### Working paper

## On calculation of the power indices with allowance for the agent preferences in the anonimous games

We consider the problem of manipulability of social choice rules in the impartial anonymous and neutral culture model (IANC) and provide a new theoretical study of the IANC model, which allows us to analytically derive the difference between the Nitzan-Kelly index in the Impartial Culture (IC) and IANC models. We show in which cases this difference is almost zero, and in which the Nitzan-Kelly index for IANC is the same as for IC. However, in some cases this difference is large enough to cause changes in the relative manipulability of social choice rules. We provide an example of such cases.

In this paper, the problem of gender identity among e-workers is considered. The Internet market is a specific structure, where there is an opportunity to both preserve almost complete anonymity and arbitrary self-presentation. Due to existing prejudices of employers on the one hand and high competition with other Internet workers are forced to adjust their self-presentation, depending on the wishes of customers, in order to obtain more orders.

This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.

In the general case, complexity of the algorithm to calculate the power indices grows exponentially with the number of voting agents. Yet the volume of calculations may be reduced dramatically if many coalitions have equal numbers of votes. The well-known algorithm for calculation of the Banzhaf and Shapley-Shubik indices was generalized, which enables fast calculation of the power indices where entry of the voting agent into a coalition depends on its preferences over the set of the rest of agents.

This article investigates the problem of identifying a person on the Internet by legal and technical means. The practice of identifying people in Russia and the UK was studiedand compared. Russia was selected because its legislation is well known to the authors, and the UK was selected as it has developed a mature system for the online identification of individuals and relationships and a certain legal regulation in this sphere.An analysis of two government programs was made, namely: the UK Identity Assurance Programme of the Government Digital Service and the Russian Government Decree on “The development of the Federal state information system”. In terms of technological background for person’s identification, the practice of using IPv4 and IPv6 was explored. Russia's specific problems are analysed via the protection of privacy in the case of personal identification and the processing of personal data on the Internet. The authorsdraw conclusions about the division of the concepts of identification and individualization of people on the Internet. Weintroduceourown definition of personal identification on the Internet and proposean amendment to the Russian concept of personal data: the definition of personal data should include the IP address of a person.

We discuss the problem of measurement of voting power distribution by means of classical power indices and power indices that take into account preferences in coalition formation. Examples of application to power distribution in the Council of the European Union and in the European Parliament are preceded by formal definition of the both types of indices, history of invention and discussion about limits to applicability.

The problem of evaluation of the real power of players when they make collective decisions is considered. The new model of the real power evaluation is proposed. The basics of the new model are: modification of the classical power Shapley - Shubik index for accounting of possibility of coalition formation, adding of the new index of the position of coincidence which is evaluating the closeness of the political position of groups and faction, and the new developed index of power efficiency. The index of power efficiency shows to what extend the players exercised their potential power which depends on the number of their votes. Besides, a new way of accounting the impact of cohesion of groups and factions in their final power score is proposed. This model is applied for the evaluation of the power distribution at the Russian State Duma of the 3^{d convocation.}

We address the external effects on public sector efficiency measures acquired using Data Envelopment Analysis. We use the health care system in Russian regions in 2011 to evaluate modern approaches to accounting for external effects. We propose a promising method of correcting DEA efficiency measures. Despite the multiple advantages DEA offers, the usage of this approach carries with it a number of methodological difficulties. Accounting for multiple factors of efficiency calls for more complex methods, among which the most promising are DMU clustering and calculating local production possibility frontiers. Using regression models for estimate correction requires further study due to possible systematic errors during estimation. A mixture of data correction and DMU clustering together with multi-stage DEA seems most promising at the moment. Analyzing several stages of transforming society’s resources into social welfare will allow for picking out the weak points in a state agency’s work.

This article is talking about state management and cultural policy, their nature and content in term of the new tendency - development of postindustrial society. It mentioned here, that at the moment cultural policy is the base of regional political activity and that regions can get strong competitive advantage if they are able to implement cultural policy successfully. All these trends can produce elements of new economic development.

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.