"Is Approval V oting Optimal Given Approval V otes?" NeurIPS-2015. The reviewer points to a paper about "threshold voting," but this is a very different idea.

We propose a novel and flexible rank-breaking-then-composite-marginal-likelihood (RBCML) framework for learning random utility models (RUMs), which include the Plackett-Luce model. We characterize conditions for the objective function of RBCML to be strictly log-concave by proving that strict log-concavity is preserved under convolution and marginalization. We characterize necessary and sufficient conditions for RBCML to satisfy consistency and asymptotic normality. Experiments on synthetic data show that RBCML for Gaussian RUMs achieves better statistical efficiency and computational efficiency than the state-of-the-art algorithm and our RBCML for the Plackett-Luce model provides flexible tradeoffs between running time and statistical efficiency.

We tackle the problem of identifiability and efficient learning of mixtures of Random Utility Models (RUMs). We show that when the PDFs of utility distributions are symmetric, the mixture of k RUMs (denoted by k-RUM) is not identifiable when the number of alternatives m is no more than 2k-1. On the other hand, when m ≥ max{4k-2,6}, any k-RUM is generically identifiable. We then propose three algorithms for learning mixtures of RUMs: an EM-based algorithm, which we call E-GMM, a direct generalized-method-of-moments (GMM) algorithm, and a sandwich (GMM-E-GMM) algorithm that combines the other two. Experiments on synthetic data show that the sandwich algorithm achieves the highest statistical efficiency and GMM is the most computationally efficient. Experiments on real-world data at Preflib show that Gaussian k-RUMs provide better fitness than a single Gaussian RUM, the Plackett-Luce model, and mixtures of Plackett-Luce models w.r.t. commonly-used model fitness criteria. To the best of our knowledge, this is the first work on learning mixtures of general RUMs.

For massive and heterogeneous modern datasets, it is of fundamental interest to provide guarantees on the accuracy of estimation when computational resources are limited. In the application of learning to rank, we provide a hierarchy of rank-breaking mechanisms ordered by the complexity in thus generated sketch of the data. This allows the number of data points collected to be gracefully traded off against computational resources available, while guaranteeing the desired level of accuracy. Theoretical guarantees on the proposed generalized rank-breaking implicitly provide such trade-offs, which can be explicitly characterized under certain canonical scenarios on the structure of the data.

A paradigmatic problem in social choice theory deals with the aggregation of subjective preferences of individuals --- represented as rankings of alternatives --- into a social ranking. We are interested in settings where individuals are uncertain about their own preferences, and represent their uncertainty as distributions over rankings. Under the classic objective of minimizing the (expected) sum of Kendall tau distances between the input rankings and the output ranking, we establish that preference elicitation is surprisingly straightforward and near-optimal solutions can be obtained in polynomial time. We show, both in theory and using real data, that ignoring uncertainty altogether can lead to suboptimal outcomes.

They pinpoint families of voting rules that exhibit robustness: they are accurate in the limit with respect to a wide Classic social choice theory assumes that votes are range of noise models, which govern the way noisy votes are independent (but possibly conditioned on an underlying generated, given the ground truth [Caragiannis et al., 2013; objective ground truth). This assumption 2014]. is unrealistic in settings where the voters are connected While these results are promising, they rely on a crucial via an underlying social network structure, modeling assumption: votes are independent. This assumption as social interactions lead to correlated votes. We is clearly satisfied in some settings -- when votes are establish a general framework -- based on random submitted by computer Go programs [Jiang et al., 2014], say.