Weakly implementable social choice rules

Previous investigations have shown that a social choice function which is partially implementable must be characterized by pervasive veto power. This paper investigates how much additional latitude in the design of social choice functions, and how much relief from this vetoers result, can be achieved by examining multi-valued social choice rules and relaxing the requirement of partial implementability to a requirement that we call weak partial implementability. We find that the power structures which characterize partially implementable social choice functions, including the veto properties, also characterize weakly partially implementable social choice rules. The conclusion is that invoking multi-valuedness and implementation of appealing social choice rules in strong Nash equilibria. Our results apparently exhaust the possibilities for implementation in strong Nash equilibrium. If any implementation possibility results are to be achieved, they can apparently come only by weakening the equilibrium requirement.     

Weak strategy proofness: The case of nonbinary social choice functions

It is now well known that under some eminently acceptable behavioral rule in comparing various power sets every nonimposed, binary, multivalued social choice mechanism is strategy-proof or oligarchic. Various attempts have been made to resolve the paradox either by relaxing binariness or by weakening the notion of strategy-proofness. By relaxing both binariness and the notion of strategy-proofness this paper shows that the trade-off between weak strategy-proofness and various unacceptable power structures, such as oligarchy or dictatorship, would remain intact.The helpful comments and suggestions of an anonymous referee are gratefully acknowledged.     

ADMISSIBILITY OF LIKELIHOOD RATIO RULES IN COVARIATE CLASSIFICATION USING DEPENDENT SAMPLES

The two populations considered for this study are two distinct time points. Samples consist of observations made at both the time points on every sampling unit. The unit to be classified is observed at one of the two time points. The observation vectors contain covariates, having same expectation at both the time points. In this set-up admissibility of some likelihood ratio rules is established.     

Adaptive Crossover Design for Normal Responses

In a response-adaptive design, we review and update the trial on the basis of outcomes in order to achive a specific goal. In clinical trials our goal is to allocate a larger number of patients to the better treatment. In the present paper, we use a response adaptive design in a two-treatment two-period crossover trial where the treatment responses are continuous. We provide probability measures to choose between the possible treatment combinations AA, AB, BA, or BB. The goal is to use the better treatment combination a larger number of times. We calculate the allocation proportions to the possible treatment combinations and their standard errors. We also derive some asymptotic results and provide solutions on related inferential problems. The proposed procedure is compared with a possible competitor. Finally, we use a data set to illustrate the applicability of our proposed design.     

Multi-treatment covariate-adjusted adaptive design under informative censoring

In the present work, we find a set of reliability functionals to fix up an allocation strategy among K(≥2) treatments when the response distributions, conditionally dependent on some continuous prognostic variable, are exponential with unknown linear regression functions as the means of the respective conditional distributions. Targeting such reliability functionals, we propose a covariate-adjusted response-adaptive randomization procedure for the multi-treatment single-period clinical trial under the Koziol–Green model for informative censoring. We compare the proposed procedure with its competitive covariate-eliminated procedure.     

Net Neutrality,Broadband Market Coverage,and Innovation at the Edge*

Net neutrality (NN) is a widely debated policy issue that has the potential to alter the dynamics of accessing online content. The focal point of the debate lies in whether broadband service providers (BSPs) should be allowed to charge content providers for the preferential delivery of their digital content. This decision will affect broadband market coverage for end consumers as well as the issues of long‐term competition and innovation in the market of digital content. Our research aims to analyze and address these issues. We propose a game theoretical model with three players—the BSP, the content providers, and the consumers—where the BSP, in its capacity as a gatekeeper between the content providers and the consumers, is modeled as a two‐sided market platform. We find that while abandoning the principle of NN might sometimes result in increased consumer surplus and broadband market coverage, it can also hinder the ability of startups to compete against established rivals and thus reduce innovation at the edge. The results should be of great interest to policymakers as they debate on this very crucial issue.     

A spatial Bayesian semiparametric mixture model for positive definite matrices with applications in diffusion tensor imaging

Studies on diffusion tensor imaging (DTI) quantify the diffusion of water molecules in a brain voxel using an estimated 3 × 3 symmetric positive definite (p.d.) diffusion tensor matrix. Due to the challenges associated with modelling matrix‐variate responses, the voxel‐level DTI data are usually summarized by univariate quantities, such as fractional anisotropy. This approach leads to evident loss of information. Furthermore, DTI analyses often ignore the spatial association among neighbouring voxels, leading to imprecise estimates. Although the spatial modelling literature is rich, modelling spatially dependent p.d. matrices is challenging. To mitigate these issues, we propose a matrix‐variate Bayesian semiparametric mixture model, where the p.d. matrices are distributed as a mixture of inverse Wishart distributions, with the spatial dependence captured by a Markov model for the mixture component labels. Related Bayesian computing is facilitated by conjugacy results and use of the double Metropolis–Hastings algorithm. Our simulation study shows that the proposed method is more powerful than competing non‐spatial methods. We also apply our method to investigate the effect of cocaine use on brain microstructure. By extending spatial statistics to matrix‐variate data, we contribute to providing a novel and computationally tractable inferential tool for DTI analysis.     

Resampling-based bias-corrected time series prediction

In this paper, we consider estimation of the mean squared prediction error (MSPE) of the best linear predictor of (possibly) nonlinear functions of finitely many future observations in a stationary time series. We develop a resampling methodology for estimating the MSPE when the unknown parameters in the best linear predictor are estimated. Further, we propose a bias corrected MSPE estimator based on the bootstrap and establish its second order accuracy. Finite sample properties of the method are investigated through a simulation study.     

Estimation of population mean in successive sampling under super-population model in presence of random non response situations

The present work is an attempt to estimate the population mean on the current occasion in two-occasion successive (rotation) sampling in presence of random non response situations. The estimation strategy has been constructed under a super-population model design approach with the help of imputation technique. The estimators proposed on the current occasion cover the cases of occurrences random non responses on either of the occasions. Detail behaviors of the proposed class of estimators have been studied and its performance has been examined with the sample mean estimator. The results are demonstrated through empirical studies which establish the effectiveness of the proposed class of estimators. Suitable recommendations have been put forward to the survey statisticians for its practical application.     

Sequential path independence and social choice

Arrow's general impossibility theorem shows that every Paretian social choice function which satisfies independence of irrelevant alternatives and the Axiom of Sequential Path Independence is necessarily dictatorial. It is shown that the existence of a dictator can be established without invoking full path independence. We propose an axiom of weak path independence of a sequential choice procedure. This axiom turns out to be independent of the factor that is critical in obtaining dictatorship or oligarchy results in the choice theoretic framework.