The widely used Plackett-Luce ranking model assumes that individuals rank items by making repeated choices from a universe of items. But in many cases the universe is too big for people to plausibly consider all options. In the choice literature, this issue has been addressed by supposing that individuals first sample a small consideration set and then choose among the considered items. However, inferring unobserved consideration sets (or item consideration probabilities) in this “consider then choose” setting poses significant challenges, because even simple models of consideration with strong independence assumptions are not identifiable, even if item utilities are known. We apply the consider-then-choose framework to top-$k$ rankings, where we assume rankings are constructed according to a Plackett-Luce model after sampling a consideration set. While item consideration probabilities remain non-identified in this setting, we prove that we can infer bounds on the relative values of consideration probabilities. Additionally, given a condition on the expected consideration set size and known item utilities, we derive absolute upper and lower bounds on item consideration probabilities. We also provide algorithms to tighten those bounds on consideration probabilities by propagating inferred constraints. Thus, we show that we can learn useful information about consideration probabilities despite not being able to identify them precisely. We demonstrate our methods on a ranking dataset from a psychology experiment with two different ranking tasks (one with fixed consideration sets and one with unknown consideration sets). This combination of data allows us to estimate utilities and then learn about unknown consideration probabilities using our bounds.

Enrollment in computer science has increased dramatically in recent years, straining capacities and leading to various strategies for managing enrollment. But some strategies increase student competition and may have disproportionate negative impacts on students from underrepresented groups. We believe success in computing education necessitates a more equitable approach to course enrollment. In this experience report, we describe our new enrollment mechanism, "the Match." Building on the Gale--Shapley stable matching algorithm, the Match was designed to encourage a liberal arts approach to course selection and attempt to broaden participation in computing. Drawing on data from three years of use, we find high student participation, with the vast majority of students having their enrollment preferences met. With Match registration, our courses have tended to be a bit more inclusive of younger students. The Match appears not to have disparate negative impacts like those of competitive enrollment, but has increased workload in the Registrar's Office. Overall, we believe the Match has decreased student and faculty angst around registration, and we argue that systems like the Match can help manage enrollment pressures in ways that are consistent with educational values.

Students come to CS1 with a wide variety of motivations and goals, which may differ across subpopulations and be indicative of their future engagement with CS. While there is a rich literature relating success in CS1 to specific constructs, such as belonging, goal-orientation, or self-efficacy, less work has examined what motivations and goals students volunteer as most important for their enrollment in CS1. Here, we use qualitative coding to identify themes from students' open-ended descriptions of why they're taking CS1 and what they hope to get out of it, collected across fifteen years. Using quantitative analysis of these coded descriptions, and word-frequency analysis, we identify and name three clusters of students that encompass the majority of students taking CS1: Explorers, Planners, and Utilitarians. We also identify motivations and goals that are more common for particular populations, such as students who have not yet declared a major or students without prior programming experience, as well as factors predicting students' later engagement with CS. This work demonstrates the potential of qualitative coding and computational analyses to enable us to better understand a population of students based on their own words.

Algorithms to find optimal alignments among strings, or to find a parsimonious summary of a collection of strings, are well studied in a variety of contexts, addressing a wide range of interesting applications. In this paper, we consider chain letters, which contain a growing sequence of signatories added as the letter propagates. The unusual constellation of features exhibited by chain letters (one-ended growth, divergence, and mutation) make their propagation, and thus the corresponding reconstruction problem, both distinctive and rich. Here, inspired by these chain letters, we formally define the problem of computing an optimal summary of a set of diverging string sequences. From a collection of these sequences of names, with each sequence noisily corresponding to a branch of the unknown tree $T$ representing the letter's true dissemination, can we efficiently and accurately reconstruct a tree $T' \approx T$? In this paper, we give efficient exact algorithms for this summarization problem when the number of sequences is small; for larger sets of sequences, we prove hardness and provide an efficient heuristic algorithm. We evaluate this heuristic on synthetic data sets chosen to emulate real chain letters, showing that our algorithm is competitive with or better than previous approaches, and that it also comes close to finding the true trees in these synthetic datasets.

The undergraduate computer science curriculum is ever-changing but has seen particular turmoil recently. Topics such as machine learning, data science, and concurrency and parallelism have grown in importance over the last few years. As the content of our curriculum changes, so too does the mathematical foundations on which it rests. Do our current theoretical courses adequately support these foundations or must we consider new pedagogy that is more relevant to our students' needs? In this BoF, we will discuss what a modern mathematics curriculum for computer scientists should cover and how we should go about accomplishing this in our classrooms.

Each user of the MySpace social network can designate a small subset of her friends as Top Friends, placing them in a rank-ordered list displayed prominently on her profile. By examining users' #1 (best) and #2 (second-best) friends, we discover that MySpace users are nearly indifferent to these two friends' popularities when choosing which to designate as their best friend. Other pairs of ranks (e.g., #1-vs.-#3, #2-vs.-#3, ...) also reveal no marked preference for a popular friend over a less popular one. To the extent that ranking decisions form a window into broader decisions about whom to befriend at all, these observations suggest that positing individuals' tendency to attach to popular people---as in network-growth models like preferential attachment---may not suffice to explain the heavy-tailed degree distributions seen in real networks.

Motivated by the spread of on-line information in general and on-line petitions in particular, recent research has raised the following combinatorial estimation problem. There is a tree T that we cannot observe directly (representing the structure along which the information has spread), and certain nodes randomly decide to make their copy of the information public. In the case of a petition, the list of names on each public copy of the petition also reveals a path leading back to the root of the tree. What can we conclude about the properties of the tree we observe from these revealed paths, and can we use the structure of the observed tree to estimate the size of the full unobserved tree T? Here we provide the first algorithm for this size estimation task, together with provable guarantees on its performance. We also establish structural properties of the observed tree, providing the first rigorous explanation for some of the unusual structural phenomena present in the spread of real chain-letter petitions on the Internet.

Motivated by the role of incentives in large-scale information systems, Kleinberg and Raghavan (FOCS 2005) studied strategic games in decentralized information networks. Given a branching process that specifies the network, the rarity of answers to a specific question, and a desired probability of success, how much reward does the root node need to offer so that it receives an answer with this probability, when all of the nodes are playing strategically? For a specific family of branching processes and a constant failure probability, they showed that the reward function exhibited a threshold behavior that depends on the branching parameter b.

Abstract Given a snapshot of a social network, can we infer which new interactions among its members are likely to occur in the near future? We formalize this question as the link‐prediction problem , and we develop approaches to link prediction based on measures for analyzing the “proximity” of nodes in a network. Experiments on large coauthorship networks suggest that information about future interactions can be extracted from network topology alone, and that fairly subtle measures for detecting node proximity can outperform more direct measures.

In traditional game theory, players are typically endowed with exogenously given knowledge of the structure of the game--either full omniscient knowledge or partial but fixed information. In real life, however, people are often unaware of the utility of taking a particular action until they perform research into its consequences. In this paper, we model this phenomenon. We imagine a player engaged in a question and- answer session, asking questions both about his or her own preferences and about the state of reality; thus we call this setting "Socratic" game theory. In a Socratic game, players begin with an a priori probability distribution over many possible worlds, with a different utility function for each world. Players can make queries, at some cost, to learn partial information about which of the possible worlds is the actual world, before choosing an action. We consider two query models: (1) an unobservable-query model, in which players learn only the response to their own queries, and (2) an observable-query model, in which players also learn which queries their opponents made.The results in this paper consider cases in which the underlying worlds of a two-player Socratic game are either constant-sum games or strategically zero-sum games, a class that generalizes constant-sum games to include all games in which the sum of payoffs depends linearly on the interaction between the players. When the underlying worlds are constant sum, we give polynomial-time algorithms to find Nash equilibria in both the observable- and unobservable-query models. When the worlds are strategically zero sum, we give efficient algorithms to find Nash equilibria in unobservablequery Socratic games and correlated equilibria in observablequery Socratic games.

We study the dynamics of information propagation in environments of low-overhead personal publishing, using a large collection of weblogs over time as our example domain. We characterize and model this collection at two levels. First, we present a macroscopic characterization of topic propagation through our corpus, formalizing the notion of long-running "chatter" topics consisting recursively of "spike" topics generated by outside world events, or more rarely, by resonances within the community. Second, we present a microscopic characterization of propagation from individual to individual, drawing on the theory of infectious diseases to model the flow. We propose, validate, and employ an algorithm to induce the underlying propagation network from a sequence of posts, and report on the results.

Given a snapshot of a social network, can we infer which new interactions among its members are likely to occur in the near future? We formalize this question as the link-prediction problem, and we develop approaches to link prediction based on measures for analyzing the “proximity” of nodes in a network. Experiments on large co-authorship networks suggest that information about future interactions can be extracted from network topology alone, and that fairly subtle measures for detecting node proximity can outperform more direct measures.

A fundamental problem that confronts peer-to-peer applications is the efficient location of the node that stores a desired data item. This paper presents Chord, a distributed lookup protocol that addresses this problem. Chord provides support for just one operation: given a key, it maps the key onto a node. Data location can be easily implemented on top of Chord by associating a key with each data item, and storing the key/data pair at the node to which the key maps. Chord adapts efficiently as nodes join and leave the system, and can answer queries even if the system is continuously changing. Results from theoretical analysis and simulations show that Chord is scalable: Communication cost and the state maintained by each node scale logarithmically with the number of Chord nodes.

In this paper, we give a theoretical analysis of peer-to-peer (P2P) networks operating in the face of concurrent joins and unexpected departures. We focus on Chord, a recently developed P2P system that implements a distributed hash table abstraction, and study the process by which Chord maintains its distributed state as nodes join and leave the system. We argue that traditional performance measures based on run-time are uninformative for a continually running P2P network, and that the rate at which nodes in the network need to participate to maintain system state is a more useful metric. We give a general lower bound on this rate for a network to remain connected, and prove that an appropriately modified version of Chord's maintenance rate is within a logarithmic factor of the optimum rate.