How should a society choose between two social alternatives if participation
in the decision process is voluntary and costly and monetary transfers are
not feasible? Considering symmetric voters with private valuations, we show
that it is utilitarian-optimal to use a linear voting rule: votes get alternativedependent
weights, and a default obtains if the weighted sum of votes stays
below some threshold. Standard quorum rules are not optimal. We develop a
perturbation method to characterize equilibria in the case of small participation
costs and show that leaving participation voluntary increases welfare for
linear rules that are optimal under compulsory participation.
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