We propose a cost-effective framework for preference elicitation and aggregation under the Plackett-Luce model with features. Given a budget, our framework iteratively computes the most cost-effective elicitation questions in order to help the agents make a better group decision. We illustrate the viability of the framework with experiments on Amazon Mechanical Turk, which we use to estimate the cost of answering different types of elicitation questions. We compare the prediction accuracy of our framework when adopting various information criteria that evaluate the expected information gain from a question. Our experiments show carefully designed information criteria are much more efficient, i.e., they arrive at the correct answer using fewer queries, than randomly asking questions given the budget constraint.
As a key role in preference elicitation, information criteria have been widely investigated for different applications. Standard information criteria include D-optimality (used in ) and E-optimality. @cite_0 and @cite_8 use minimax-regret-based criterion for stable matching and aggregation respectively. @cite_9 proposed yet another criterion, defined on the certainty of the least certain pairwise comparison over the intrinsic utilities (part of the parameter of their general random utility models) of all alternatives. Our MPC criterion extends the criterion by @cite_9 . To predict a single agent's top @math preference, we search over a subset of all pairwise comparisons (see ). To help make a group decision, we search over all pairwise comparisons of all agents in the key group to find the least certain pairwise comparison (Equation ).
@cite_0 @cite_9 @cite_8
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We investigate robust decision-making under utility uncertainty, using the maximin criterion, which optimizes utility for the worst case setting. We show how it is possible to efficiently compute the maximin optimal recommendation in face of utility uncertainty, even in large configuration spaces. We then introduce a new decision criterion, setwise maximin utility SMMU, for constructing optimal recommendation sets: we develop algorithms for computing SMMU and present experimental results showing their performance. Finally, we discuss the problem of elicitation and prove analogously to previous results related to regret-based and Bayesian elicitation that SMMU leads to myopically optimal query sets. We study the House Allocation problem (also known as the Assignment problem), i.e., the problem of allocating a set of objects among a set of agents, where each agent has ordinal preferences (possibly involving ties) over a subset of the objects. We focus on truthful mechanisms without monetary transfers for finding large Pareto optimal matchings. It is straightforward to show that no deterministic truthful mechanism can approximate a maximum cardinality Pareto optimal matching with ratio better than 2. We thus consider randomized mechanisms. We give a natural and explicit extension of the classical Random Serial Dictatorship Mechanism (RSDM) specifically for the House Allocation problem where preference lists can include ties. We thus obtain a universally truthful randomized mechanism for finding a Pareto optimal matching and show that it achieves an approximation ratio of eovere-1. The same bound holds even when agents have priorities (weights) and our goal is to find a maximum weight (as opposed to maximum cardinality) Pareto optimal matching. On the other hand we give a lower bound of 18 over 13 on the approximation ratio of any universally truthful Pareto optimal mechanism in settings with strict preferences. In the case that the mechanism must additionally be non-bossy, an improved lower bound of eovere-1 holds. This lower bound is tight given that RSDM for strict preference lists is non-bossy. We moreover interpret our problem in terms of the classical secretary problem and prove that our mechanism provides the best randomized strategy of the administrator who interviews the applicants. We consider how to combine the preferences of multiple agents despite the presence of incompleteness and incomparability in their preference orderings. An agent's preference ordering may be incomplete because, for example, there is an ongoing preference elicitation process. It may also contain incomparability as this is useful, for example, in multi-criteria scenarios. We focus on the problem of computing the possible and necessary winners, that is, those outcomes which can be or always are the most preferred for the agents. Possible and necessary winners are useful in many scenarios including preference elicitation. First we show that computing the sets of possible and necessary winners is in general a difficult problem as is providing a good approximation of such sets. Then we identify general properties of the preference aggregation function which are sufficient for such sets to be computed in polynomial time. Finally, we show how possible and necessary winners can be used to focus preference elicitation. In this paper we present a general treatment of the preference aggregation problem, in which multiple preferences over objects must be combined into a single consensus ranking. We consider two instances of this problem: unsupervised aggregation where no information about a target ranking is available, and supervised aggregation where ground truth preferences are provided. For each problem class we develop novel learning methods that are applicable to a wide range of preference types. Specifically, for unsupervised aggregation we introduce the Multinomial Preference model (MPM) which uses a multinomial generative process to model the observed preferences. For the supervised problem we develop a supervised extension for MPM and then propose two fully supervised models. The first model employs SVD factorization to derive effective item features, transforming the aggregation problems into a learning-to-rank one. The second model aims to eliminate the costly SVD factorization and instantiates a probabilistic CRF framework, deriving unary and pairwise potentials directly from the observed preferences. Using a probabilistic framework allows us to directly optimize the expectation of any target metric, such as NDCG or ERR. All the proposed models operate on pairwise preferences and can thus be applied to a wide range of preference types. We empirically validate the models on rank aggregation and collaborative filtering data sets and demonstrate superior empirical accuracy.