Hot Hands, Streaks and Coin-flips: Numerical Nonsense in the New York Times

The existence of "Hot Hands" and "Streaks" in sports and gambling is hotly debated, but there is no uncertainty about the recent batting-average of the New York Times: it is now two-for-two in mangling and misunderstanding elementary concepts in probability and statistics; and mixing up the key points in a recent paper that re-examines earlier work on the statistics of streaks. In so doing, it's high-visibility articles have added to the general-public's confusion about probability, making it seem mysterious and paradoxical when it needn't be. However, those articles make excellent case studies on how to get it wrong, and for discussions in high-school and college classes focusing on quantitative reasoning, data analysis, probability and statistics. What I have written here is intended for that audience

Beauty and Distance in the Stable Marriage Problem

The stable marriage problem has been introduced in order to describe a complex system where individuals attempt to optimise their own satisfaction, subject to mutually conflicting constraints. Due to the potential large applicability of such model to describe all the situation where different objects has to be matched pairwise, the statistical properties of this model have been extensively studied. In this paper we present a generalization of this model, introduced in order to take into account the presence of correlations in the lists and the effects of distance when the player are supposed to be represented by a position in space.Comment: 8 pages, 3 figures, submitted to ep

The stable roommates problem with ties

We study the variant of the well-known stable roommates problem in which participants are permitted to express ties in their preference lists. In this setting, more than one definition of stability is possible. Here we consider two of these stability criteria, so-called super-stability and weak stability. We present a linear–time algorithm for finding a super-stable matching if one exists, given a stable roommates instance with ties. This contrasts with the known NP-hardness of the analogous problem under weak stability. We also extend our algorithm to cope with preference lists that are incomplete and/or partially ordered. On the other hand, for a given stable roommates instance with ties and incomplete lists, we show that the weakly stable matchings may be of different sizes and the problem of finding a maximum cardinality weakly stable matching is NP-hard, though approximable within a factor of 2

Erving Was a Brilliant Scholar and a Mensch

This interview with Joseph Gusfield, Professor Emeritus of Sociology at the the University of California, San Diego, was recorded over the phone on December 19, 2008. Dmitri Shalin transcribed the interview, after which Dr. Gusfield edited the transcript and gave his approval for posting the present version in the Erving Goffman Archives. Breaks in the conversation flow are indicated by ellipses. Supplementary information and additional materials inserted during the editing process appear in square brackets. Undecipherable words and unclear passages are identified in the text as “[?]”

Parametric Inference for Biological Sequence Analysis

One of the major successes in computational biology has been the unification, using the graphical model formalism, of a multitude of algorithms for annotating and comparing biological sequences. Graphical models that have been applied towards these problems include hidden Markov models for annotation, tree models for phylogenetics, and pair hidden Markov models for alignment. A single algorithm, the sum-product algorithm, solves many of the inference problems associated with different statistical models. This paper introduces the \emph{polytope propagation algorithm} for computing the Newton polytope of an observation from a graphical model. This algorithm is a geometric version of the sum-product algorithm and is used to analyze the parametric behavior of maximum a posteriori inference calculations for graphical models.Comment: 15 pages, 4 figures. See also companion paper "Tropical Geometry of Statistical Models" (q-bio.QM/0311009

G\"odel for Goldilocks: A Rigorous, Streamlined Proof of (a variant of) G\"odel's First Incompleteness Theorem

Most discussions of G\"odel's theorems fall into one of two types: either they emphasize perceived philosophical, cultural "meanings" of the theorems, and perhaps sketch some of the ideas of the proofs, usually relating G\"odel's proofs to riddles and paradoxes, but do not attempt to present rigorous, complete proofs; or they do present rigorous proofs, but in the traditional style of mathematical logic, with all of its heavy notation and difficult definitions, and technical issues which reflect G\"odel's original approach and broader logical issues. Many non-specialists are frustrated by these two extreme types of expositions and want a complete, rigorous proof that they can understand. Such an exposition is possible, because many people have realized that variants of G\"odel's first incompleteness theorem can be rigorously proved by a simpler middle approach, avoiding philosophical discussions and hand-waiving at one extreme; and also avoiding the heavy machinery of traditional mathematical logic, and many of the harder detail's of G\"odel's original proof, at the other extreme. This is the just-right Goldilocks approach. In this exposition we give a short, self-contained Goldilocks exposition of G\"odel's first theorem, aimed at a broad, undergraduate audience.Comment: Version 2 corrects typos and one definition in the first version, and expands or contracts parts of the exposition, but the main content remains the same. Version 3 removes an unnecessary comment in Version

Guest editorial: Special issue on matching under preferences

No abstract available

The Stable Roommates problem with short lists

We consider two variants of the classical Stable Roommates problem with Incomplete (but strictly ordered) preference lists SRI that are degree constrained, i.e., preference lists are of bounded length. The first variant, EGAL d-SRI, involves finding an egalitarian stable matching in solvable instances of SRI with preference lists of length at most d. We show that this problem is NP-hard even if d=3. On the positive side we give a (2d+3)/7-approximation algorithm for d={3,4,5} which improves on the known bound of 2 for the unbounded preference list case. In the second variant of SRI, called d-SRTI, preference lists can include ties and are of length at most d. We show that the problem of deciding whether an instance of d-SRTI admits a stable matching is NP-complete even if d=3. We also consider the "most stable" version of this problem and prove a strong inapproximability bound for the d=3 case. However for d=2 we show that the latter problem can be solved in polynomial time.Comment: short version appeared at SAGT 201

Manipulating Tournaments in Cup and Round Robin Competitions

In sports competitions, teams can manipulate the result by, for instance, throwing games. We show that we can decide how to manipulate round robin and cup competitions, two of the most popular types of sporting competitions in polynomial time. In addition, we show that finding the minimal number of games that need to be thrown to manipulate the result can also be determined in polynomial time. Finally, we show that there are several different variations of standard cup competitions where manipulation remains polynomial.Comment: Proceedings of Algorithmic Decision Theory, First International Conference, ADT 2009, Venice, Italy, October 20-23, 200