Axiomatic foundations for fairness-motivated preferences

Much work in social choice theory takes individual preferences as uninvestigated inputs into aggregation functions designed to reflect considerations of fairness. Advances in experimental and behavioural economics show that fairness can also be an important motivation in the preferences of individuals themselves. A proper characterisation of how fairness concerns enter such preferences can enrich the informational basis of many social choice exercises. This paper proposes axiomatic foundations for individual fairness-motivated preferences that cover most of the models developed to rationalise observed behaviour in experiments. These models fall into two classes: Outcome-based models, which see preferences as defined only over distributive outcomes, and context-dependent models, which allow rankings over distributive outcomes to change systematically with non-outcome factors. I accommodate outcome-based and context-sensitive fairness concerns by modelling fairness-motivated preferences as a reference-dependent preference structure. I first present a set of axioms and two theorems that generate commonly used outcome-based models as special cases. I then generalise the axiomatic basis to allow for reference-dependence, and derive a simple functional form in which the weight on each person’s payoff depends on a reference vector of how much each person deserves.     

Gamson’s law and hedonic games

This note adds one celebrated coalition formation game due to Gamson (Am Soc Rev 26:373–382 1961a, Am Soc Rev 26:565–573, 1961b) in the list of applications of the theory of hedonic games explored by Banerjee et al. (Soc Choice Welf 18:135–153, 2001) and Bogomolnaia and Jackson (Games Econ Behav 38: 204–230, 2002). We apply their results to study the original Gamson game and offer extensions both to a multi-dimensional characteristics space and to an infinite number of players.     

Clustering and combinatorial optimization in recursive supervised learning

The use of combinations of weak learners to learn a dataset has been shown to be better than the use of a single strong learner. In fact, the idea is so successful that boosting, an algorithm combining several weak learners for supervised learning, has been considered to be the best off the shelf classifier. However, some problems still exist, including determining the optimal number of weak learners and the over fitting of data. In an earlier work, we developed the RPHP algorithm which solves both these problems by using a combination of global search, weak learning and pattern distribution. In this chapter, we revise the global search component by replacing it with a cluster based combinatorial optimization. Patterns are clustered according to the output space of the problem, i.e., natural clusters are formed based on patterns belonging to each class. A combinatorial optimization problem is therefore created, which is solved using evolutionary algorithms. The evolutionary algorithms identify the “easy” and the “difficult” clusters in the system. The removal of the easy patterns then gives way to the focused learning of the more complicated patterns. The problem therefore becomes recursively simpler. Over fitting is overcome by using a set of validation patterns along with a pattern distributor. An algorithm is also proposed to use the pattern distributor to determine the optimal number of recursions and hence the optimal number of weak learners for the problem. Empirical studies show generally good performance when compared to other state of the art methods.     

A note on the paradox of smaller coalitions

We consider hedonic coalition formation games that are induced by a simple TU-game and a cooperative solution. For such models, Shenoy’s (Int J Game Theory 8:133–164, 1979) absence of the paradox of smaller coalitions provides a sufficient condition for core existence. We present three different versions of his condition in order to compare it to the top coalition property of Banerjee et al. (Social Choice Welfare 18:135–153, 2001) that guarantees nonemptiness of the core in more general models. As it turns out, the top coalition property implies a condition in which Shenoy’s paradox is not present for at least one minimal winning coalition. Conversely, if for each non-null player Shenoy’s paradox is not present for at least one minimal winning coalition containing that player, then the induced hedonic game satisfies the top coalition property.     

Analysis of breeding bird communities along an urban-rural gradient in Berlin,Germany, by Hasse Diagram Technique

Breeding bird communities in Berlin were investigated at five study sites, which represent an structural urban-rural gradient, from densely built-up areas with sealed ground to green areas such as large parks. In this paper, we tested the Hasse Diagram Technique (HDT), an approach belonging to partial order theory, for its appropriateness to extract information about changes in species composition from our data set. As expected, the overall number of bird species was positively correlated with the urban-rural gradient, increasing from 12 found in the city center to 28 in an urban park. By HDT analysis, four different sub-groups of birds could be identified, contributing differentially to the increase in species number: (1) ubiquists, i.e., species found at each study site, (2) a sub-group, the species’ number of which was positively correlated with the urban-rural gradient, increasing with increasingly green areas, (3) a sub-group, the species’ number of which was negatively correlated with the urban-rural gradient, decreasing with a declining density of buildings, and (4) species, the distribution of which did not show any correlation with the urban-rural gradient. The results show that HDT is a suitable tool for formalized analysis of the pattern of species’ communities along an environmental gradient.     

Civil Society Opposition to Nonferrous Metals Mining in Montana

This paper discusses the opposition of civil society to nonferrous metals mining in Montana. The mineral resources and mining history of Montana are discussed, as is the vibrant civil society of that state. Montana’s civil society has opposed mining due to its environmental effects, particularly upon areas of high conservation value. This opposition has involved litigation and the implementation of a ban on the use of cyanide by the mining industry. The paper concludes with a discussion of whether this opposition to mining has damaged the economy of the state and Montana’s future as an example of the “New West,” wherein amenities based growth act as the principal agent of economic activity.     

Simulated classical tests in multinomial probit models

This paper compares the application of different versions of the simulated counterparts of the Wald test, the score test, and the likelihood ratio test in one- and multiperiod multinomial probit models. Monte Carlo experiments show that the use of the simple form of the simulated likelihood ratio test delivers relatively robust results regarding the testing of several multinomial probit model specifications. In contrast, the inclusion of the Hessian matrix of the simulated loglikelihood function into the simulated score test and (in the multiperiod multinomial probit model) particularly the inclusion of the quasi-maximum likelihood theory into the simulated likelihood ratio test leads to substantial computational problems. The combined application of the quasi-maximum likelihood theory with the simulated Wald test or the simulated score test is not systematically superior to the application of the other versions of these two simulated classical tests either. Neither an increase in the number of observations nor in the number of random draws in the incorporated Geweke-Hajivassiliou-Keane simulator systematically lead to more precise conformities between the frequencies of type I errors and the basic significance levels. An increase in the number of observations only decreases the frequencies of type II errors, particularly regarding the simulated classical testing of multiperiod multinomial probit model specifications.     

Time with Children: Do Fathers and Mothers Replace Each Other When One Parent is Unemployed?

This article aims to study the substitution of parental time between the mother and the father. Taking the “experience” of unemployment as a release from the time constraint, we analyse time transfers between partners in such a situation. A bivariate Tobit model is applied on the French time-use data. It shows that parents quite rarely substitute the time devoted to children between each other, except for child transportation and childcare. Parents do not want to relinquish their parental activities, a fact which reflects their desire to contribute to the children’s education, and the contribution of parental time to the balance of power between spouses. Exchanges remain asymmetric: non-employed fathers release less their partner from parental tasks than unemployed mothers do, which reflects the weight of gender social norms.     

A Parallel between Regret Theory and Outranking Methods for Multicriteria Decision Making Under Imprecise Information

Incorporation of the behavioral issues of the decision maker (DM) is among the aspects that each Multicriteria Decision Making (MCDM) method implicitly or explicitly takes into account. As postulated by regret theory, the feelings of regret and rejoice are among the behavioral issues associated with the entire decision making process. Within the context of MCDM, the DM may feel regret, when the chosen alternative is compared with another one having at least one better criterion value. PROMETHEE II is a widely known MCDM method that makes no explicit incorporation of regret attitude of the DM. In this paper, we elaborate on the applicability of regret theory to MCDM context. In particular, we investigate the findings of regret theory and explore the parallel between regret theory and PROMETHEE II method. Relying on the concepts of regret theory, we demonstrate how a decision that is made using a PROMETHEE II based outranking method conforms to the regret attitude of the DM.