Vote budgets and Dodgson’s method of marks

We examine voting rules that are inspired by Dodgson’s method of marks (to be distinguished from the procedure that is commonly referred to as Dodgson’s rule) by means of two criteria. Each voter decides how to allocate a vote budget (which is common to all voters, and need not be exhausted) to the candidates. Our first criterion is a richness condition: we demand that, for any possible preference ordering a voter may have, there is a feasible allocation of votes that reflects these preferences. A (tight) lower bound on the vote budget is established. Adding a strategy-proofness condition as a second criterion, we recommend that the vote budget be given by the lower bound determined in our first result.