  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.
