Ambiguous Criteria Weights in AHP: Consequences and Solutions*

Two related streams of criticism of the analytic hierarchy process (AHP) have not yet been satisfactorily resolved, although both date from the early 1980s. The first relates to ambiguity in the meaning of the relative importance of one criterion as compared to another. The second is concerned with reversals of rank alleged to be possible when new options are introduced in an AHP problem. Both proponents and critics of AHP agree that rank reversals occur, but disagree on the legitimacy of such reversals. This paper shows that there is a necessary correspondence between the manner in which criteria importances are interpreted and computed and the manner in which the weights of the options under each criterion are normalized. In general, if this relationship is ignored, incorrect weights are generated for options under consideration regardless of whether new options are added or deleted. A rank reversal on the addition of an option is merely symptomatic of this fact, and such reversals do not occur when the correspondence condition is met.     

Need-service matching in substance abuse treatment: Racial/ethnic differences

This study examines the impact of ancillary health and social services matched to client needs in substance abuse treatment for African Americans, Latinos and Whites. The study uses data collected from 1992 to 1997 for the National Treatment Improvement Evaluation Study, a prospective cohort study of substance abuse treatment programs and their clients. The analytic sample consists of 3142 clients (1812 African Americans, 486 Latinos, 844 Whites) from 59 treatment facilities. Results show that racial/ethnic minorities are underserved compared to Whites in the substance abuse service system. Different racial/ethnic groups come into treatment with distinct needs and receive distinct services. Although groups respond differentially to service types, substance abuse counseling and matching services to needs is an effective strategy both for retaining clients in treatment and for reducing post-treatment substance use for African Americans and Whites. Receipt of access services was related to reduced post-treatment substance use for Latinos. Study findings are relevant to planning special services for African Americans and Latinos.     

Evaluating school and parent reports of the national student achievement testing system (SIMCE) in Chile: Access,comprehension, and use

This evaluation examined school and parent reports of the national student achievement testing system (SIMCE) in Chile regarding three dimensions: access, comprehension, and use. We conducted phone surveys with a representative sample of directors (N = 375), teachers (N = 1145) and parents (N = 625), and we collected more in-depth data through interviews and focus groups in 16 of these schools. The results indicate that access to the reports is not an obstacle to use for school actors, but it is for parents. While summative ratings of the reports in terms of their clarity and utility were generally very positive, the actual recall and interpretation of even basic information (assessed through case scenarios) was incorrect for a majority of teachers and parents, and reported uses of the information were both intended and unintended in nature. We also found some statistically significant differences regarding comprehension and use among subgroups of our sample. Our findings are especially relevant given the expectations attached to the use of the reports for school improvement on the one hand, and parents’ behavior as critical consumers of education on the other hand.     

“Which One Is Yours?”: Children and Ethnography

This paper explores roles that children play in ethnographic research. Based on the limited literature on children in the field, and drawing on examples from ethnographies across disciplines, I identify four roles for children: 1) as “wedges,” or as instrumentally important in helping adult ethnographers gain access in various ways; 2) as collaborators; 3) as objects of study; and 4) as subjects of study. I also discuss the ways in which these roles illuminate key methodological issues in ethnography, like reflexivity, ethics, and agency. The paper synthesizes and integrates previously disconnected research on the presence of children in the field with ethnographies in which children and childhood are the topics of research. I draw on my own fieldwork experiences for further illustration.

$${\mathcal{Q}}$$-anonymous social welfare relations on infinite utility streams

This paper studies a class of social welfare relations (SWRs) on the set of infinite utility streams. In particular, we examine the SWRs satisfying -Anonymity, an impartiality axiom stronger than Finite Anonymity, as well as Strong Pareto and a certain equity axiom. First, we characterize the extension of the generalized Lorenz SWR by combining -Anonymity with Strong Pareto and Pigou–Dalton Equity. Second, we replace Pigou–Dalton Equity with Hammond Equity for characterizing the extended leximin SWR. Third, we give an alternative characterization of the extended utilitarian SWR by substituting Incremental Equity for Pigou–Dalton Equity.     

The NIP graph of a social welfare function

We consider the fraction of pairs of m distinct alternatives on which a social welfare function f may be nondictatorially independent and Pareto when the domain of f satisfies the free k-tuple property. When k = 4 we improve the existing upper bound to . When there are at least 26 alternatives and we obtain an original upper bound, . To obtain these results we define and analyze the graph formed from the nondictatorial independent and Pareto pairs and combine the results of this analysis with known results from extremal graph theory. The authors extend special thanks to the two reviewers and the editor for their comments.     

Minimal covering set solutions

We study necessary and sufficient conditions for a multi-valued solution S to be rationalized in the following sense: there exists a complete asymmetric relation T (a tournament) such that, for each feasible (finite) set, the solution set of S coincides with the minimal covering set of T restricted to that feasible set. Our characterization result relies only on properties relating S across feasible choice sets.     

Moral hazard and free riding in collective action

Most political and economic theorists point to moral hazard in teams as the main obstacle to lobbies’ collective action. In this paper, we address this important issue with a coalition-formation game. In the process of doing so, we characterize equilibrium lobby structures both in the absence and in the presence of moral hazard. Three notable results emerge from such an exercise: (1) an equilibrium lobby structure exists under both specifications of the model, (2) moral hazard in teams may raise large groups’ equilibrium lobby size, and (3) it may also raise the level of collective action of large groups with low organizational costs. I wish to express my appreciation to Helmuth Cremer, Philippe De Donder, Kai A. Konrad, Michel Le Breton, Daniel Seidmann, Shlomo Weber, an associate editor of this journal and a referee for valuable comments and suggestions. I am also grateful to Paul Belleflamme, Francis Bloch, Robert Dur, Joan Esteban, Debraj Ray, and the audience at the CESifo Area Conference on Public Sector Economics 2006 and at the 15th Aix-Marseille SSIEIO for helpful discussions.     

To be or not to be involved: a questionnaire-experimental view on Harsanyi’s utilitarian ethics

According to standard theory founded on Harsanyi (J Polit Econ 61:434–435, 1953; 63:309–321, 1955) a social welfare function can be appropriately based on the individual’s approach to choice under uncertainty. We investigate how people really do rank distributions in terms of welfare. According to Harsanyi, the evaluation can be done from the standpoint of an uninvolved external judge, a public official, for example, or by a person who knows that she holds one of the positions in society, with an equal chance for any of the available positions. Are these two structures to be viewed differently? We use a questionnaire experiment to focus on the two different interpretations of the Harsanyi approach. There are important, systematic differences that transcend the cultural background of respondents.     

Gender and Transnational Gossip

Transnational social networks powerfully shape Mexican migration and enable families to stretch internationally. In an atmosphere of such high dependence on social networks, it would be rare for families not to be affected by the opinions of others. This article analyzes this often-overlooked aspect of social networks, gossip. I analyze gossip stories prevalent for one type of migrant family, those in which parents and children live apart. Drawing on over 150 ethnographic interviews and observation with members of Mexican transnational families and their neighbors in multiple sites, I describe both parents’ and children’s experiences with transnational gossip. I show that in a transnational context, gossip is a highly gendered activity with different consequences for men and women. Although targeting both women and men, transnational gossip reinforces the expectations that mothers be family caregivers and fathers be family providers even when physical separation makes these activities difficult to accomplish.