We develop new voting mechanisms for the case when voters and candidates are located in an arbitrary unknown metric space, and the goal is to choose a candidate minimizing social cost: the total distance from the voters to this candidate. Previous work has often assumed that only ordinal preferences of the voters are known (instead of their true costs), and focused on minimizing distortion: the quality of the chosen candidate as compared with the best possible candidate. In this paper, we instead assume that a (very small) amount of information is known about the voter preference strengths, not just about their ordinal preferences. We provide mechanisms with much better distortion when this extra information is known as compared to mechanisms which use only ordinal information. We quantify tradeoffs between the amount of information known about preference strengths and the achievable distortion. We further provide advice about which type of information about preference strengths seems to be the most useful. Finally, we conclude by quantifying the ideal candidate distortion, which compares the quality of the chosen outcome with the best possible candidate that could ever exist, instead of only the best candidate that is actually in the running.
Attempts to exploit preference strength information have led to various approaches for modeling, eliciting, measuring, and aggregating people's preference intensities in a variety of fields, including Likert scales, semantic differential scales, sliders, constant sum paired comparisons, graded pair comparisons, response times, willingness to pay, vote buying, and many others (see @cite_26 @cite_21 @cite_12 for summaries). In our work we specifically consider only a small amount of coarse information about preference strengths, since obtaining detailed information is extremely difficult. Intuitively, any rule used to aggregate preference strengths must ask under what circumstances an apathetic majority' should win over a more passionate minority @cite_10 , and we provide a partial answer to this question when the objective is to minimize distortion.
@cite_26 @cite_10 @cite_21 @cite_12
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Stated preference elicitation techniques, such as discrete choice experiments and best-worst scaling, are now widely used in health research to explore the public’s choices and preferences. In this paper, we propose an alternative stated preference elicitation technique, which we refer to as ‘trio-wise’. We explain this new technique, its relative advantages, modeling framework, and how it compares to the best-worst scaling method. To better illustrate the differences and similarities, we utilize best-worst scaling Case 2, where individuals make best and worst (most and least) choices for the attribute levels that describe a single profile. We demonstrate this new preference elicitation technique using an empirical case study that explores preferences among the general public for ways to involve them in decisions concerning the health care system. Our findings show that the best-worst scaling and trio-wise preference elicitation techniques both retrieve similar preferences. However, the capability of our trio-wise method to provide additional information on the strength of rank preferences and its ability to accommodate indifferent preferences lead us to prefer it over the standard best-worst scaling technique. 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. To help their users to discover important items at a particular time, major websites like Twitter, Yelp, TripAdvisor or NYTimes provide Top-K recommendations (e.g., 10 Trending Topics, Top 5 Hotels in Paris or 10 Most Viewed News Stories), which rely on crowdsourced popularity signals to select the items. However, different sections of a crowd may have different preferences, and there is a large silent majority who do not explicitly express their opinion. Also, the crowd often consists of actors like bots, spammers, or people running orchestrated campaigns. Recommendation algorithms today largely do not consider such nuances, hence are vulnerable to strategic manipulation by small but hyper-active user groups. To fairly aggregate the preferences of all users while recommending top-K items, we borrow ideas from prior research on social choice theory, and identify a voting mechanism called Single Transferable Vote (STV) as having many of the fairness properties we desire in top-K item (s)elections. We develop an innovative mechanism to attribute preferences of silent majority which also make STV completely operational. We show the generalizability of our approach by implementing it on two different real-world datasets. Through extensive experimentation and comparison with state-of-the-art techniques, we show that our proposed approach provides maximum user satisfaction, and cuts down drastically on items disliked by most but hyper-actively promoted by a few users. 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. The concept of preference intensity has been criticized over the past sixty years for having no substantive meaning. Much of the controversy stems from the inadequacy of measurement procedures. In reviewing the shortcomings of existing procedures, we identify three objectives for developing a satisfactory procedure: (1) the capability of validating expressed preference differences by actual choices among naturally occurring options, (2) compatibility with the existing problem structure, and (3) no confounding of extraneous factors in the measurement of preference intensity. Several recently developed measurement procedures are criticized for failing one or more of these objectives. We then examine three different approaches for measuring preference intensity based on multiple perspectives. Thereplication approach emerges as a promising way of satisfying the three objectives above. This methodology applies to problems where an attribute can be replicated by “parallel components” that are independent, identical copies of the attribute. We illustrate the approach with two applications reported in the decision analysis literature. We also offer guidance on how to construct parallel components satisfying the requisite properties. Voting is a general method for aggregating the preferences of multiple agents. Each agent ranks all the possible alternatives, and based on this, an aggregate ranking of the alternatives (or at least a winning alternative) is produced. However, when there are many alternatives, it is impractical to simply ask agents to report their complete preferences. Rather, the agents' preferences, or at least the relevant parts thereof, need to be elicited. This is done by asking the agents a (hopefully small) number of simple queries about their preferences, such as comparison queries, which ask an agent to compare two of the alternatives. Prior work on preference elicitation in voting has focused on the case of unrestricted preferences. It has been shown that in this setting, it is sometimes necessary to ask each agent (almost) as many queries as would be required to determine an arbitrary ranking of the alternatives. In contrast, in this paper, we focus on single-peaked preferences. We show that such preferences can be elicited using only a linear number of comparison queries, if either the order with respect to which preferences are single-peaked is known, or at least one other agent's complete preferences are known. We show that using a sublinear number of queries does not suffice. We also consider the case of cardinally single-peaked preferences. For this case, we show that if the alternatives' cardinal positions are known, then an agent's preferences can be elicited using only a logarithmic number of queries; however, we also show that if the cardinal positions are not known, then a sublinear number of queries does not suffice. We present experimental results for all elicitation algorithms. We also consider the problem of only eliciting enough information to determine the aggregate ranking, and show that even for this more modest objective, a sublinear number of queries per agent does not suffice for known ordinal or unknown cardinal positions. Finally, we discuss whether and how these techniques can be applied when preferences are almost single-peaked. This article revisits the problem of preference intensity modelling by proposing and analysing the novel concept of preference intensity functions. These retain what are argued to be the most essential properties expected from the consistent numerical representation of preference intensity orderings and the ordinary preferences induced by them. Their existence is characterized by simple and clearly interpretable axioms, while they are also shown to be genuinely ordinally unique and more general than utility functions associated with utility-difference representations. The empirical content of this model is then pinned down by means of a testable, intuitive and comparatively weak necessary and sufficient condition on observable behavioural data. In line with recent developments in the literature, these data are assumed to include choices and an additional variable foregone resource with intensity-revealing potential such as response times, willingness to pay or desirability ratings. We study the behavior of random walks along the edges of the stable marriage lattice for various restricted families of allowable preference sets. In the "k-attribute model," each man is valued in each of k attributes, and each woman's ranking of the men is determined by a linear function, representing her relative ranking of those attributes; men's rankings of the women are determined similarly. We show that sampling with a random walk on the marriage lattice can take exponential time, even when k = 2. Moreover, we show that the marriage lattices arising in the k-attribute model are more restrictive than in the general setting; previously such a restriction had only been shown for the sets of preference lists. The second model we consider is the "k-range model," where each person lies in a position in [i, i + k - 1], for some i, on every preference list of the opposite sex. When k = 1 there is a unique stable marriage. When k = 2 there already can be an exponential number of stable marriages, but we show that a random walk on the stable marriage lattice always converges quickly to equilibrium. However, when k ≥ 5, there are preference sets such that the random walk on the lattice will require exponential time to converge. Lastly, we show that in the extreme case where each gender's rankings of the other are restricted to one of just a constant k possible preference lists, there are still instances for which the Markov chain mixes exponentially slowly, even when k = 4. This oversimplification of the general model helps elucidate why Markov chains based on spouse-swapping are not good approaches to sampling, even in specialized scenarios. In multiagent settings where the agents have different preferences, preference aggregation is a central issue. Voting is a general method for preference aggregation, but seminal results have shown that all general voting protocols are manipulable. One could try to avoid manipulation by using protocols where determining a beneficial manipulation is hard. Especially among computational agents, it is reasonable to measure this hardness by computational complexity. Some earlier work has been done in this area, but it was assumed that the number of voters and candidates is unbounded. Such hardness results lose relevance when the number of candidates is small, because manipulation algorithms that are exponential only in the number of candidates (and only slightly so) might be available. We give such an algorithm for an individual agent to manipulate the Single Transferable Vote (STV) protocol, which has been shown hard to manipulate in the above sense. This motivates the core of this article, which derives hardness results for realistic elections where the number of candidates is a small constant (but the number of voters can be large). The main manipulation question we study is that of coalitional manipulation by weighted voters. (We show that for simpler manipulation problems, manipulation cannot be hard with few candidates.) We study both constructive manipulation (making a given candidate win) and destructive manipulation (making a given candidate not win). We characterize the exact number of candidates for which manipulation becomes hard for the plurality, Borda, STV, Copeland, maximin, veto, plurality with runoff, regular cup, and randomized cup protocols. We also show that hardness of manipulation in this setting implies hardness of manipulation by an individual in unweighted settings when there is uncertainty about the others' votes (but not vice-versa). To our knowledge, these are the first results on the hardness of manipulation when there is uncertainty about the others' votes. As technology advances, new products (e.g., digital cameras, computer tablets, etc.) have become increasingly more complex. Researchers often face considerable challenges in understanding consumers’ preferences for such products. This paper proposes an adaptive decompositional framework to elicit consumers’ preferences for complex products. The proposed method starts with collaborative-filtered initial part-worths, followed by an adaptive question selection process that uses a fuzzy support vector machine active learning algorithm to adaptively refine the individual-specific preference estimate after each question. Our empirical and synthetic studies suggest that the proposed method performs well for product categories equipped with as many as 70 to 100 attribute levels, which is typically considered prohibitive for decompositional preference elicitation methods. In addition, we demonstrate that the proposed method provides a natural remedy for a long-standing challenge in adaptive question design by gauging the possibility of response errors on the fly and incorporating the results into the survey design. This research also explores in a live setting how responses from previous respondents may be used to facilitate active learning of the focal respondent’s product preferences. Overall, the proposed approach offers new capabilities that complement existing preference elicitation methods, particularly in the context of complex products.Data, as supplemental material, are available at http: dx.doi.org 10.1287 mksc.2015.0946 . Couples looking for jobs in the same labor market may cause instabilities. We deter- mine a natural preference domain, the domain of weakly responsive preferences, that guarantees stability. Under a restricted unemployment aversion condition we show that this domain is maximal for the existence of stable matchings. We illustrate how small deviations from (weak) responsiveness, that model the wish of couples to be closer together, cause instability, even when we use a weaker stability notion that excludes myopic blocking. Our remaining results deal with various properties of the set of stable matchings for "responsive couples markets," viz., optimal- ity, filled positions, and manipulation. Journal of Economic Literature Classification Numbers: C78; J41. We present theoretical and empirical results demonstrating the usefulness of social choice functions in crowdsourcing for participatory democracies. First, we demonstrate the scalability of social choice functions by defining a natural notion of epsilon-approximation, and giving algorithms which efficiently elicit such approximations for two prominent social choice functions: the Borda rule and the Condorcet winner. This result circumvents previous prohibitive lower bounds and is surprisingly strong: even if the number of ideas is as large as the number of participants, each participant will only have to make a logarithmic number of comparisons, an exponential improvement over the linear number of comparisons previously needed. Second, we apply these ideas to Finland's recent off-road traffic law reform, an experiment on participatory democracy in real life. This allows us to verify the scaling predicted in our theory and show that the constant involved is also not large. In addition, by collecting data on the time that users take to complete rankings of varying sizes, we observe that eliciting partial rankings can further decrease elicitation time as compared to the common method of eliciting pairwise comparisons. The need to rank items based on user input arises in many practical applications such as elections, group-decision making and recommendation systems. The primary challenge in such scenarios is to decide a global ranking based on partial preferences provides by users. The standard approach to address this challenge is to ask users to provide explicit numerical ratings (cardinal information) of a subset of items. The main appeal of such an approach is the ease of aggregation. However, the rating scale as well as the individual ratings are often arbitrary and may not be consistent from one user to another. A more natural alternative to numerical ratings requires users to compare pairs of items (ordinal information). In contrast to cardinal information, such comparisons provide an “absolute” indicator of the user's preference. However, it is often hard to combine or aggregate comparisons to obtain a consistent global ranking. In this work, we provide a tractable framework for utilizing comparison data as well as first-order marginal information for the purpose of ranking. We treat the available information as partial samples from an unknown distribution over permutations. Using the Principle of Maximum Entropy, we devise a concise parameterization of distribution consistent with observations using only O(n2) parameters, where n is the number of items in question. We propose a distributed, iterative algorithm for estimating the parameters of the distribution. We establish the correctness of the algorithm as well as identify the rate of convergence explicitly. Using the learnt distribution, we provide efficient approach to (a) learn the mode of the distribution using ‘maximum weight matching’, (b) identification of top k items, and (c) an aggregate ranking of all n items. Through evaluation of our approach on real-data, we verify effectiveness of our solutions as well as the scalability of the algorithm. As users implicitly express their preferences to items on many real-world applications, the implicit feedback based collaborative filtering has attracted much attention in recent years. Pairwise methods have shown state-of-the-art solutions for dealing with the implicit feedback, with the assumption that users prefer the observed items to the unobserved items. However, for each user, the huge unobserved items are not equal to represent her preference. In this paper, we propose a Multiple Pairwise Ranking (MPR) approach, which relaxes the simple pairwise preference assumption in previous works by further tapping the connections among items with multiple pairwise ranking criteria. Specifically, we exploit the preference difference among multiple pairs of items by dividing the unobserved items into different parts. Empirical studies show that our algorithms outperform the state-of-the-art methods on real-world datasets. We present a systematic study of Plurality elections with strategic voters who, in addition to having preferences over election winners, also have secondary preferences, governing their behavior when their vote cannot affect the election outcome. Specifically, we study two models that have been recently considered in the literature: lazy voters, who prefer to abstain when they are not pivotal, and truth-biased voters, who prefer to vote truthfully when they are not pivotal. For both lazy and truth-biased voters, we are interested in their behavior under different tie-breaking rules (lexicographic rule, random voter rule, random candidate rule). Two of these six combinations of secondary preferences and tie-breaking rules have been studied in prior work; for the remaining four, we characterize pure Nash equilibria (PNE) of the resulting strategic games and study the complexity of related computational problems. We then use these results to analyze the impact of different secondary preferences and tie-breaking rules on the election outcomes. Our results extend to settings where some of the voters are non-strategic. We study a generic framework that provides a unified view on two important classes of problems: (i) extensions of the k-median problem where clients are interested in having multiple facilities in their vicinity (e.g., due to the fact that, with some small probability, the closest facility might be malfunctioning and so might not be available for using), and (ii) finding winners according to some appealing multiwinner election rules, i.e., election system aimed for choosing representatives bodies, such as parliaments, based on preferences of a population of voters over individual candidates. Each problem in our framework is associated with a vector of weights: we show that the approximability of the problem depends on structural properties of these vectors. We specifically focus on the harmonic sequence of weights for which the objective function interpreted in a multiwinner election setup reflects to the well-known Proportional Approval Voting (PAV) rule. Our main result is that, due to the specific (harmonic) structure of weights, the problem allows constant factor approximation. This is surprising since the problem can be interpreted as a variant of the k-median problem where we do not assume that the connection costs satisfy the triangle inequality. The algorithm we propose is based on dependent rounding [Srinivasan, FOCS'01] applied to the solution of a natural LP-relaxation of the problem. The rounding process is well known to produce distributions over integral solutions satisfying Negative Correlation (NC), which is usually sufficient for the analysis of approximation guarantees offered by rounding procedures. In our analysis, however, we need to use the fact that the carefully implemented rounding process satisfies a stronger property, called Negative Association (NA), which allows us to apply standard concentration bounds for conditional random variables. The growth of Internet commerce has stimulated the use of collaborative filtering (CF) algorithms as recommender systems. Such systems leverage knowledge about the known preferences of multiple users to recommend items of interest to other users. CF methods have been harnessed to make recommendations about such items as web pages, movies, books, and toys. Researchers have proposed and evaluated many approaches for generating recommendations. We describe and evaluate a new method called personality diagnosis (PD). Given a user's preferences for some items, we compute the probability that he or she is of the same "personality type" as other users, and, in turn, the probability that he or she will like new items. PD retains some of the advantages of traditional similarity-weighting techniques in that all data is brought to bear on each prediction and new data can be added easily and incrementally. Additionally, PD has a meaningful probabilistic interpretation, which may be leveraged to justify, explain, and augment results. We report empirical results on the EachMovie database of movie ratings, and on user profile data collected from the CiteSeer digital library of Computer Science research papers. The probabilistic framework naturally supports a variety of descriptive measurements--in particular, we consider the applicability of a value of information (VOI) computation. We theoretically and experimentally study voter behavior in a setting characterized by plurality rule and mandatory voting, where voters choose from three options. We are interested in the occurrence of strategic voting in an environment where Condorcet cycles may occur. In particular, we focus on how information about the distribution of preferences affects strategic behavior. We also vary the relative importance of the second preferred option to investigate how this affects the strategic vote. Quantal response equilibrium analysis is used to analyze the game and proves to be a good predictor for the experimental data. Our results indeed show that strategic voting arises, the extent of which depends on (i) the availability of information; (ii) the relative importance of the intermediate candidate; (iii) the electorate's relative support for one's preferred candidate; and (iv) the relative position of the plurality-supported candidate in a voter's preference ordering. Our results show that information serves as a coordination device where strategic voting does not harm the plurality-preferred candidate's chances of winning. Customer preferences for products are drifting over time. Product perception and popularity are constantly changing as new selection emerges. Similarly, customer inclinations are evolving, leading them to ever redefine their taste. Thus, modeling temporal dynamics is essential for designing recommender systems or general customer preference models. However, this raises unique challenges. Within the ecosystem intersecting multiple products and customers, many different characteristics are shifting simultaneously, while many of them influence each other and often those shifts are delicate and associated with a few data instances. This distinguishes the problem from concept drift explorations, where mostly a single concept is tracked. Classical time-window or instance decay approaches cannot work, as they lose too many signals when discarding data instances. A more sensitive approach is required, which can make better distinctions between transient effects and long-term patterns. We show how to model the time changing behavior throughout the life span of the data. Such a model allows us to exploit the relevant components of all data instances, while discarding only what is modeled as being irrelevant. Accordingly, we revamp two leading collaborative filtering recommendation approaches. Evaluation is made on a large movie-rating dataset underlying the Netflix Prize contest. Results are encouraging and better than those previously reported on this dataset. In particular, methods described in this paper play a significant role in the solution that won the Netflix contest. In this paper, we provide a simple game-theoretic model of an online question and answer forum. We focus on factual questions in which user responses aggregate while a question remains open. Each user has a unique piece of information and can decide when to report this information. The asker prefers to receive information sooner rather than later, and will stop the process when satisfied with the cumulative value of the posted information. We consider two distinct cases: a complements case, in which each successive piece of information is worth more to the asker than the previous one; and a substitutes case, in which each successive piece of information is worth less than the previous one. A best-answer scoring rule is adopted to model Yahoo! Answers, and is effective for substitutes information, where it isolates an equilibrium in which all users respond in the first round. But we find that this rule is ineffective for complements information, isolating instead an equilibrium in which all users respond in the final round. In addressing this, we demonstrate that an approval-voting scoring rule and a proportional-share scoring rule can enable the most efficient equilibrium with complements information, under certain conditions, by providing incentives for early responders as well as the user who submits the final answer.