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 finding is fragile, however, in that preference polarization along constituency lines quickly calls for plain proportionality.