Majority voting and Pareto optimality

6. Summary

This investigation of the majority voting decision under various tax structures makes the following points. First, that majority voting cannot be relied upon to choose the Pareto optimal level of output of the public good if the structure of taxes is predetermined. What is chosen is an output level of the public good that is Pareto optimal with respect to the particular tax structure. Another tax structure might exist that provides a better solution.

Secondly, the choice of a tax structure should not be made independent of the choice of the output of the public good if Pareto efficiency is the objective. Pareto efficiency is guaranteed because the change in the contribution to the candidate of a marginal change in any after-tax endowment, λi U ⁱ _Y, is equal for all individuals. Consequently, individuals capable of offering high marginal contributions, λⁱ, will be rewarded with low tax rates. attaining Pareto efficiency via this pairing, however, may require a significant altering of the after tax distribution of income. If, for example, all individuals have identical utility functions and equal marginal contributions, equation (12b) requires equal after tax incomes (equal marginal sacrifice).

This system of voting and taxation is the antithesis of that developed independently by Clarke (1971) and Groves and Loeb (1975). Clarke, and Groves and Loeb determine the output level of the public good by maximizing the sum of stated valuation functions for the public good for given tax rates associated with the public good. Because penalties may be imposed if people misrepresent their valuations, true and complete representations are forthcoming (this results in β _i = 1 for all i in equations (9) and (10)). Here the approach is to reward voting intensity with reductions in the tax on private endowments until and individuals have equal voting intensity (i.e., β _i = β for all i). Both systems overlook equity considerations.

Finally, individual tax burdens associated with a public project should be made known to the individual. Uncertainty about the individual cost of a joint project will lead to suboptimal output, even though the aforementioned conditions for Pareto optimality are met.

An extrapolation of these results might suggest that, to the extent that persons are more homogeneous within regions than across regions, a wider range of tax structures might be needed to assure Pareto efficiency at the aggregate level than at the local level. This provides a rationale for the fact that state and regional income tax rates are often uniform while federal income tax rates are graduated according to income. Conversely, if all taxing bodies are subject to the same tax structure constraints, one would expect the provision of local public goods to more closely approximate the Pareto ideal than the provision of pure public goods at the national level.