Social choice, optimal inference and figure skating

The theory of social choice is concerned with the problem of aggregating the preferences of several persons into a single preference order. The problem has the same structure as that of aggregating the preference orders of a single person with regard to several aspects of alternatives into a single preference order on the set of alternatives. For this reason, the theory of social choice comes logically not under the topic of collective action (as one might suppose) but rather under the topic of multi-objective decisions. This is so because the several participants in a situation defined as a problem of social choice do not really select courses of action among several available ones when they present their preference orders on a set of alternatives. Therefore they are not ‘actors’, as actors are defined in the theory of decision. To be sure, there are situations where voters do choose strategies, that is, choose among different preference orders to present, which may or may not represent their true preferences but which they believe will be more likely to lead to a more desirable aggregated order. These situations can be considered as n-person decision problems, and we will examine them in the context of non-cooperative n-person games (see Chapter 14. At this time, however, we will suppose that each voter acts ‘sincerely’, that is, presents his ‘actual’ preference order. The decision is now up to some agency, which must combine all these submitted preference orders into a ‘social’ preference order.KeywordsSocial ChoicePreference OrderPareto OptimalitySocial Welfare FunctionSimple MajorityThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The extraordinary technological progress we have witnessed in recent years has made it possible to generate and exchange multimedia content at an unprecedented rate. As a consequence, massive collections of multimedia objects are now widely available to a large population of users. As the task of browsing such large collections could be daunting, Recommender Systems are being developed to assist users in finding items that match their needs and preferences. In this article, we present a novel approach to recommendation in multimedia browsing systems, based on modeling recommendation as a social choice problem. In social choice theory, a set of voters is called to rank a set of alternatives, and individual rankings are aggregated into a global ranking. In our formulation, the set of voters and the set of alternatives both coincide with the set of objects in the data collection. We first define what constitutes a choice in the browsing domain and then define a mechanism to aggregate individual choices into a global ranking. The result is a framework for computing customized recommendations by originally combining intrinsic features of multimedia objects, past behavior of individual users, and overall behavior of the entire community of users. Recommendations are ranked using an importance ranking algorithm that resembles the well-known PageRank strategy. Experiments conducted on a prototype of the proposed system confirm the effectiveness and efficiency of our approach.

In this paper, we provide axiomatic foundations for social choice rules on a domain of convex and comprehensive social choice problems when agents have cardinal utility functions. We translate the axioms of three well known approaches in bargaining theory (Nash 1950; Kalai and Smorodinsky 1975; Kalai 1977) to the domain of social choice problems and provide an impossibility result for each. We then introduce the concept of a reference function which, for each social choice set, selects a point from which relative gains are measured. By restricting the invariance and comparison axioms so that they only apply to sets with the same reference point, we obtain characterizations of social choice rules that are natural analogues of the bargaining theory solutions.

Markov Chain Monte Carlo (MCMC) is widely applied to fit complex, practical models in various disciplines, such as engineering, physics, agriculture, etc. Indeed, when the target density $f$ is not available in closed form, a Markov chain is constructed with stationary density $f$ for forming Monte Carlo estimators of means with respect to $f$. Although a Harris ergodic Markov chain will converge to the target distribution as the Monte Carlo sample size tends to infinity, and the population means can be consistently estimated by the corresponding MCMC estimators, in practice, it is important to estimate the standard errors associated with these Monte Carlo estimates due to the availability of only a finite sample. Therefore, the geometric ergodicity of a Markov Chain is highly desired as it is the most standard method for guaranteeing a central limit theorem (CLT) for MCMC estimators and finding its standard errors. Among the different MCMC algorithms, Metropolis-Hastings (MH) algorithms are predominant. This thesis establishes conditions under which MH algorithms with a position-dependent proposal covariance matrix will or will not have the geometric convergence rate. Indeed, we provide these results for MH algorithms where the normal proposal density has a general mean function $c(x)$ and a covariance matrix $G(x)$ depending on the current position $x$ of the Markov chain. For modern variants of the popular Metropolis adjusted Langevin algorithms (MALA), like the manifold MALA (MMALA) that adapt to the geometry of the target distributions, the proposal covariance matrix changes in every iteration. Thus, we provide conditions for the geometric ergodicity of different variations of the Langevin algorithms, e.g., MMALA, position-dependent MALA (PMALA), and the pre-conditioned MALA (PCMALA). We also provide conditions guaranteeing geometric ergodicity of the pre-conditioned unadjusted Langevin algorithms (PCULA). Generalized linear mixed models (GLMMs), where the response variable is allowed to follow a non-Gaussian distribution, are popular statistical models, although their likelihood functions are not available in closed form. GLMMs can handle the over-dispersion often present in real-world data, and MCMC methods are generally used to fit frequentist and Bayesian GLMMs. Since the likelihood function for GLMMs is not available in closed form, Monte Carlo EM or Monte Carlo maximum likelihood methods are often used for making inferences from GLMMs. Simulation from the conditional (on the data) distribution of the random effects is, in turn, needed for implementing the Monte Carlo EM or Monte Carlo maximum likelihood methods. In this thesis, our general conditions for geometric ergodicity of variants of Langevin algorithms are also verified in the context of conditional simulation from the two most popular GLMMs, namely the binomial GLMM with the logit link and the Poisson GLMM with the log link. These results have important practical implications as users can now confidently fit these models by attaching asymptotically valid standard errors with their Markov chain-based Monte Carlo estimates. Spatial generalized linear mixed models (SGLMMs) are GLMMs where the random effects form a spatial process and are useful for modeling spatially correlated data. We compare the performance of different variants of MALA mentioned above as well as other popular MH algorithms like Random Walk Metropolis in the context of conditional simulation from SGLMMs. Next, we consider MCMC algorithms for full Bayesian analysis of GLMMs. Blocking and reparameterization are techniques used to improve the efficiency and convergence properties of MCMC algorithms. We combine these strategies with pre-conditioning to develop efficient Langevin algorithms for Bayesian GLMMs and SGLMMs. We illustrate our algorithms using extensive real and simulated data analyses.

Layback spin is considered as one of the most beautiful and elegant spins performed in figure skating. It is also one of the required spins in competitive short program in female category. Different techniques of executing layback spin with variations in changing the positions of free parts of the body, as well as the evaluation of layback spin in accordance with ISU rules and regulations, which have been used in all International Skating Federation competitions since 2004 (World and European championships, Olympic Games) are presented in this paper. Due to very difficult position of the body while performing a layback spin, it is essential that the skaters who want to master it should have excellent agility (especially of the spinal column and shoulder and knee joints) and balance. Layback spin performance requires significant skating knowledge, so it cannot be performed by beginners. Depending on the fl exibility and creativity, a skater can execute various positions of the head, arms, body and free leg while performing a layback spin. In some cases, these variations can increase the level of difficulty, and in others only the mark given for executing this spin.

This chapter discusses media coverage of figure skates. Media interest in figure skating has grown steadily since 1962, when ABC's Wide World of Sports began covering the World Championships. However, the Olympic Games have provided the most popular televised skating events. Increased visibility spurred unprecedented interest in figure skating. Television audiences wanted to see in person those competitors they had watched compete for World and Olympic medals. The result has been phenomenal. An ever-increasing number of ice shows and professional competitions have provided opportunities for former competitors to enjoy lucrative careers while continuing to excite audiences. Some have sustained unusual longevity. Two, Scott Hamilton and Kurt Browning, can be classified as matinee idols.

Social choice problems with fixed sets of alternatives

Arrow's theorem is really a theorem about the independence condition. In order to show the very crucial role that this condition plays, the theorem is proved in a refined version, where the use of the Pareto condition is almost avoided. A distinction is made between group preference functions and group decision functions, yielding respectively preference relations and optimal subsets as values. Arrow's theorem is about the first kind, but some ambiguities and mistakes in his book are explained if we assume that he was really thinking of decision functions. The trouble then is that it is not clear how to formulate the independence condition for decision functions. Therefore the next step is to analyse Arrow's argument for accepting the independence condition. The most frequent ambiguity depends on an interpretation of A as the set of all conceivable alternatives, while the variable subset B is the set of all feasible or available alternatives. He then argues that preferences between alternatives that are not feasible shall not influence the choice from the set of available alternatives. But even if this principle is accepted, it only forces us to require independence with respect to some specific set B and not to every B simultaneously. Therefore the independence condition cannot be accepted on these grounds. Another argument is about an election where one of the candidates dies. On one interpretation this argument can be taken to support an independence requirement which leads to a contradiction. On another interpretation it is a condition about connexions between choices from different sets. The so-called problem of binary choice is found to be different from the independence problem and it plays no essential role in Arrow's impossibility result. Other impossibility results by Sen, Batra and Pattanaik and by Schwartz are of a different character. In the last section, several weaker independence conditions are presented. Their relations to Arrow's condition are stated and the arguments supporting them are discussed.

The study aimed to (a) investigate the effect of treatment location on clinical outcomes for patients receiving psychological therapy (a clinic effect, akin to the concept of a therapist effect) and (b) assess the impact of explanatory individual and aggregate demographic and process variables on the clinic and therapist effects. The sample comprised 26,888 patients, seen by 462 therapists, across 30 clinics. Mean patient age was 38 years (69% female, 90% White, 92% planned ending). The dependent variable was patients' posttherapy score on the Clinical Outcomes in Routine Evaluation-Outcome Measure. An incremental 3-level multilevel model was constructed. Markov Chain Monte Carlo estimation created 95% probability intervals for the clinic and therapist effects. A 3-level model with no explanatory variables detected a clinic effect of 8.2%, significantly larger than the therapist effect of 3.2%. Adding explanatory variables significantly reduced the clinic effect to 1.9% but did not significantly alter the therapist effect (3.4%). Patient-level symptom severity and employment status, and clinic-level percentage of White patients and health care sector, explained the most clinic outcome variance and overall outcome variance. Substantial variability in clinical outcomes was found between clinics providing psychological therapy. Socioeconomic mix of patients explained significant proportions of variability at the clinic level but not the therapist level. Clinical implications include the need to go beyond the therapist-patient interaction to deliver effective psychological therapy. Future research is also needed to identify the mechanisms by which clinic and/or area-level factors impact on clinical outcomes. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

We propose a consumption-based capital asset pricing model with state-dependent risk aversion. The corresponding risk premium includes consumption risk and the risk associated with variations in preferences. Our model can be estimated without specifying the functional form linking risk aversion with state variables. The estimates are based on Markov chain Monte Carlo estimation of exact discrete-time parameterizations for linear diffusion processes. We find estimates for relative risk aversion that are reasonable by usual standards, correlated with both consumption and returns, and indicative of an additional preference risk of holding the assets.

Purpose– The purpose of this paper is to analyze the influence of different forms of RMB foreign exchange rates on Chinese foreign trade.Design/methodology/approach– This paper constructed spatial panel model and Markov Chain Monte Carlo estimation method and collected the data of 25 countries’ (including China) quarterly macroeconomic data from first quarter of 1993 until third quarter of 2013 to conduct the data analysis.Findings– This paper finds that USD/CNY, which is widely used in trade settlement, is more significant in effecting Chinese export. Totally, 1 percent appreciation of CNY against USD will lead to 1.532 percent decline of Chinese export, while 1 percent appreciation of CNY NEER only 0.42 percent. What is more, 1 percent increases of the volatility of USD/CNY results in 0.579 percent decline of Chinese export. As policy suggestions, we should further reform the foreign exchange derivative market in China, and provide more currency derivatives, so that the ability of Chinese economy to deal with foreign exchange risk could be improved.Research limitations/implications– Effect of exchange rate on imports and exports relates to the future direction of China’s exchange rate policy. This paper claims that China should accelerate the construction of foreign exchange derivatives market, improving the ability to respond quickly to foreign currency risk.Practical implications– First, denominated exchange rate has more significant impact on the Chinese export trade to other countries than effective exchange rate. Second, the RMB exchange rate fluctuations also significantly affect the export trade. Third, China’s import and export trade have significant spatial effect.Social implications– This paper recommends the construction of the RMB currency futures market as soon as possible, providing a richer foreign exchange derivatives and other risk hedging instruments, thus to enhance the ability to respond to exchange rate risks.Originality/value– This paper uses spatial panel model with the refined data to study various factors on the import and export trade, and thus more comprehensive analysis on the impact of the exchange rate on the import and export trade with other major countries.

Multilevel data structures are known as consisting of multiple units of analysis, one clustered within the other. The concept of multilevel data modelling has been developed for several years mainly because the researchers have realized the disadvantages of ignoring such multilevel data structures. This study aims to find out factors affecting the General Certificate of Education Ordinary Level (G.C.E. O/L) pass rate at schools located in civil war affected provinces in Sri Lanka. The study also extends to observe the multilevel data structure by schools, districts and provinces, and determine how these levels have an impact on the G.C.E. O/L pass rate. The above has been undertaken by the application of advanced analysis focused on developing Generalized Linear Multilevel Model for ordered categorical response using the Bayesian Markov Chain Monte Carlo estimation method employing MLwiN 2.10 software. Finally, the partial non-proportional odds model was selected as the most appropriate model for the Educational data used in this study based on account of its simplicity and accuracy.

The evolution of communities in dynamic (time-varying) network data is a prominent topic of interest. A popular approach to understanding these dynamic networks is to embed the dyadic relations into a latent metric space. While methods for clustering with this approach exist for dynamic networks, they all assume a static community structure. This paper presents a Bayesian nonparametric model for dynamic networks that can model networks with evolving community structures. Our model extends existing latent space approaches by explicitly modeling the additions, deletions, splits, and mergers of groups with a hierarchical Dirichlet process hidden Markov model. Our proposed approach, the hierarchical Dirichlet process latent position cluster model (HDP-LPCM), incorporates transitivity, models both individual and group level aspects of the data, and avoids the computationally expensive selection of the number of groups required by most popular methods. We provide a Markov chain Monte Carlo estimation algorithm and demonstrate its ability to detect evolving community structure in a network of military alliances during the Cold War and a narrative network constructed from the Game of Thrones television series.

Based on a data set comprising 2879 animals and 17 nuclear microsatellite DNA markers, we propose the most comprehensive in-depth study mapping the genetic structure and specifying the assignment success rates in horse breeds at the Czech population scale. The STRUCTURE program was used to perform systematic Bayesian clustering via the Markov chain Monte Carlo estimation, enabling us to explain the population stratification and to identify genetic structure patterns within breeds worldwide. In total, 182 different alleles were found over all the populations and markers, with the mean number of 10.7 alleles per locus. The expected heterozygosity ranged from 0.459 (Friesian) to 0.775 (Welsh Part Bred), and the average level reached 0.721. The average observed heterozygosity corresponded to 0.709, with the highest value detected in the Czech Sport Pony (0.775). The largest number of private alleles was found in Equus przewalskii. The population inbreeding coefficient F<sub>IS</sub> ranged from –0.08 in the Merens to 0.14 in the Belgian Warmblood. The total within-population inbreeding coefficient was estimated to be moderate. As expected, very large genetic differentiation and small gene flow were established between the Friesian and Equus przewalskii (F<sub>ST </sub>= 0.37, Nm = 0.43). Zero F<sub>ST</sub> values indicated no differences between the Czech Warmblood–Slovak Warmblood and the Czech Warmblood–Bavarian Warmblood. A high level of breeding and connectivity was revealed between the Slovak Warmblood–Bavarian Warmblood, Dutch Warmblood–Oldenburg Horse, Bavarian Warmblood–Dutch Warmblood, and Bavarian Warmblood–Oldenburg Horse. The breeds’ contribution equalled about 6% of the total genetic variability. The overall proportion of individuals correctly assigned to a population corresponded to 82.4%. The posterior Bayesian approach revealed a hierarchical dynamic genetic structure in four clusters (hot-blooded, warm-blooded, cold-blooded, and pony). While most of the populations were genetically distinct from each other and well-arranged with solid breed structures, some of the entire sets showed signs of admixture and/or fragmentation.

The exploratory and confirmatory approaches of factor analysis lie on two ends of a continuum of substantive input for scale development. Recent advancements in Bayesian regularization methods enable more flexibility in covering a wide range of the substantive continuum. Based on the Bayesian Lasso (least absolute shrinkage and selection operator) methods for the regression model and covariance matrix, this research proposes a partially confirmatory approach to address the loading and residual structures at the same time. With at least one specified loading per item, a one-step procedure can be applied to figure out both structures simultaneously. With a few specified loadings per factor, a two-step procedure is preferred to capture the model configuration correctly. In both cases, the Bayesian hierarchical formulation is implemented using Markov Chain Monte Carlo estimation with different Lasso or regular priors. Both simulated and real data sets were analyzed to evaluate the validity, robustness, and practical usefulness of the proposed approach across different situations. (PsycInfo Database Record (c) 2021 APA, all rights reserved).