Cardinal versus ordinal criteria in choice under risk with disconnected utility ranges

This paper provides a formal justification for the existence of subjective random components intrinsic to the outcome evaluation process of decision makers and explicitly assumed in the stochastic choice literature. We introduce the concepts of admissible error function and generalized certainty equivalent, which allow us to analyze two different criteria, a cardinal and an ordinal one, when defining suitable approximations to expected utility values. Contrary to the standard literature requirements for irrational preferences, adjustment errors arise in a natural way within our setting, their existence following directly from the disconnectedness of the range of the utility functions. Conditions for the existence of minimal errors are also studied. Our results imply that neither the cardinal nor the ordinal criterion do necessarily provide the same evaluation for two or more different prospects with the same expected utility value. As a consequence, a rational decision maker may define two different generalized certainty equivalents when presented with the same prospect in two different occasions.     

Path analysis with partial association measures

This paper discusses the use of partial association measures for carrying out path analyses on categorical data. The measures considered are essentially PRE (proportion of reduction in error of prediction) measures for nominal variables and concordance-discordance indices for ordinal ones. These measures provide a natural way to evaluate the strength of the path linking a non-measurable response variable to one of several categorical explanatory factors. Concerning the decomposition of raw association into direct and indirect effects, it is shown, however, that they do not share the properties of conventional path coefficients for measurable variables. Especially purely nominal association measures need to be interpreted with care. The scope of the partial measures for path analysis is illustrated through a study of the relationships between the educational styles experienced by swiss adolescents and their selfesteem.     

The ordinal Nash social welfare function

A social welfare function entitled ‘ordinal Nash’ is proposed. It is based on risk preferences and assumes a common, worst social state (origin) for all individuals. The crucial axiom in the characterization of the function is a weak version of independence of irrelevant alternatives. This axiom considers relative risk positions with respect to the origin. Thus, the resulting social preference takes into account non-expected utility risk preference intensity by directly comparing certainty equivalent probabilities. The function provides an interpretation of the Nash-utility-product preference aggregation rule. Necessary and sufficient conditions for the function to produce complete and transitive binary relations are characterized.     

The effects of sampling on measures of association between variables based on sample means

Many studies that involve people's perceptions or behaviors focus on aggregate rather than individual responses. For example, variables describing public perceptions for some set of events may be represented as mean scores for each event. Event mean scores then become the unit of analysis for each variable. The variance of these mean scores for a variable is not only a function of the variation among the events themselves, but is also due to the variation among respondents and their possible responses. This is also the case for the covariances between variables based on event mean scores. In many contexts the variance and covariance components attributable to the sampling of respondents and their responses may be large; these components can be described as measurement error. In this paper we show how to estimate variances and covariances of aggregate variables that are free of these sources of measurement error. We also present a measure of reliability for the event means and examine the effect of the number of respondents on these spurious components. To illustrate how these estimates are computed, forty-two respondents were asked to rate forty events on seven risk perception variables. Computing the variances and covariances for these variables based on event means resulted in relatively large components attributable to measurement error. A demonstration is given of how this error is removed and the resulting effect on our estimates.     

On the choice of measures of reliability and validity in the content-analysis of texts

The paper discusses several reliability measures: Scott’s pi, Krippendorff’s alpha, free marginal adjustment (Bennett, Alpert and Goldstein’s \(S\) ), Cohen’s kappa, and Perreault and Leigh’s \(I\) and the assumptions on which they are based. It is suggested that correlation coefficients between, on one hand, the distribution of qualitative codes and, on the other hand, word co-occurrences and the distribution of the categories identified with the help of the dictionary based on substitution complement the other reliability measures. The paper shows that the choice of the reliability measure depends on the format of the text (stylistic versus rhetorical) and the type of reading (comprehension versus interpretation). Namely, Cohen’s kappa and Bennett, Alpert and Goldstein’s \(S\) emerge as reliability measures particularly suited for perspectival reading of rhetorical texts. Outcomes of the content analysis of 57 texts performed by four coders with the help of computer program QDA Miner inform the analysis.     

Nash bargaining in ordinal environments

We analyze the implications of Nash’s (Econometrica 18:155–162, 1950) axioms in ordinal bargaining environments; there, the scale invariance axiom needs to be strenghtened to take into account all order-preserving transformations of the agents’ utilities. This axiom, called ordinal invariance, is a very demanding one. For two-agents, it is violated by every strongly individually rational bargaining rule. In general, no ordinally invariant bargaining rule satisfies the other three axioms of Nash. Parallel to Roth (J Econ Theory 16:247–251, 1977), we introduce a weaker independence of irrelevant alternatives (IIA) axiom that we argue is better suited for ordinally invariant bargaining rules. We show that the three-agent Shapley–Shubik bargaining rule uniquely satisfies ordinal invariance, Pareto optimality, symmetry, and this weaker IIA axiom. We also analyze the implications of other independence axioms.     

Inducing relations on incomplete ordinal data

Let X denote a set of n elements or stimuli which have an underlying linear ranking L based on some attribute of comparison. Incomplete ordinal data is known about L, in the form of a partial order P on X. This study considers methods which attempt to induce, or reconstruct, L based only on the ordinal information in P. Two basic methods for approaching this problem are the cardinal and sequel construction methods. Exact values are computed for the expected error of weak order approximations of L from the cardinal and sequel construction methods. Results involving interval orders and semiorders for P are also considered. Previous simulation comparisons for cardinal and sequel construction methods on interval orders were found to depend on the specific model that was used to generate random interval orders, and were not found to hold for interval orders in general. Finally, we consider the likelihood that any particular linear extension of P is the underlying L.     

Dealing with heterogeneity in ordinal responses

Quality & Quantity - In sample surveys where people are asked to express their personal opinions it is conceivable to register a high level of indecision among respondents and this circumstance...     

Estimating linear models with ordinal qualitative regressors

The theory and application of ordinal qualitative dependent variable models have been given considerable attention in the social science and statistical literatures. Linear models with ordinal qualitative regressors have, however, been neglected. In this paper a simple specification for such models is developed and a consistent asymptotically normal estimator is offered. The estimator is compared to the conventional dummy variable approach using simulated data. The simulation results indicate that substantial gains with regard to bias and efficiency can be achieved relative to estimation using a conventional dummy variable scheme. Said gains appear to increase as the number of ordinal categories increases. The asymptotic properties of the estimator are detailed in the appendices.     

Determining implied relationships on incomplete ordinal data

A method is presented for determining ordinal relationships implied by data. If the dataset is incomplete, the method can determine which relationships are implied by the set as well as diagnose inconsistencies in the data. The method is an extension of computational techniques for defining the space of all vectors satisfying a given set of linear inequalities.     

改革路径的产生和选择

经济体制的改革必将要引起政治体制的改革 ,而改革最优路径的产生完全取决于我们对思想的解放和理论创新。     

中国审计的国际化选择

经济全球化已成为当今世界经济发展的主旋律。经济全球化必然导致审计环境发生巨变,进而引发各国审计的对接、整合。审计国际化是大势所趋,是中国审计的必然选择。一、审计国际化带来中国审计的全新课题1、审计目标移位,审计效能强化。审计目标是审