Appendix 1 to Afterward -- Examples of Demand Revealing Governance

For readers that have little or no familiarity with the demand revealing process and those interested in recent extensions of the theory elaborated in this Afterward, I present simple examples intended to demonstrate how "a Clarke tax" and a broader "market solution to the public goods problem" works. Part A describes simple textbook examples, based on Varian's Microeconomic Analysis (1989).. Part B elaborates in terms of extensions of my earlier work in Bailey's A Constitution for A Future Country. (The Bailey book is reviewed in Appendix ). I also include in Part C an example of a practical application drawn from Clarke 1997.

A. Examples of Demand Revealing Governance

The examples build on the notion of "solutions" to the benefit taxation" problem of efficiently providing public goods. The problem, as set forth in Buchanan (1968), Clarke (1971, 1980) is the difficultly of obtaining efficient solutions where (a.) preferences among individuals differ or (b.) they are so distributed that if we took the preferences of a median voter as reflecting those of the overall population, we would obtain inefficient solutions through majority rule.

Consider, for example, differing preferences of nonidentical individuals. If such individuals with identical demands face equal tax prices, they would agree on same quantity. If they did not and were asked to reveal their demands with the tax prices varying in accordance with the revealed demands, there would be an incentive to behave strategically and to understate one's own preferences.

To help solve this problem and look at the possibilities in "benefit taxation", we explore the possibility of using a preference or demand-revealing rule to make decisions on a public good. This combination voting and tax scheme would work as indicated in Table 1. With reference to case (b.) above, we have a situation where majority voting with equal sharing of costs is likely to lead to a very inefficient outcome.

A Numerical Example (adapted from Varian, 1989).

The incentive effects of such a procedure can be seen in the following discrete case example. (See Table A-1). We charge the special "incentive tax" to any voter who is "pivotal" in changing the outcome.

Table A-1 presents a case where we have three voters (or representatives) who have to decide whether they want a communications technology (called E, or elasticity) in their community. It is tentatively decided that if the decision to acquire E, they will each bear an equal per capita share of the costs ($100), the total costs to them being $300. Voters 1 and 2 (call them John and Mary) are willing to pay $50 each for E while Henry is willing to pay $250. See Table A-1.

In this case, E provides a positive net value only to Henry. Thus majority voting would result in a decision not to acquire E. However, it is efficient to acquire E since the sum of the values ($350) exceeds the cost ($300).

Consider how the incentive tax works in this example. For either John or Mary, the sum of the net values in the absence of their participation is $100, and the net value for each is -$50. Thus neither John or Mary is pivotal. Since both are made worse off by the acquisition of E, either might be tempted to understate his or her preferences. In order to ensure that E is not acquired, either would have to state values of $100 or less. But if this were done, then John (or Mary) would become pivotal, and would have to pay an incentive tax equal to the amount the other two people bid (150+150=100). Thus if either understated their bid, they could each save $50, but there would be a resulting increased cost that voter of $100 in incentive taxes, leaving either with a net loss of $50.

Voter 3 (Henry) is faced with a similar situation. However, he is pivotal. Without his vote, E would not be provided and with his vote, E is provided. Henry receives a net value from the public good of $150 but pays a $100 incentive tax, leaving him with a net value from his actions of $50. By increasing his bid above the true value, he would not change any of his payoffs. By reducing it below true value, he lowers the chance that E will be provided and doesn't change the amount of tax he would have to pay. Thus, it is in the interest of John, Mary and Henry to each reveal the net value of the good.

Table A-1 Example of A Clarke Tax (adapted from Varian,1989)

Person Cost Share Value Net Value Clarke Tax
A (John) $100 $50 - $50 0
B (Mary) 100 50 -50 0
C (Henry 100 250 150 100
Net Benefit 100 (total)

Problems with the Incentive Tax

The textbook descriptions of demand revealing also recount certain problems with the process, including coalitions, lack of information by the individual voter, and potential "waste" in the process. These problems are discussed at length in Chapter 3 of the book and potential solutions are described at length elsewhere in the book. Bailey's treatment (1997 and forthcoming) is the most satisfactory treatment that has been formulated to date.

According to Bailey, the only reasonably satisfactory way to get around these difficulties is through a combination of mechanisms One might, for example, think of a staged process. The "pivotal" mechanism might be used at the initial "agenda setting" stage using a sample of voters chosen by lot to represent the taste and preferences (and tax relevant, demographic) characteristics of a larger underlying population. Through appropriate incentives, also for some body that tries to approximate "benefit taxes" for each proposal put on the agenda, we may get nearly unanimous agreement on the details of most government programs and projects. However, on very major issues (involving, say, budget size and other controversial procedures, we might need to turn to more complex combinations of preference revelation mechanisms.

Entrepreneurship and Incentives to Approximate Benefit Taxes.

To illustrate such a process and suggests also how it might ameliorate the problems with "pivotal voting", we turn now to slightly more complicated combinations of mechanisms and the incentives which could drive legislative committees and public goods "entrepreneurs" towards socially desired solutions.

Consider our three voters who might, for example, be a representative sample of citizens who "mirror" a larger community. They could vote on alternatives to be presented to the latter, serving essentially as "agenda-setters". They would be given a collective incentive that would be some function of the net positive benefits from the choice of E (say a % of the $50 in net benefit from acquiring E). Their "performance payment" would also be negatively related to the dollar votes cast against the acquisition of E (i. e. a % of the $100 voted by John and Mary against the proposal).

Table A-2 Solving the Problem Through Competitive Supply of the Public Good.

(a.) Before Making Price Adjustments

Person Supplier 1 Supplier 2 Clarke Tax
John 0 -50 0
Mary 0 -50 0
Henry 50 110 100
Net Benefit 50 60

(B.) After Price Adjustments

Person Supplier 1 Supplier 2 Clarke Tax
John 0 0 0
Mary 0 0 0
Henry 50 60 0
Net Benefit 50 60

Accompanying this agenda setting function, we would also have an independent group (i. e. a regulatory body or "Commission") trying to set initial tax-prices as closely as possible to the "perfect" benefit-tax prices and this price setting body (or Commission) would also receive appropriate "performance payments". The Commission could also use the information generated by the actions of the sample of citizens to determine the appropriate tax prices. Of course, if the sample of citizens voted as a perfect "mirror" of the underlying population, there would be no surplus or incentive tax wastes to be disposed of, nor would coalitions arise.

Consider also the potential of the procedure to "drive" supply-side competition in a manner that mimics the operation of a perfectly competitive market. Setting aside for the moment a process, elaborated in the following chapters, by which a final selection of alternatives might be made by the underlying population through a "combination of demand revealing and other mechanisms), consider the potential of having two "agenda setting" legislative committees and/or permit private parties to submit alternative proposals. In turn, the committee or party which "wins" in the final selection will get a percentage (say 3%) of net revealed benefits less 0.5% of negative votes against the proposal.

It is possible to design procedures (incentives) that would induce entrepreneurs to "find" the combination of public goods and the financial terms of payment for them that will generate the highest net social benefit and minimize redistributive harm. These incentives would also avoid political competition aimed at redistributing income in the community in a way that would increase redistributive harm.

Take, for example, the situation shown in Table A-2. With the assistance of the regulatory price setter, supplier/committee 1 might come up with a configuration of services for E that generates $50 in net benefit, revealed by the legislative process described above (maximum net benefits and no redistributive harm). If supplier 2 (see Table A-2) offered an alternative configuration which reflects slightly higher net values (a net value of $60 as opposed to $50, or $10 more to Henry, the Commission has the incentive to adjust the distribution to achieve a distribution of net values comparable to those generated by supplier 1. Under traditional voting, and particularly if the Commission were unable to approximate the distribution shown in Table A-2, there would have been disagreement over the proposals advanced by supplier 2 and probable choice of an inefficient alternative (supplier 1's proposal or "no action").

To help avoid the problems inherent in the "incentive tax" or "pivotal" mechanism (coalitions and wastes) and to give voters a positive incentive to take the time and effort to become informed, economists have recently discovered that a combination of the "pivotal" mechanism and an "insurance" mechanism could be used at the final decision-making or referendum stage in a manner that exploits the advantages of each mechanism while mitigating their comparative disadvantages.

Use of the "insurance" mechanism at the referendum stage, for example, allows the Commission to evaluate deliberations in the legislature(s) so as to assess the probabilities of which of the two alternatives (supplier 1 or 2's) would "win" in a referendum". Each individual will then vote by "insuring against" against its less preferred alternative. If the odds of either event were judged as equiprobable (putting zero probability on the status quo), then Henry would pay ($160-50 x .5 = $55) to vote against supplier 1's package and John and Mary would vote $25 each against supplier 2's package. Supplier 2 would be chosen with a surplus of $5 over the amounts of compensation paid to John and Mary (whose net losses would be reduced from $50 to $25 each).

The insurance system, standing alone, would not always induce the accurate revelation of demands if citizens experienced both material and nonmaterial harm (i. e. a portion of their preferences reflected what they thought was good for society). For example, Henry's net value for supplier 2's package reflected $90 in material welfare and $70 to influence John and Mary's elasticity consumption. Using the mechanisms in combination could result in incentive taxes at the referendum stage (if, for example, Henry's $70 expression of material harm swung the election, so that he paid a $10 incentive tax in addition to his insurance of $90 x .5 = $45). The only difference would be a slightly higher combined insurance and incentive tax surplus. In a large community, however, the number of voters who swing the outcome is likely to be very small, so that all most all of the surplus is in the form of amounts over and above that required to compensate losers. In some cases, however, where a community may be evenly divided on an issue, and some voters have very strong 'non-material" preferences, there could be a significant number of pivotal voters, each of whom pays a small incentive tax. [The final chapter presents an example of the combination of "pivotal' and "insurance" mechanisms in a larger community setting].

The use of a combination of preference revealing mechanisms can be used to exploit the advantages of each while reducing their disadvantages. For example, the "insurance mechanism" is mostly immune to coalitions while generating a much larger incentive for voters to ensure that the process of decisions will accurately express their preferences. It also sharply diminishes the magnitude of any surpluses which, relative to those which might be generated by "pivotal voting", are used to compensate voters for choices of less preferred outcomes and to provide rewards or incentives to "winning" suppliers and sponsoring legislative committees. Future progress in the design, and more widespread understanding of such mechanisms may eventually provide a means of blending market and political instruments in a way so as to provide "a major advance in civilization" (Bailey (1996c). I elaborate on this in Appendix B in comments on Bailey's Constitution (1997 and forthcoming)..

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