Meaningful environmental indices: a social choice approach

This paper provides a characterization of meaningful environmental indices. Based on the interpretation of environmental indices as representations of a preference ordering on multi-dimensional environmental states, a meaningful index is defined as an index whose underlying preference ordering is independent of admissible transformations of the variables which describe environmental states. Admissible types of transformation are classified into categories of measurability and comparability, and these categories determine which indices are meaningful. One major finding is that indices in the form of an arithmetic mean are mostly not meaningful because the variables do not satisfy the required property of interval-scale unit comparability. For environmental variables in the non-negative domain whose observations are strictly positive and whose admissible transformations are mere expansions meaningful indices take the form of a geometric mean.