set of criteria in which the members of the same category do not share any specific set of features but rather have what Wittgenstein referred to as “family resemblance.” Such concepts are conglomerations with less precise boundaries, such as happiness, prestige, social exclusion, and the like.

Definitions depend on their purpose. Bradburn recalled Pollak’s mention of disability and marital status as examples of concepts that could be defined for a scientific use in order to fit into a theory or be used to make predictions, or they could be related to policy needs or social descriptive purposes. He said that concepts can be characterized by explicit definition (e.g., formulas, such as income = consumption + savings), by implicit definition (e.g., from scientific uses or attempting axiomatic definitions), or by operational definition (e.g., IQ). The usual trade-off with respect to common metrics is between the accuracy of characterization and the purpose and breadth of applicability.

Once there is a definition, the next concern is that the representation matches the concept. Thus, concepts referring to specific features like age or income to some extent can have single-value functions that measure the values of concern. However, Ballungen concepts are often measured by indicators or indices. It is often difficult to do much more than simply count up different indicators, unless some mathematical structure can be imposed on them. Measurement procedures may combine variables with different underlying relations to other concepts (e.g., happiness and satisfaction). Bradburn observed that one of the tensions in the social sciences is that the more one refines a concept and the more precise one tries to make it, the more one may lose some of the associations and original meaning, and comparability across uses may suffer. To consider large numbers of indicators over time, one ends up reducing or weighting them. Where the weights come from is of crucial importance to the validity of the measure. Bradburn saw the need to address these issues of narrowing and redefinition if a particular set of indicators are to be used for prediction or explanation.

He turned next to two aspects of procedures. One is accuracy in terms of getting the true value of what one is trying to measure, and the other is precision or getting a narrow range of estimation. In the social sciences, researchers do not do much with instrumentation. The issue he identified is whether survey questions actually measure what one thinks they are measuring. He observed that there is no gold standard for almost all measures of concepts of interest to social scientists. However, in psychology at least, this problem was addressed years ago using the multitrait, multimethod approach—that is, using different measurement modes and different aspects of the concept to measure something in different ways, which all roughly converge on the same answer. Such empirical regularities strengthen the view that the measurement is correct, particularly if it is for scientific pur-

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