The Goldilocks principle: applying the exclusive disjunction to fuzzy sets

Qualitative Comparative Analysis (QCA), a technique by which the tools of Boolean algebra are applied to equifinal causal conditions, is gaining popularity amongst scholars. This paper draws upon a distinction largely overlooked by the QCA literature: the difference between inclusive- and exclusive-or (OR and XOR). I argue that XOR should be included amongst the tools of QCA, explain why XOR is more easily applied to crisp- than fuzzy-set QCA, and provide two original techniques for applying XOR to fuzzy sets: mechanical and calibrated. With the calibrated technique, the application of the exclusive-or is related to substantive knowledge of the cases with two threshold values: (1) how large two fuzzy set values need to be in order to violate a prior commitment or overshoot a target outcome, and (2) how similar two values need to be in order to violate the rule: ‘A or B, but not both’. This paper improves the capacity of QCA expressions to mirror natural language closely, formalize conversational implicature, and deal with mutually exclusive clusters of sufficiency conditions. It includes a helpful step-by-step guide for QCA practitioners.     

Exploring the robustness of set theoretic findings from a large n fsQCA: an illustration from the sociology of education

Ragin’s Qualitative Comparative Analysis (QCA) is often used with small to medium samples where the researcher has good case knowledge. Employing it to analyse large survey datasets, without in-depth case knowledge, raises new challenges. We present ways of addressing these challenges. We first report a single QCA result from a configurational analysis of the British National Child Development Study dataset (highest educational qualification as a set theoretic function of social class, sex and ability). We then address the robustness of our analysis by employing Du?a and Thiem’s R QCA package to explore the consequences of (i) changing fuzzy set theoretic calibrations of ability, (ii) simulating errors in measuring ability and (iii) changing thresholds for assessing the quasi-sufficiency of causal configurations for educational achievement. We also consider how the analysis behaves under simulated re-sampling, using bootstrapping. The paper offers suggested methods to others wishing to use QCA with large n data.     

On rationalizability of choice functions: A characterization of the median

In this paper we characterize choice behaviour that picks the median element from a set of feasible alternatives. It is easily seen that this choice behaviour violates most of the standard consistency conditions for set contraction and set expansion. The paper offers a complete characterization in terms of pure choice function conditions, and contrasts the new axiom set with the traditional consistency conditions. It also suggests alternative external references which could explain the choice of the median. Received: 2 June 1997/Accepted: 27 July 1998     

Identifying X-Consumers Using Causal Recipes: “Whales” and “Jumbo Shrimps” Casino Gamblers

X-consumers are the extremely frequent (top 2–3%) users who typically consume 25% of a product category. This article shows how to use fuzzy-set qualitative comparative analysis (QCA) to provide “causal recipes” sufficient for profiling X-consumers accurately. The study extends Dik Twedt’s “heavy-half” product users for building theory and strategies to nurture or control X-behavior. The study here applies QCA to offer configurations that are sufficient in identifying “whales” and “jumbo shrimps” among X-casino gamblers. The findings support the principle that not all X-consumers are alike. The theory and method are applicable for identifying the degree of consistency and coverage of alternative X-consumers among users of all product-service category and brands.     

QCA as competing or complementary method? A qualitative comparative analysis approach to protest event data

Studies of state repression of protest have focused on theories of threat and weakness, in which states repress movements that threaten state authority or elite interest or movements that lack organizational or political strength. Empirical studies have most often used regression analysis of protest-event datasets. This paper proposes qualitative comparative analysis (QCA) as an alternative approach to protest-event data that retains more qualitative complexity and captures the conjunctural and heterogeneous nature of causation during events. The paper applies both methods to protest data from the United States (1963–1973). While both methods provide strong evidence for the threat and weakness hypotheses, QCA more effectively illustrates how combinations of threat and weakness factors increase the risk of repression. The paper argues that QCA is a viable alternative approach to event data, but it should also be seen as a valuable complementary method that can improve regression-based approaches.     

Book Review: The Death Knell of the Utilitarianism: A Review and Theoretical Implications of To Profit or Not to Profit

This paper uses the edited volume To Profit or Not to Profit; The Commercial Transformation of the Nonprofit Sector as an opportunity to review the theories of the nonprofit sector based on the utility maximization behavioral model linked to neoclassical economics. The existence of a large nonprofit sector and its increasing commercialism undermines the logical sufficiency of these theories to explain organizational behavior. The book in question is an effort to solve that problem and reconcile the utility maximization model with seemingly contradicting evidence. In the end, however, these efforts are not very successful and lead to the partial acceptance of an alternative model, grounded in the neo-institutional theory of organizations.     

“Site Fights”: Explaining Opposition to Pipeline Projects in the Developing World1

Fifty years ago, the main challenges to large infrastructure projects were technical or scientific. Today, the greatest hurdles faced by such projects are almost always social and/or political. Whether constructing large dams in the developing world or siting liquefied natural gas terminals in the United States, the onset of these projects often triggers intense popular opposition. But not always, and therein lays the animating aim of this project. We undertake a systematic comparative case analysis of mobilization efforts against 11 oil and gas pipeline projects spanning 16 countries in the developing world. Using theories from the social movement and facility siting literatures and the technique of fuzzy set/qualitative comparative analysis (fs/QCA), we examine the “causal conditions” linked to political and legal opposition to these projects. We find that both Western funding of projects and public consultation serve as necessary political opportunities encouraging mobilization. In addition, not compensating the host country for involvement in the project is linked to mobilization. Finally, some risk from the project, in the form of environmental or social impact, is associated with mobilization; however, this impact does not have to be very significant for mobilization to occur.     

The Effects of Calibration Target,Screen Location,and Movement Type on Infant Eye‐Tracking Data Quality

During infant eye‐tracking, fussiness caused by the repetition of calibration stimuli and body movements during testing are frequent constraints on measurement quality. Here, we systematically investigated these constraints with infants and adults using EyeLink 1000 Plus. We compared looking time and dispersion of gaze points elicited by stimuli resembling commonly used calibration animations. The adult group additionally performed body movements during gaze recording that were equivalent to movements infants spontaneously produce during testing. In our results, infants’ preference for a particular calibration target did not predict data quality elicited by that stimulus, but targets exhibiting the strongest contrasts in their center or targets with globally distributed complexity resulted in the highest accuracy. Our gaze measures from the adult movement tasks were differentially affected by the type of movement as well as the location where the target appeared on the screen. These heterogeneous effects of movement on measures should be taken into account when planning infant eye‐tracking experiments. Additionally, to improve data quality, infants’ tolerance for repeated calibrations can be facilitated by alternating between precise calibration targets.     

Making hermeneutics explicit: how QCA supports an insightful dialogue between theory and cases

Typically, qualitative comparative analysis (QCA) is praised for its hermeneutic dialogue between theory and empirical cases. However, in reporting research with QCA, these hermeneutic processes will usually not be illustrated. This paper aims at showing clear how QCA induces this dialogue between theory and data. As an illustrative example, I use a research situation dealing with a genuine research question of Legislative Studies: the causes of party unity. Using the classical dichotomous and the MV-QCA approach, the paper mainly shows how to deal productively with contradictory theoretical statements and how stepping from simpler to more complex models adds explanation while still making clear further routes to improve insights into the substantive research topic: both theoretically and empirically. Finally, non-observed configuration (‘logical remainders’) will be used to simplify the resulting theory, and its theoretical and empirical plausibility will be evaluated. The whole paper makes explicit how the QCA approach forces researchers to reveal the dialogue between theory and cases – just as it was intended by the inventor of this analytical tool.     

Analyzing multilevel data with QCA: a straightforward procedure

The social sciences are witnessing a growing body of multilevel theories and debates about the proper methodological tools for the analysis of multilevel data. In a recent contribution to this journal, multilevel Qualitative Comparative Analysis (QCA) was proposed as a new methodological tool for discerning set-relational patterns in multilevel data. I argue that the presentation of multilevel QCA is erroneous in two respects. First, multilevel QCA ignores the fact that equifinal solutions entail diversity and therefore leads one to overestimate the complexity of QCA solutions. Second, the ordinary minimization procedure of truth tables that contain multilevel data yields the same solutions as multilevel QCA, but is much easier to implement. I conclude that the established inventory of QCA does not need to be extended by a special multilevel approach.     

Contraction consistent stochastic choice correspondence

We model a general choice environment via probabilistic choice correspondences, with (possibly) incomplete domain and infinite universal set of alternatives. We offer a consistency restriction regarding choice when the feasible set contracts. This condition, ‘contraction consistency’, subsumes earlier notions such as Chernoff’s Condition, Sen’s α and β, and regularity. We identify a restriction on the domain of the stochastic choice correspondence (SCC), under which contraction consistency is equivalent to the weak axiom of revealed preference in its most general form. When the universal set of alternatives is finite, this restriction is also necessary for such equivalence. Analogous domain restrictions are also identified for the special case where choice is deterministic but possibly multi-valued. Results due to Sen (Rev Econ Stud 38:307–317, 1971) and Dasgupta and Pattanaik (Econ Theory 31:35–50, 2007) fall out as corollaries. Thus, conditions are established, under which our notion of consistency, articulated only in reference to contractions of the feasible set, suffices as the axiomatic foundation for a general revealed preference theory of choice behaviour.     

Agreement, separability, and other axioms for quasi-linear social choice problems

A quasi-linear social choice problem is concerned with choosing one among a finite set of public projects and determining side payments among agents to cover the cost of the project, assuming each agent has quasi-linear preferences. We first investigate the logical relations between various axioms in this context. They are: agreement, separability, population solidarity, consistency, converse consistency, and population-and-cost solidarity. Also, on the basis of these axioms, we present alternative characterizations of egalitarian solutions; each solution assigns to each agent an equal share of the surplus derived from the public project over some reference utility level, but uses a different method to compute the reference utility level. Received: 18 May 1998/Accepted: 1 July 1999     

A Confirmatory Factor Analysis of Home Environment and Home Social Behavior Data from the Elementary School Success Profile for Families

The purpose of the current study was to test the factor structure and scale quality of data provided by caregivers about the home environment and child behavior at home using the Elementary School Success Profile (ESSP) for Families. The ESSP for Families is one component of the ESSP, an online social-environmental assessment that also collects information from students and teachers. Confirmatory factor analyses with Mplus and weighted least squares means and variances adjusted estimation took into account the hierarchical nature and ordinal level of the data. The sample comprised caregivers of 692 third- through fifth-grade students from 13 elementary schools in four districts. A primary model and an alternative model were tested. Models were tested on a random calibration sample and validated with another sample. A nine-factor first-order solution demonstrated superior fit to the data. Scores from the nine scales also demonstrated acceptable internal consistency reliability. Implications for practice and further research are presented.     

“I Try Not to Depend on Anyone but Me”: Welfare‐Reliant Women's Perspectives on Self‐Sufficiency,Work, and Marriage*

Welfare reformers sought to reduce “dependency,” or reliance on state‐supported cash benefits and deployed a discourse of “self‐sufficiency” to promote the legitimacy of efforts to remove welfare recipients from publicly funded cash assistance through either wage labor or marriage. We use longitudinal, qualitative interview data collected from 38 initially welfare‐reliant women to examine what self‐sufficiency means to them and their perspectives on how work and marriage affect their ability to be self‐sufficient. Grounded theory analysis revealed that for these women, self‐sufficiency means formal independence from both the state (i.e., Temporary Assistance to Needy Families [TANF]) and men (i.e., marriage). Although they value marriage as an institution and would ideally marry, they do not consider marriage to be a likely route to self‐sufficiency given the pool of men available to them. Rather, they embrace their own market‐based wage labor as the means by which they can attain some measure of independence. Taking our lead from the women in this study, we challenge the emphasis on marriage in current welfare policy. We argue that employment training that results in better jobs for women and men and work supports that make low‐wage work pay are clearly the appropriate direction for policy aimed at the welfare‐reliant and working poor.     

Combined Effects: The Influence of Organizational Form and Structural Characteristics on Contract Performance in Mixed Sector Markets

Social service contracting to nongovernmental organizations is popular form of privatization across the world. Although nonprofits are preferable social service providers for legal and normative reasons, governments in the United States increasingly rely on for-profit organizations to deliver social services. This trend warrants further exploration about whether nonprofits or for-profits perform according to theoretical expectations when they exist in the same market. This study employs qualitative comparative analysis (QCA) to examine how sector-public, nonprofit, and for-profit-combines with structural variables to produce acceptable contract performance in juvenile justice programs. QCA is a discovery-oriented research tool that determines whether combinations of variables within cases produce a specific outcome and whether those combinations are consistent across cases. I find sector is not a necessary or sufficient predictor of acceptable performance on its own. Rather it combines with market factors to lead to acceptable contract performance. Combinations vary by sector, indicating that sectors behave differently in similar circumstances. The primary theoretical contribution of this paper is to provide a nuanced account of contract performance in mixed sector markets.     

The equivalence of the cost share equilibria and the core of a voting game in a public goods economy

We consider a social situation where individuals choose one or some alternative(s) from a set of feasible alternatives. When one alternative is socially chosen, each individual must share the cost for it according to an exogenously given sharing rule. Individuals are allowed to collude among themselves through money transfers. As the mechanism of choosing a social alternative, we consider the cost share equilibrium and a voting game. The cost share equilibrium is an allocation where each individual maximizes his/her utility independently and where unanimity is still maintained. We will show the equivalence between the set of all equilibrium allocations and the core of the voting game with compensation.I would like to thank Professors Mamoru Kaneko, Kotaro Suzumura, William Thomson, Mikio Nakayama, Hiroo Sasaki, Mr. Ken-ichi Shimomura and anonymous referees for their many useful suggestions and comments. I also acknowledge grammatical suggestions of Mr. Ronald M. Siani.     

Sophisticated voting outcomes and agenda control

Necessary and sufficient conditions for an alternative to be a sophisticated voting outcome under an amendment procedure are derived. The uncovered set, as first defined by Miller (1980), is shown to be potentially reducible, and conditions are determined for which this reduction equals the set of sophisticated voting outcomes. In addition, simple methods are given for calculating both the uncovered set and its reduction.Presented at the 1984 Annual Meeting of the Public Choice Society, Phoenix AZ, March 1984. I would like to thank Gerald Kramer, Nicholas Miller, Norman Schofield, two anonymous referees, and especially Richard McKelvey for helpful suggestions and comments.     

Arrow's Theorem with a fixed feasible alternative

Arrow's Theorem, in its social choice function formulation, assumes that all nonempty finite subsets of the universal set of alternatives is potentially a feasible set. We demonstrate that the axioms in Arrow's Theorem, with weak Pareto strengthened to strong Pareto, are consistent if it is assumed that there is a prespecified alternative which is in every feasible set. We further show that if the collection of feasible sets consists of all subsets of alternatives containing a prespecified list of alternatives and if there are at least three additional alternatives not on this list, replacing nondictatorship by anonymity results in an impossibility theorem.Most of the research for this article was completed while we were participants in the Public Choice Institute held at Dalhousie University during the summer of 1984. We wish to record here our thanks to the Institute Director, E.F. McClennen, and its sponsors, the Council for Philosophical Studies, the U.S. National Science Foundation, and the Social Science and Humanities Research Council of Canada. We are grateful to our referees for their comments and the Center for Mathematical Studies in Economics and Management Science at Northwestern University, where Weymark was a visitor during 1985–86, for secretarial assistance.     

On the leximin and utilitarian overtaking criteria with extended anonymity

We present an extension of the overtaking criterion, called fixed-step overtaking social welfare relation (SWR), and its leximin counterpart, called fixed-step W-leximin SWR, for the evaluation of infinite utility streams. Our SWRs satisfy Fixed-step Anonymity. First, we characterize them by using the consistency, called Weak Fixed-step Indifference Consistency, which links indifference for infinite utility streams to indifference for their truncated vectors that are taken periodically. Second, we characterize another utilitarian extension, called S{\mathcal{S}}-overtaking SWR, by replacing the consistency with Fixed-step Anonymity. The S{\mathcal{S}}-overtaking SWR is a subrelation of the fixed-step overtaking SWR. Meanwhile, the leximin counterpart of the S{\mathcal{S}}-overtaking SWR coincides with the fixed-step W-leximin SWR, and we obtain its alternative characterization using Fixed-step Anonymity. Finally, we generalize the impossibility of combining Fixed-step Anonymity with the catching-up SWR by showing the Pareto and strong consistency axioms satisfied by the catching-up SWR come in conflict with Fixed-step Anonymity.     

A Multivariate Analysis of Bivariate Attitude-Behavior Relationships Based on Marginal Popularities*

The results of a contextual analysis of bivariate attitude-behavior findings, which is based on marginal popularities, are presented. The substantial rise in consistency as the popularity of behavior increases suggests that behavioral popularity has a strong contextual effect on the attitude-behavior relationship. Attitudinal popularity, however, is not positively related to consistency. The implications of the findings for the reference group approach to the attitude-behavior problem are considered, and it is suggested that the behavioral popularities may be indexing behavioral climates that are affecting consistency. An alternative individual-level behavioral competency interpretation of the results is also discussed.