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Top-k voting is a common form of preference elicitation due to its conceptual simplicity both on the voters' side and on the decision maker's side. In a typical setting, given a set of candidates, the voters are required to submit only the k-length prefixes of their intrinsic rankings of the candidates. The decision maker then tries to correctly predict the winning candidate with respect to the complete preference profile according to a prescribed voting rule. This raises a tradeoff between the communication cost (given the specified value of k), and the ability to correctly predict the winner.We focus on arbitrary positional scoring rules in which the voters' scores for the candidates is given by a vector that assigns the ranks real values. We study the performance of top-k elicitation under three probabilistic models of preference distribution: a neutral distribution (impartial culture); a biased distribution, such as the Mallows distribution; and a worst-case (but fully known) distribution.For an impartial culture, we provide a technique for analyzing the performance of top-k voting. For the case of arbitrary positional scoring rules, we provide a succinct set of criteria that is sufficient for obtaining both lower and upper bounds on the minimal k necessary to determine the true winner with high probability. Our lower bounds pertain to any implementation of a top-k voting scheme, whereas for our upper bound, we provide a concrete top-k elicitation algorithm. We further demonstrate the use of this technique on Copeland's voting rule.For the case of biased distributions, we show that for any non-constant scoring rule, the winner can be predicted with high probability without ever looking at the votes. For worst-case distributions, we show that for exponentially decaying scoring rules, k = O(log m) is sufficient for all distributions.

Motivated by applications to word-of-mouth advertising, we consider a game-theoretic scenario in which competing advertisers want to target initial adopters in a social network. Each advertiser wishes to maximize the resulting cascade of influence, modeled by a general network diffusion process. However, competition between products may adversely impact the rate of adoption for any given firm. The resulting framework gives rise to complex preferences that depend on the specifics of the stochastic diffusion model and the network topology.We study this model from the perspective of a central mechanism, such as a social networking platform, that can optimize seed placement as a service for the advertisers. We ask: given the reported demands of the competing firms, how should a mechanism choose seeds to maximize overall efficiency? Beyond the algorithmic problem, competition raises issues of strategic behaviour: rational agents should not be incentivized to underreport their budget demands.We show that when there are two players, the social welfare can be 2-approximated by a polynomialtime strategyproof mechanism. Our mechanism is defined recursively, randomizing the order in which advertisers are allocated seeds according to a particular greedy method. For three or more players, we demonstrate that under additional assumptions (satisfied by many existing models of influence spread) there exists a simpler strategyproof e e−1 -approximation mechanism; notably, this second mechanism is not necessarily strategyproof when there are only two players.Keywords. Game Theory, social networks, mechanism design, influence diffusion IntroductionThe concept of word-of-mouth advertising is built upon the idea that referrals between individuals can lead to a contagion of opinion in a population. In this way, a small number of initial adopters can generate a cascade of influence, significantly impacting the adoption of a new product. While this concept has been very well studied in the marketing and sociology literature [1,2,3,4,5], recent popularity of online social networking has made it possible to obtain rich data and directly target individuals based on network topology. Indeed, a potential advantage of advertising served via online social networks is that the platform could preferentially target central individuals, impacting the overall effectiveness of its advertisers' campaigns.Various models of network influence spread have arisen recently in the literature, with a focus on the algorithmic problem of deciding which individuals to target as initial adopters (or "seeds") [6,7,8]. One commonality among many of these (stochastic) models is that the expected number of eventual adopters is a non-decreasing submodular function of the seed set. This implies that natural greedy methods [9] can be used to choose initial adopters to approximately maximize an advertiser's expected influence. Of course, actually applying such algorithms requires intimate knowledge of the social network, which may not be readily available to all adverti...

We study combinatorial problems with real world applications such as machine scheduling, routing, and assignment. We propose a method that combines Reinforcement Learning (RL) and planning. This method can equally be applied to both the offline, as well as online, variants of the combinatorial problem, in which the problem components (e.g., jobs in scheduling problems) are not known in advance, but rather arrive during the decision-making process. Our solution is quite generic, scalable, and leverages distributional knowledge of the problem parameters. We frame the solution process as an MDP, and take a Deep Q-Learning approach wherein states are represented as graphs, thereby allowing our trained policies to deal with arbitrary changes in a principled manner. Though learned policies work well in expectation, small deviations can have substantial negative effects in combinatorial settings. We mitigate these drawbacks by employing our graph-convolutional policies as non-optimal heuristics in a compatible search algorithm, Monte Carlo Tree Search, to significantly improve overall performance. We demonstrate our method on two problems: Machine Scheduling and Capacitated Vehicle Routing. We show that our method outperforms custom-tailored mathematical solvers, state of the art learning-based algorithms, and common heuristics, both in computation time and performance.

Summaries of fictional stories allow readers to quickly decide whether or not a story catches their interest. A major challenge in automatic summarization of fiction is the lack of standardized evaluation methodology or high-quality datasets for experimentation. In this work, we take a bottomup approach to this problem by assuming that story authors are uniquely qualified to inform such decisions. We collect a dataset of one million fiction stories with accompanying author-written summaries from Wattpad, an online story sharing platform. We identify commonly occurring summary components, of which a description of the main characters is the most frequent, and elicit descriptions of main characters directly from the authors for a sample of the stories. We propose two approaches to generate character descriptions, one based on ranking attributes found in the story text, the other based on classifying into a list of pre-defined attributes. We find that the classification-based approach performs the best in predicting character descriptions.