WEIGHTED VOTING: A MATHEMATICAL ANALYSIS FOR INSTRUMENTAL JUDGMENTS,

Abstract : A paradox is suggested: that those whom its advocates say are its beneficiaries are probably those who are hurt by weighted voting, while those whom its opponents say are its victims probably gain from it. Typically the reason (whether publicly stated or not) for advocating weighted voting has been that the advocate wishes to save the seats of representatives from small districts which are likely to be consolidated under reapportionment into districts of equal size. It has almost invariably been the citizens of large districts who have brought suits against the adoption of weighted voting in legislatures, presumably because they feared that their influence would be less under a system of weighted voting than under a system of districts of equal size. If the analysis given is correct, both advocates and opponents have been wrong and each have taken positions contrary to their own best interests. The explanation of the paradox is that both parties to the dispute have apparently assumed that the citizens and legislators from the smaller districts would have more power than citizens and legislators from larger districts simply because the former have more legislators than the latter.