Скачать или смотреть Первый день . Осенняя школа МЦАВР "Advances in Decision Analysis" Часть 2

Докладчик: Арунава Сен (Indian Statistical Institute, New Dehli)
Название доклада: Teacher Redistribution in Public Schools
Аннотация: The Right to Free and Compulsory Education Act (2009) (RTE) of the Government of India prescribes teacher-student ratios for state-run schools. One method advocated by the Act to achieve its goals is the redeployment of teachers from surplus to deficit schools. We consider a model where teachers can either remain in their initially assigned schools or be transferred to a deficit school in their acceptable set. Transfers cannot turn a surplus school into a deficit school and a deficit school cannot be made a surplus school. The planner's objective is specified in terms of the post-transfer deficit vector that can be achieved. We formulate the problem as a network-flow problem. We show that there exists a transfer policy that generates a post-transfer deficit vector that Lorenz dominates all achievable post-transfer deficit vectors. We also show that the Lorenz-dominant post-transfer deficit vector can be achieved as the outcome of a strategy-proof mechanism.

Докладчик: Ахмет Алкан (Sabanci University, Turkey)
Название доклада: The Revealed Preference Lattice and The Lattice of Stable Matchings
Аннотация: In economic theory agents in a market are often described by preference orderings. This is also the case in stable many-to-many matching theory where agents are additionally described by choice functions compatible with their preference orderings. In fact the theory can be worked out entirely if agents are described by choice functions alone and use is made of the revealed preference relation associated with a choice function. First, we consider an individual described by a choice function C on a universal set U. The collection of all chosen sets is the consumption set Z of the individual. Given any two S,S’ in Z, we say S is revealed better than S’ if C chooses S from the union of S and S’. We will show that the revealed preference relation so defined is a lattice if C is path independent. Next, we consider the standard many-to-many matching market, say with firms F and workers W. Each firm is described by a choice function on W and each worker by a choice function on F. It is easily seen by the Deferred Acceptance Procedure that stable matchings exist if the choice functions are path independent. A stable matching M is said to be group-revealed-preferred to another stable matching M’ if every firm revealed-prefers its set of workers in M to its set of workers in M’. We will show that stable matchings form a natural lattice under this group-revealed-preference relation provided the choice functions are path independent and “size monotone”. Further, this lattice is distributive and has other nice properties. We will conclude with some remarks on the rationalizability literature where the aim is to characterize path independent (and size monotone) choice functions with utility functions over Z or U having certain properties.

Докладчик: Марио Гуаррачино (University of Cassino and Souther Lazio (Italy), HSE University (Russia))
Название доклада: A Short Journey through Whole Graph Embedding Techniques
Аннотация: Networks provide suitable models in many applications, ranging from social to life sciences. Such representations are able to capture interactions and dependencies among variables or observations, and can be extended to consider ensembles of networks, thus providing simple and powerful modeling of phenomena. Whole graph embedding involves the projection of ensembles of graphs into a vector space, while retaining their structural properties. In recent years, several embedding techniques using graph kernels, matrix factorization, and deep learning architectures have been developed to learn low dimensional graph representations. These embeddings can then be used for feature extraction, graph clustering or for building classification models. In these lectures, we survey embedding techniques which jointly embed whole graphs for classification tasks. We compare them and evaluate their performance on undirected synthetic and real world network datasets on different learning tasks.

Докладчик: Эрик Маскин (Harvard University (USA), HSE University (Russia))
Название доклада: An Election System Resistant to Strategic Voting
Аннотация: No reasonable voting system is always immune from strategic voting. However, we will present evidence that, in political elections, voters’ preferences are approximately single-peaked. For this case, we demonstrate that there is a (unique) voting rule that is strategy-resistant. It elects the Condorcet winner.