Seat allocation distributions and seat biases of stationary apportionment methods for proportional representation

In a proportional representation system, apportionment methods are used to round the vote proportion of a party to an integer number of seats in parliament. Assuming uniformly distributed vote proportions, we derive the seat allocation distributions for stationary divisor methods. An important characteristic of apportionment methods are seat biases, that is, expected differences between actual seat numbers and ideal shares of seats, when the parties are ordered from largest to smallest. We obtain seat bias formulas for the stationary divisor methods and for the quota method of greatest remainders.Acknowledgement. We thank Friedrich Pukelsheim for many fruitful discussions.Received March 2004     

Asymptotic seat bias formulas

Apportionment methods are used to round the vote proportions of parties in a proportional representation system to integer numbers of seats in the parliament. Seat biases quantify by how much on average a particular apportionment method favors larger (or smaller) parties. In this paper, we prove a previous conjecture on asymptotic seat biases of stationary divisor methods and the quota method of greatest remainders, as the size of the parliament tends to infinity.     

Minimum distance estimators for count data based on the probability generating function with applications

This paper studies properties of parameter estimators obtained by minimizing a distance between the empirical probability generating function and the probability generating function of a model for count data. Specifically, it is shown that, under certain not restrictive conditions, the resulting estimators are consistent and, suitably normalized, asymptotically normal. These properties hold even if the model is misspecified. Three applications of the obtained results are considered. First, we revisit the goodness-of-fit problem for count data and propose a weighted bootstrap estimator of the null distribution of test statistics based on the above cited distance. Second, we give a probability generating function version of the model selection test problem for separate, overlapping and nested families of distributions. Finally, we provide an application to the problem of testing for separate families of distributions. All applications are illustrated with numerical examples.     

基于蚁群算法的应急物流配送车辆调度研究

以车辆配送问题为背景,运用了蚁群算法来求解应急物流配送车辆调度模型。在带有时间窗的基础上考虑应急系统各节点的运输距离和费用构造模型。根据模型的特点,设计了蚁群算法求解方法,并针对蚂蚁路径选择做了改进性分析。实例研究结果表明．蚁群算法在应急物流配送车辆调度问题中具有合理性、可行性和有效性。     

Forecasting government support in Irish general elections: Opinion polls and structural models

Election forecasting is a cottage industry among pollsters, the media, political scientists, and political anoraks. Here, we plow a fresh field in providing a systematic exploration of election forecasting in Ireland. We develop a structural forecast model for predicting incumbent government support in Irish general elections between 1977 and 2020 (the Iowa model). We contrast this structural model with forecasts from opinion polls, the dominant means of predicting Ireland’s elections to date. Our results show that with appropriate lead-in time, structural models perform similarly to opinion polls in predicting government support when the dependent variable is vote share. Most importantly, however, the Iowa model is superior to opinion polls in predicting government seat share, the ultimate decider of government fate in parliamentary systems, and especially significant in single transferable vote (STV) systems where vote and seat shares are not always in sync. Our results provide cumulative evidence of the potency of structural electoral forecast models globally, with the takeaway that the Iowa model estimating seat share outpaces other prediction approaches in anticipating government performance in Irish general elections.     

Randomized decision rules in voting games: a model for strict proportional power

The concept of strict proportional power is introduced, as a means of formalizing a desire to avoid discrepancy between the seat distribution in a voting body and the actual voting power in that body, as measured by power indices in common use. Proportionality is obtained through use of a randomized decision rule (majority rule). Some technical problems which arise are discussed in terms of simplex geometry. Practical implications and problems in connection with randomized decision rules are indicated.     

An algorithm for the solution of stochastic optimal control problems for large nonlinear econometric models

This paper considers the problem of solving an optimal control problem for large dynamic economic models which are both nonlinear and stochastic. It proposes a technique which combines conventional deterministic optimal control algorithms with the procedure of stochastic simulation, which calculates a numerical approximation to the distribution of the models endogenous variables. The new technique is computationally feasible for even large nonlinear models and, as an illustration of this, the Bank of England's large quarterly forecasting model is used in an example.     

Union authorization card signatures and union certification election vote

One stage of the union organizing process involves the legal requirement that at least 30% of the employees in a potential bargaining unit express a desire for union representation by signing union authorization cards. Beyond the necessary legal requirement, do the data generated by card signing provide a potentially valuable source of information that may be useful to the union organizer in formulating campaign tactics? In addition, do authorization cards provide a sufficiently valid basis for establishing bargaining unit recognition as is the case in Canada? In order to explore these possibilities, the relationship between card signing behavior and certification vote in six union representation elections is examined. Although card signing and vote for certification are significantly related, overall results indicate that relying on union authorization card data as an indicator of vote at the individual level is questionable.     

A decision model for bank branch site selection: Define branch success and do not deviate

Site selection is one of the most important decision making processes for firms since, if done correctly, it provides access to the best customers and the greatest market potential. In contrast, poor location choices are costly and difficult to reverse.This paper deals with the single branch site selection problem in the banking context. Due to the high level of complexity (several factors have to be taken into consideration in the decision making process as well as a wide range of entities' internal requirements), to date there is no single procedure that fits all needs. This paper attempts to provide a solution to this problem by proposing a unified method based on minimizing the distance from the candidate-branch to the most successful branches, taking into account each banking institution’ notion of branch success. This methodology would work well at the lowest possible cost.     

Multilevel analysis of the changing relationship between class and party in Britain 1964–1992

Previous analyses of the changing relationship between class and vote in Britain have assumed that the British Election Surveys constitute simple random samples. In fact, they are all clustered samples, and the number of sampling points has varied substantially over time. The paper uses the statistical technique of multi-level modelling to investigate the effects of this clustering and compares the results with those obtained with single-level logistic models. In general, the multilevel and single-level models lead to similar conclusions about the changing relation between class and vote; they both show evidence of a change in the class/vote relationship over time. However, the multilevel models also show that, while the clustering does not affect conclusions about the class dealignment debate, there are other important substantive findings which emerge from the multilevel approach. First, there is clear evidence of substantial constituency differences in the intercepts; that is, individuals had very different propensities to vote Conservative in different constituencies. Second, there were also significant constituency differences in class voting, that is, constituencies seemed to vary in their level of class polarization.     

Investment planning for irrigation development projects

This paper considers the problem of choosing among the technologies available for irrigation by tubewells to obtain an investment plan which maximizes the net agricultural benefits from a proposed project in a developing country. Cost and benefit relationships are derived and incorporated into a mathematical model which is solved using a modification of the dynamic programming procedure for solving the knapsack problem. The optimal schedule is seen to favor small capacity wells, drilled by indigenous methods, with supplementary water distribution systems.     

蚂蚁算法在复杂性运输路径问题中的应用——多车场多车型路径问题

车辆路径问题中,行驶路线往往取决于一系列约束条件,如配送中心个数,货物需求量,交发货时间,车辆容量限制等。要想达到一定的目标,如路程最短,费用最小,时间尽量少,车辆尽量少等,就得借劲于合适的算法去解决实际的问题。蚂蚁算法在解决著名的旅行商（TSP）问题上已取得了很好的成效,目前已陆续渗透到其他问题的求解上。文章主要针对多车场多车型车辆路径问题,用蚁群算法以及蚁群算法的优化算法去解决一些实际问题。     

Dynamics in the fragmentation of political party systems

Fragmentation is an important dimension of political party systems. It concerns the proliferation of minor parties and the willingness of voters to vote for them. Past research relates party fragmentation to the voting system in a country; by Duverger's hypothesis, fragmentation should be highest in counties with proportional representation. The entropy measure is used to quantify fragmentation. The upper limit of fragmentation is analyzed in 24 countries, and the patterns of change in fragmentation are identified with mathematical difference equations, testing the idea that voters and parties evolve toward an equilibrium in fragmentation. The highest level of fragmentation is found comparable with a psychological limit on human information processing. In 17 of 22 countries, fragmentation moves toward an equilibrium, regardless of the type of voting system, and countries with higher equilibrium levels usually evolve more slowly. The results affirm the stability of democratic governments but raise questions about voters' strategies and suggest that some voters may try to control fragmentation when they vote.     

A social choice function implementable via backward induction with values in the ultimate uncovered set

We prove the existence of a social choice function implementable via backward induction which always selects within the ultimate uncovered set. Whereas the uncovered set is the set of maximal elements of the covering relation, the ultimate uncovered set is the set obtained by iterative application of this covering operation. Dutta and Sen (1993) showed that any social choice function which is the solution of a generalized binary voting procedure is implementable via backward induction. Our result follows from Dutta and Sen's theorem, in that we construct a binary voting procedure always selecting within the ultimate uncovered set. We use the classical multistage elimination procedure, which always selects an alternative within the uncovered set. When this procedure is also used to select among all of the possible agendas or orderings of alternatives within the procedure, the alternative selected (from the agenda selected) will be within the uncovered set of the uncovered set. Our result follows from repeated application of this construction. Intuitively, the procedure constructed consists of requiring agents to vote on how they should vote and so on. Received: 7 April 1997 / Accepted: 15 October 1998     

Decision-making in the supply chain: Examining problem solving approaches and information availability

In this paper we investigate the role of two types of problem solving approaches on supply chain performance. Additionally, we investigate how the level of information availability moderates problem solving approach on supply chain performance. We draw on construal level theory from the experimental psychology literature to explain how the problem solving approaches (abstract problem solving approach vs. concrete problem solving approach) contribute to supply chain performance. From this foundation, we run a series of behavioral experiments to test our hypotheses that problem solving approaches and information availability impact supply chain performance as presented in the beer distribution game. A key finding of this study is that individuals who take an abstract problem solving approach are able to perform better than individuals who take a concrete problem solving approach in the context of limited information availability. However, in the context of complete information availability, the impact of both types of problem solving approaches on performance becomes negligible.     

Choosing union representation: the role of attitudes and emotions

In the United States, most unions are recognised by a majority vote of employees through union representation elections administered by the government. Most empirical studies of individual voting behaviour during union representation elections use a rational choice model. Recently, however, some have posited that voting is often influenced by emotions. We evaluate competing hypotheses about the determinants of union voting behaviour by using data collected from a 2010 representation election at Delta Air Lines, a US‐based company. In addition to the older rational choice framework, multiple regression results provide support for an emotional choice model. Positive feelings toward the employer are statistically significantly related to voting ‘no’ in a representation election, while positive feelings toward the union are related to a ‘yes’ vote. Effect sizes for the emotion variables were generally larger than those for the rational choice variables, suggesting that emotions may play a key role in representation election outcomes.     

An efficient nonparametric estimator for models with nonlinear dependence

We provide a convenient econometric framework for the analysis of nonlinear dependence in financial applications. We introduce models with constrained nonparametric dependence, which specify the conditional distribution or the copula in terms of a one-dimensional functional parameter. Our approach is intermediate between standard parametric specifications (which are in general too restrictive) and the fully unrestricted approach (which suffers from the curse of dimensionality). We introduce a nonparametric estimator defined by minimizing a chi-square distance between the constrained densities in the family and an unconstrained kernel estimator of the density. We derive the nonparametric efficiency bound for linear forms and show that the minimum chi-square estimator is nonparametrically efficient for linear forms.     

Relative efficiency and deficiency of kernel type estimators of smooth distribution functions

Abstract  The problem is investigated whether a given kernel type estimator of a distribution function at a single point has asymptotically better performance than the empirical estimator. A representation of the relative deficiency of the empirical distribution function with respect to a kernel type estimator is established which gives a complete solution to this problem. The problem of finding optimal kernels is studied in detail.     

Spectral utility,wiener-hopf techniques,and rational expectations

Purely classical, frequency-domain methods are useful for solving linear-quadratic dynamic rational expectations models. To illustrate this, generic scalar and multiple-variable problems are solved completely in the frequency domain. The procedure, which utilizes Wiener-Hopi methods to maximize the frequency-domain representation of the objective function, makes ordinarily troublesome second-order conditions transparent, allows infinite-order costs of adjustment, and handles moving average errors easily.