Informational requirements of social choice rules to avoid the Condorcet loser: A characterization of the plurality with a runoff

We consider informational requirements of social choice rules satisfying anonymity, neutrality, monotonicity, and efficiency, and never choosing the Condorcet loser. Among such rules, we establish the existence of a rule operating on the minimal informational requirement. Depending on the number of agents and the number of alternatives, either the plurality rule or the plurality with a runoff is characterized. In some cases, the plurality rule is the most selective rule among the rules operating on the minimal informational requirement. In the other cases, each rule operating on the minimal informational requirement is a two-stage rule, and among them, the plurality with a runoff is the rule whose choice at the first stage is most selective. These results not only clarify properties of the plurality rule and the plurality with a runoff, but also explain why they are widely used in real societies.     

Information aggregation in multicandidate elections under plurality rule and runoff voting

I consider a model in which imperfectly informed voters with common interests participate in a multicandidate election decided by either plurality rule or a runoff. Prior to the election, each voter receives a private signal corresponding to the candidate the voter thinks is best. Voters are relatively more likely to think a given candidate is best if the candidate is a relatively better candidate. I show that there is a sequence of equilibrium strategies for the voters such that, as the number of voters goes to infinity, the probability that the best candidate is elected goes to 1. I further show that all candidates receive significant vote shares in any equilibrium in which information fully aggregates under plurality rule and that voters do at least as well when the election is decided by a runoff as they do when the election is decided by plurality rule.     

Informational requirements of social choice rules

The required amount of information to make a social choice is the cost of information processing, and it is a practically important feature of social choice rules. We introduce informational aspects into the analysis of social choice rules and prove that (i) if an anonymous, neutral, and monotonic social choice rule operates on minimal informational requirements, then it is a supercorrespondence of either the plurality rule or the antiplurality rule, and (ii) if the social choice rule is furthermore Pareto efficient, then it is a supercorrespondence of the plurality rule.     

Strong and coalition-proof political equilibria under plurality and runoff rule

We analyze the effects of voter coordination on the equilibrium of voting games. Specifically, we analyze the concepts of strong equilibrium and coalition-proof equilibrium for plurality rule and runoff rule elections. We characterize these equilibria in the three candidate case, and provide results for important special cases in the general multicandidate case.      

Choice from a Three-Element Set: Some Lessons of the 2000 Presidential Campaign in the United States

We consider the behavior of four choice rules—plurality voting, approval voting, Borda count, and self-consistent choice—when applied to choose the best option from a three-element set. It is assumed that the two main options are preferred by a large majority of the voters, while the third option gets a very small number of votes and influences the election outcome only when the two main options receive a close number of votes. When used to rate the main options, Borda count and self-consistent choice contain terms that allow both for the strength of preferences of the voters and the rating of the main candidates by voters who vote for the third option. In this way, it becomes possible to determine more reliably the winner when plurality voting or approval voting produce close results.     

Existence of solutions for systems of generalized quasi‐equilibrium problems

In this paper, first of all, we consider a generalized game in choice form with 2 constraints and its corresponding equilibrium in choice. We assert new conditions under which the equilibrium in choice exists. As a consequence, we establish the existence of the equilibrium for generalized abstract economies. Then, we apply the obtained theorems to prove the existence of solutions for systems of quasi‐equilibrium problems. We do this by considering new hypotheses for the properties of the involved correspondences. This approach leads us to results which differ a lot from the ones existing in literature.     

Algorithms of filtration and extrapolation for discrete-time dynamical systems

The bases of theory and the recursive filtration algorithms ensuring the guaranteed precision of estimate for an extrapolated state of a dynamic system are described. A determined precision is ensured by corresponding choice of algorithm parameters.The different algorithms of filtration and extrapolation are investigated. These algorithms may be used in constructing tracking systems, organizing of corresponding measurements and estimation of parameters in information systems.     

Theories of mathematics education: European perspectives, commentaries and viable research directions

We briefly comment on different perspectives on (1) the role of mathematics education theories, (2) the issue of plurality and healthy heterogeneity versus consolidation; (3) underlying inquiry systems or the implicit role of philosophy in theories of mathematics education. This paper also outlines developments within the European research scene on theory usage in mathematics education research, which complement the discussion at the 29th PME research forum in Melbourne.     

Evaluating correct classification probability for weighted voting classifiers with plurality voting

Weighted voting classifiers (WVCs) consist of N units that each provide individual classification decisions. The entire system output is based on tallying the weighted votes for each decision and choosing the winning one (plurality voting) or one which has the total weight of supporting votes greater than some specified threshold (threshold voting). Each individual unit may abstain from voting. The entire system may also abstain from voting if no decision is ultimately winning. Existing methods of evaluating the correct classification probability (CCP) of WVCs can be applied to limited special cases of these systems (threshold voting) and impose some restrictions on their parameters. In this paper a method is suggested which allows the CCP of WVCs with both plurality and threshold voting to be exactly evaluated without imposing constraints on unit weights. The method is based on using the modified universal generating function technique.     

Entanglement of Multipartite Fermionic Coherent States for Pseudo-Hermitian Hamiltonians

We study the entanglement of multiqubit fermionic pseudo-Hermitian coherent states (FPHCSs) described by anticommutative Grassmann numbers. We introduce pseudo-Hermitian versions of well-known maximally entangled pure states, such as Bell, GHZ, Werner, and biseparable states, by integrating over the tensor products of FPHCSs with a suitable choice of Grassmannian weight functions. As an illustration, we apply the proposed method to the tensor product of two- and three-qubit pseudo-Hermitian systems. For a quantitative characteristic of entanglement of such states, we use a measure of entanglement determined by the corresponding concurrence function and average entropy.     

Solving sparse linear systems by an abs-method that corresponds toLU-decomposition

Abaffy, Broyden, and Spedicato (ABS) have recently proposed a class of direct methods for solving nonsparse linear systems. It is the purpose of this paper to demonstrate that with proper choice of parameters, ABS methods exploit sparsity in a natural way. In particular, we study the choice of parameters which corresponds to an LU-decomposition of the coefficient matrix. In many cases, the fill-in, represented by the nonzero elements of the deflection matrix, uses less storage than the corresponding fill-in of an explicit LU factorization. Hence the above can be a viable and simple method for solving sparse linear systems. A simple reordering scheme for the coefficient matrix is also proposed for the purpose of reducing fill-in of the deflection matrices.     

Consistent social choice functions and systems of distinct representatives

This paper concerns Peleg's construction of a strongly consistent voting system. The authors characterize the alternatives selected by the corresponding social choice correspondence in terms of systems of distinct representatives. This result allows the use of ‘rapid’ computational algorithms for this correspondence.     

Nonholonomic LR Systems as Generalized Chaplygin Systems with an Invariant Measure and Flows on Homogeneous Spaces

We consider a class of dynamical systems on a compact Lie group G with a left-invariant metric and right-invariant nonholonomic constraints (so-called LR systems) and show that, under a generic condition on the constraints, such systems can be regarded as generalized Chaplygin systems on the principle bundle G \to Q = G/H, H being a Lie subgroup. In contrast to generic Chaplygin systems, the reductions of our LR systems onto the homogeneous space Q always possess an invariant measure. We study the case G = SO(n), when LR systems are ultidimensional generalizations of the Veselova problem of a nonholonomic rigid body motion which admit a reduction to systems with an invariant measure on the (co)tangent bundle of Stiefel varieties V(k, n) as the corresponding homogeneous spaces. For k = 1 and a special choice of the left-invariant metric on SO(n), we prove that after a time substitution the reduced system becomes an integrable Hamiltonian system describing a geodesic flow on the unit sphere S^n-1. This provides a first example of a nonholonomic system with more than two degrees of freedom for which the celebrated Chaplygin reducibility theorem is applicable for any dimension. In this case we also explicitly reconstruct the motion on the group SO(n).     

Lack of exponential stability to Timoshenko system with viscoelastic Kelvin–Voigt type

We study the Timoshenko systems with a viscoelastic dissipative mechanism of Kelvin–Voigt type. We prove that the model is analytical if and only if the viscoelastic damping is present in both the shear stress and the bending moment. Otherwise, the corresponding semigroup is not exponentially stable no matter the choice of the coefficients. This result is different to all others related to Timoshenko model with partial dissipation, which establish that the system is exponentially stable if and only if the wave speeds are equal. Finally, we show that the solution decays polynomially to zero as \({t^{-1/2}}\) , no matter where the viscoelastic mechanism is effective and that the rate is optimal whenever the initial data are taken on the domain of the infinitesimal operator.     

Construction of systems of sets related to the plurality functions

In the present paper we provide a way of construction of all m-elements consistent systems. These kinds of families of sets are the parameters determining the solutions of some functional equation, which express the consistency condition appearing in characterizing the plurality functions. First, we formulate the idea of extending p-elements family to such m-tuples families which are m-elements consistent systems. Then we study some of their properties and we use them in the constructing of extending p-elements families to m-elements consistent systems and all such systems. Finally, we deal with m-elements consistent systems which satisfy an additional condition.     

Generalized shift-splitting iteration method for a class of two-by-two linear systems

In this paper, we propose a generalized-shift splitting (GSS) iteration method for solving a broad class of two-by-two linear systems. The convergence theory of the GSS iteration method is established and the spectral properties of the corresponding preconditioned matrix of some special choices for the parameter matrices are analyzed. In addition, the optimal choice of the iterative parameter is discussed. Numerical experiments are used to verify the validity of the theoretical results and the effectiveness of the new method.     

An experimental study of voting rules and polls in three-candidate elections

We report the results of elections conducted in a laboratory setting, modelled on a threecandidate example due to Borda. By paying subjects conditionally on election outcomes, we create electorates with (publicly) known preferences. We compare the results of experiments with and without non-binding pre-election polls under plurality rule, approval voting, and Borda rule. We also refer to a theory of voting “equilibria,” which makes sharp predictions concerning individual voter behavior and election outcomes. We find that Condorcet losers occasionally win regardless of the voting rule or presence of polls. Duverger's law (which asserts the predominance of two candidates) appears to hold under plurality rule, but close three-way races often arise under approval voting and Borda rule. Voters appear to poll and vote strategically. In elections, voters usually cast votes that are consistent with some strategic equilibrium. By the end of an election series, most votes are consistent with a single equilibrium, although that equilibrium varies by experimental group and voting rule.     

The binary nonlinearization of generalized Toda hierarchy by a special choice of parameters

A new discrete matrix spectral problem with two arbitrary constants is introduced. The corresponding 2-parameter hierarchy of integrable lattice equations, which can be reduced to the hierarchy of Toda lattice, is obtained by discrete zero curvature representation. Moreover, the Hamiltonian structure and a hereditary operators are deduced by applying the discrete trace identity. Finally, an integrable symplectic map and a family of finite-dimensional integrable systems are given by the binary nonlinearization for the resulting hierarchy by a special choice of parameters.     

A transversely isotropic elastic model of geomaterials

Under consideration is the choice of parameters of a transversely isotropic elastic model for describing the linear deformation of geomaterials. We also discuss some analytical and numerical methods of solving the corresponding dynamic equations.     

多元Lanchester方程在装备战损量预计中的应用

在战时装备保障中,装备战损量预计是一难点问题.本文从分析影响装备战损的因素出发,采用多元Lanchester方程寻求解决方案.提出了基于指数多元Lanchester方程的装备战损量预计模型和模型中毁伤系数的确定方法.据此,建立了一种新的装备战损量预计方法,并举例验证.该方法较好的满足了未来信息化条件下作战装备保障的需要,具有重要的参考价值.