A Social Choice Trade-off Between Alternative Fairness Concepts: Solidarity versus Flexibility

In this paper, we define simple measures of two properties that social choice functions may embody in different degrees in public goods environments. First, a measure of solidarity is proposed such that Thomson's (1990) replacement monotonicity property is a particular case in which the full amount of solidarity is required. Secondly, we introduce a measure of the degree of flexibility of a social choice function and prove that a trade-off in Campbell and Kelly's (1993) sense exists between both properties. More solidarity can only be achieved in exchange of less flexibility of the decision rule. When we restrict ourselves to the family of voting schemes called generalized Condorcet winner solutions, introduced by Moulin (1980), we find the exact trade-off and we can easily find the degrees of fulfillment of both properties, which amount to some generalization of the idea of ''qualified majority''.