The place of philosophy of law between justice and efficiency

A discussion regarding the complex relationship that exists between the concepts of efficiency and justice goes a long way back and raises several relevant arguments. One of them, and it must be rejected in advance, is that justice is in the realm of public law, while efficiency in that of private law. Is it unacceptable that the balance between public and private law leads to the belief of a divided legal system; one system, one set of laws, one legal system. Legislators and judges are responsible for determining a balance and no theory can postulate that the balance will always be found with a simple cut between public and private law to distinguish when the criterion should be justice or when it should be efficiency. It is reductionist to confine the discussion to single goals of efficiency and justice, when human dignity and human rights should also be considered when one is discussing law. Moreover, a discussion limited to only the concepts of justice and efficiency, relies on a belief that the terms are mutually exclusive. Posner has said that the economic analysis of law has limits and philosophy of law plays an extremely important role in this discourse, which must be interdisciplinary. There can be no goal other than the realization of human rights and there can be no justice if not shared by all of mankind

Regression games

The solution of a TU cooperative game can be a distribution of the value of the grand coalition, i.e. it can be a distribution of the payo (utility) all the players together achieve. In a regression model, the evaluation of the explanatory variables can be a distribution of the overall t, i.e. the t of the model every regressor variable is involved. Furthermore, we can take regression models as TU cooperative games where the explanatory (regressor) variables are the players. In this paper we introduce the class of regression games, characterize it and apply the Shapley value to evaluating the explanatory variables in regression models. In order to support our approach we consider Young (1985)'s axiomatization of the Shapley value, and conclude that the Shapley value is a reasonable tool to evaluate the explanatory variables of regression models

Entropy Criterion In Logistic Regression And Shapley Value Of Predictors

Entropy criterion is used for constructing a binary response regression model with a logistic link. This approach yields a logistic model with coefficients proportional to the coefficients of linear regression. Based on this property, the Shapley value estimation of predictors’ contribution is applied for obtaining robust coefficients of the linear aggregate adjusted to the logistic model. This procedure produces a logistic regression with interpretable coefficients robust to multicollinearity. Numerical results demonstrate theoretical and practical advantages of the entropy-logistic regression

Priorities in Thurstone Scaling and Steady-State Probabilities in Markov Stochastic Modeling

Thurstone scaling is widely used in marketing and advertising research where various methods of applied psychology are utilized. This article considers several analytical tools useful for positioning a set of items on a Thurstone scale via regression modeling and Markov stochastic processing in the form of Chapman-Kolmogorov equations. These approaches produce interval and ratio scales of preferences and enrich the possibilities of paired comparison estimation applied for solving practical problems of prioritization and probability of choice modeling

Multiple Regression in Pair Correlation Solution

Behavior of the coefficients of ordinary least squares (OLS) regression with the coefficients regularized by the one-parameter ridge (Ridge-1) and two-parameter ridge (Ridge-2) regressions are compared. The ridge models are not prone to multicollinearity. The fit quality of Ridge-2 does not decrease with the profile parameter increase, but the Ridge-2 model converges to a solution proportional to the coefficients of pair correlation between the dependent variable and predictors. The Correlation-Regression (CORE) model suggests meaningful coefficients and net effects for the individual impact of the predictors, high quality model fit, and convenient analysis and interpretation of the regression. Simulation with three correlations show in which areas the OLS regression coefficients have the same signs with pair correlations, and where the signs are opposite. The CORE technique should be used to keep the expected direction of the predictor’s impact on the dependent variable

Regression Split by Levels of the Dependent Variable

Multiple regression coefficients split by the levels of the dependent variable are examined. The decomposition of the coefficients can be defined by points on the ordinal scale or by levels in the numerical response using the Gifi system of binary variables. This approach permits consideration of specific values of the coefficients at each layer of the response variable. Numerical results illustrate how to identify levels of interpretable regression coefficients

How Good is Best? Multivariate Case of Ehrenberg-Weisberg Analysis of Residual Errors in Competing Regressions

A.S.C. Ehrenberg first noticed and S. Weisberg then formalized a property of pairwise regression to keep its quality almost at the same level of precision while the coefficients of the model could vary over a wide span of values. This paper generalizes the estimates of the percent change in the residual standard deviation to the case of competing multiple regressions. It shows that in contrast to the simple pairwise model, the coefficients of multiple regression can be changed over a wider range of the values including the opposite by signs coefficients. Consideration of these features facilitates better understanding the properties of regression and opens a possibility to modify the obtained regression coefficients into meaningful and interpretable values using additional criteria. Several competing modifications of the linear regression with interpretable coefficients are described and compared in the Ehrenberg-Weisberg approach