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.

翻译：在我们要汇总人们主观评价的环境下,当大量低努力的人总是报告“好”而不管真正质量如何时,多元投票可能毫无意义。 “ 令人惊讶的受欢迎” 方法, 选择了与先前相比最令人惊讶的答案, 在某种程度上处理这一问题。 但是, 这对于人们的战略来说仍然不够强大。 在这样的背景下, 大量的人被要求回答少量的多选择问题( 多任务, 大群体), 我们提议一种对人们的战略来说是强大的信息汇总方法。 有趣的是, 这个方法可以被视为旋转的“ 良好 ” 。 “ 令人惊讶的受欢迎” 方法, 选择了与先前相比最令人惊讶的答案, 在某种程度上, 但是对于人们来说, 它仍然不够强大。 在这样的环境下, DMI- 集中是一个普通的组合方法, 它是一个普通的组合方法, 它旨在最大限度地增加由每个组合组成的简单组合组成的组合的体数量, 意味着组合体的产值的乘积。 有趣的是, 当 DMI- 数据分组中, 当一个简单的组合体的解算法, 是一个常态的分类法, 它是一个不使用任何的解式的内, 。