  Consider the following collective choice problem: a group of budget
constrained agents must choose one of several alternatives. Is there a budget
balanced mechanism that: i) does not depend on the specific characteristics of
the group, ii) does not require unaffordable transfers, and iii) implements
utilitarianism if the agents' preferences are quasilinear and their private
information? We study the following procedure: every agent can express any
intensity of support or opposition to each alternative, by transferring to the
rest of the agents wealth equal to the square of the intensity expressed; and
the outcome is determined by the sums of the expressed intensities. We prove
that as the group grows large, in every equilibrium of this quadratic-transfers
mechanism, each agent's transfer converges to zero, and the probability that
the efficient outcome is chosen converges to one.
