of 1/√n for independent preferences. Motivated by rank-order models from machine learning, we introduce two examples of positively-correlated models, namely Conditional Mallows and Conditional Plackett-Luce. Conditional Mallows satisfies Kendall-Tau correlation and fits our positive result. We also prove that Conditional Plackett-Luce becomes EPIC exponentially quickly.

Peer prediction mechanisms incentivize agents to truthfully report their signals, in the absence of a verification mechanism, by comparing their reports with those of their peers. Prior work in this area is essentially restricted to the case of homogeneous agents, whose signal distributions are identical. This is limiting in many domains, where we would expect agents to differ in taste, judgment and reliability. Although the Correlated Agreement (CA) mechanism [30] can be extended to handle heterogeneous agents, the new challenge is with the efficient estimation of agent signal types. We solve this problem by clustering agents based on their reporting behavior, proposing a mechanism that works with clusters of agents and designing algorithms that learn such a clustering. In this way, we also connect peer prediction with the Dawid and Skene [5] literature on latent types. We retain the robustness against coordinated misreports of the CA mechanism, achieving an approximate incentive guarantee of ε-informed truthfulness. We show on real data that this incentive approximation is reasonable in practice, and even with a small number of clusters.