Information Elicitation Meets Clustering
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In the setting where we want to aggregate people's subjective evaluations, plurality vote may be meaningless when a large amount of low-effort people always report "good" regardless of the true quality. "Surprisingly popular" method, picking the most surprising answer compared to the prior, handle this issue to some extent. However, it is still not fully robust to people's strategies. Here in the setting where a large number of people are asked to answer a small number of multi-choice questions (multi-task, large group), we propose an information aggregation method that is robust to people's strategies. Interestingly, this method can be seen as a rotated "surprisingly popular". It is based on a new clustering method, Determinant MaxImization (DMI)-clustering, and a key conceptual idea that information elicitation without ground-truth can be seen as a clustering problem. Of independent interest, DMI-clustering is a general clustering method that aims to maximize the volume of the simplex consisting of each cluster's mean multiplying the product of the cluster sizes. We show that DMI-clustering is invariant to any non-degenerate affine transformation for all data points. When the data point's dimension is a constant, DMI-clustering can be solved in polynomial time. In general, we present a simple heuristic for DMI-clustering which is very similar to Lloyd's algorithm for k-means. Additionally, we also apply the clustering idea in the single-task setting and use the spectral method to propose a new aggregation method that utilizes the second-moment information elicited from the crowds.
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