A simple two-axiom characterization of the Nash solution

The oldest and best-known cooperative bargaining solution concept is the Nash solution. Nash [2] characterized his seminal solution concept by using the axioms of ‘Independence of Irrelevant Alternatives’ (IIA), ‘Weak Pareto Optimality’ (WPO), ‘Symmetry’ (SYM), and ‘Scale Invariance’ (SI). Except for WPO, these axioms have been at the center of controversy (especially the most crucial axiom, IIA). This paper considers a new and simple axiom ‘Focal Relevance of a Pareto-optimal Midpoint’ (FRPM). It turns out that the Nash solution can be characterized by WPO and FRPM only.

Weakest collective rationality and the Nash bargaining solution

We propose a new axiom, weakest collective rationality (WCR) which is weaker than both weak Pareto optimality (WPO) in Nash’s (Econometrica 18:155–162, 1950) original characterization and strong individual rationality (SIR) in Roth’s (Math Oper Res 2:64–65, 1977) characterization of the Nash bargaining solution. We then characterize the Nash solution by symmetry (SYM), scale invariance (SI), independence of irrelevant alternatives (IIA) and our weakest collective rationality (WCR) axiom.

Distributive justice and the Nash bargaining solution

Suppes-Sen dominance or SS-proofness (SSP) is a commonly accepted criterion of impartiality in distributive justice. Mariotti (Review of Economic Studies, 66, 733–741, 1999) characterized the Nash bargaining solution using Nash’s (Econometrica, 18, 155–162, 1950) scale invariance (SI) axiom and SSP. In this article, we introduce equity dominance (E-dominance). Using the intersection of SS-dominance and E-dominance requirements, we obtain a weaker version of SSP (WSSP). In addition, we consider α − SSP, where α measures the degree of minimum acceptable inequity aversion; α − SSP is weaker than weak Pareto optimality (WPO) when α = 1. We then show that it is still possible to characterize the Nash solution using WSSP and SI only or using α -SSP, SI, and individual rationality (IR) only for any a Î [0,1)[01). Using the union of SS-dominance and E-dominance requirements, we obtain a stronger version of SSP (SSSP). It turns out that there is no bargaining solution that satisfies SSSP and SI, but the Egalitarian solution turns out to be the unique solution satisfying SSSP.

Objective classification of fabric pilling based on the two-dimensional discrete wavelet transform

A number of methods for automated objective ratings of fabric pilling based on image analysis are described in the literature. The periodic structure of fabrics makes them suitable candidates for frequency domain analysis. We propose a new method of frequency domain analysis based on the two-dimensional discrete wavelet transform to objectively measure pilling intensity in sample images. We present a preliminary evaluation of the proposed method based on analysis of two series of standard pilling evaluation test images. The initial results suggest that the proposed method is feasible, and that the ability of the method to discriminate between levels of pilling intensity depends on the wavelet analysis scale being closely matched to the fabric interyarn pitch. We also present a heuristic method for optimal selection of an analysis wavelet and associated analysis scale.

Stereo image matching using wavelet scale-space representation

A multi-resolution technique for matching a stereo pair of images based on translation invariant discrete multi-wavelet transform is presented. The technique uses the well known coarse to fine strategy, involving the calculation of matching points at the coarsest level with consequent refinement up to the finest level. Vector coefficients of the wavelet transform modulus are used as matching features, where modulus maxima defines the shift invariant high-level features (multiscale edges) with phase pointing to the normal of the feature surface. The technique addresses the estimation of optimal corresponding points and the corresponding 2D disparity maps. Illuminative variation that can exist between the perspective views of the same scene is controlled using scale normalization at each decomposition level by dividing the details space coefficients with approximation space and then using normalized correlation. The problem of ambiguity, explicitly, and occlusion, implicitly, is addressed by using a geometric topological refinement procedure and symbolic tagging.

Measurement invariance of English and French Health Education Impact Questionnaire (heiQ) empowerment scales validated for cancer

PURPOSE: If measurement invariance (MI) is demonstrated for a scale completed by respondents from two different language groups, it means that the scale measures the same construct in the same way in both groups. We assessed MI of the French- and English-language versions of the five Health Education Impact Questionnaire (heiQ) empowerment scales validated for the cancer setting. METHODS: Data came from two cross-sectional studies of Canadian cancer survivors (704 English, 520 French). Single-group confirmatory factor analysis (CFA) was used to test whether the hypothesized factor structure of the French-language heiQ empowerment scales fit the data. Multi-group CFAs were conducted to assess different levels of MI conditions (configural, metric, scalar, strict, as well as MI of factor variances, covariances, and latent means) of the French- and English-language heiQ empowerment scales. RESULTS: The correlated five-factor model showed good fit in both language groups (goodness-of-fit indices: CFI ≥ .97; RMSEA ≤ .07). Goodness-of-fit indices and tests of differences in fit between models supported MI of the five-factor model across the two language groups (∆CFI ≤ -.010 combined with ∆RMSEA ≤ .015). CONCLUSIONS: The French- and English-language heiQ empowerment scales measure the same five dimensions of empowerment in the same way across both language groups. Thus, any observed similarities or differences between French- and English-speaking respondents completing these scales are valid and reflect similarities or differences in empowerment across language groups, not measurement artifact. Consequently, heiQ empowerment data from English- and French-speaking respondents can be directly pooled or contrasted in data analyses.