On the Democratic Weights of Nations

Abstract

Which voting weights ought to be allocated to single delegates of differently sized groups from a democratic fairness perspective? We operationalize the ‘one person, one vote’ principle by demanding every individual’s influence on collective decisions to be equal a priori. The analysis differs from previous ones by considering intervals of alternatives. New reasons lead to an old conclusion: weights should be proportional to the square root of constituency sizes if voter preferences are independent and identically distributed. This is knife-edged, however, in that preference polarization along constituency lines quickly calls for a Shapley value-based variation of simple proportionality.

Keywords: institutional design; two-tier voting; collective choice; Shapley value; pivot probability; equal representation; random order values

JEL Classification: D02; D63; D70; H77