Constructing Summary Indices of Social Well-Being: A Model for the Effect of Heterogeneous Importance Weights 1

TLDR: In this paper, a model for measuring the extent to which individuals with differing importance weights for the component indicators agree on a summary QOL index was proposed, and conditions under which an index will be endorsed by a majority of a social group were derived.

Abstract: We consider problems associated with the construction of summary indices for a social unit (eg, cities, states, nations) These problems are motivated by the question of how to construct a social well-being or Quality-of-Life (QOL) index that summarizes many social indicators, and that a majority of individuals can agree with We specify a model for measuring the extent to which individuals with differing importance weights for the component indicators agree on a summary QOL index, and derive conditions under which an index will be endorsed by a majority of a social group We show that, in every case, intuition greatly underestimates the extent of agreement among individuals who have different importance weights for the components Two types of QOL indices are distinguished: (1) those rating multiple social units (eg, cities, states, countries) in the same time period (cross-sectional data), and (2) those rating a single social unit on multiple time periods (time-series data) In the first case, we show that it is easy to create a QOL index on which most people in society agree In the second case, we show that it is more difficult, but define conditions under which it is possible In particular, we show that the equal-weighting strategy is privileged in that it minimizes disagreement among all possible individuals’ weights When the actual distribution of individuals’ weights is known, one can improve agreement further by using the mean weights applied by individuals Finally, we examine nationally representative surveys of importance weights and show that they meet the conditions for successful construction of a QOL index that will be endorsed by a majority of individuals in a country We conclude with recommendations for measuring weights and creating QOL indices that have high levels of support among individual members of social units