Revealing Expressiveness: The Demand Rev ealing Process with Expressive Voters
Eric Crampton
[email protected] University of Canterbury
Draft June 2003. Do not cite without permission.
The author thanks David Bernstein, Bryan Caplan, Ed Clarke, Tyler Cowen, Fred Foldvary, Nicolas Tideman, Gordon Tullock, and participants at the 2003 Public Choice Meetings for useful comments and discussion. The standard disclaimer applies.
I.
Introduction
The demand revealing process (DRP) enjoys a rich tradition in the public choice literature as a superior mechanism for inducing truthful preference revelation and thereby achieving optimal provision of public goods. Tideman and Tullock’s (1976) application of the Clarke (1971) procedure as a social choice mechanism sparked a period of vociferous debate over the DRP, including a supplemental edition of Public Choice (1977). Interest in the mechanism has waxed and waned in the period since. While theoretical objections have been raised against the use of the DRP, proponents of the DRP have worked to solidify its foundations. Margolis (1982) hints at a more fundamental problem facing the real world application of the DRP. Specifically, the individual voter faces low expected Clarke taxes should he misrepresent his demand schedule. While Tullock (1982) critiques Margolis’s thought experiment, the Margolis objection remains trenchant. We argue here that Margolis’s objection is stronger than he anticipated. Not only may individuals have an instrumental interest in misrepresenting their preferences, but more importantly, the low probability that any voter will be required to pay Clarke taxes makes the mechanism highly vulnerable to the elicitation of expressive preferences. After revisiting the DRP mechanism and the expressive voting framework, we argue that the DRP is undesirable as a social choice mechanism because of expressive voting considerations.
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II.
The Demand Revealing Process
As noted earlier, the demand revealing process enjoys a rich history in public choice and should be well familiar to the reader. Consequently, only a brief overview of the mechanism is here presented. While several variants on the process exist, the fundamentals of the mechanism are similar across the different applications (see Green and Laffont, 1977; Margolis, 1983). The mechanisms seek to induce truthful preference revelation as either a Nash or dominant strategy. The simplest case, the “pivot” mechanism demonstrated in Tideman and Tullock (1976), illustrates the principles involved. In this case, voters are offered a binary choice either to implement a public expenditure project of fixed size, or to reject the project’s implementation. For example, voters in the Washington DC metropolitan area might be asked whether or not the metro transit system should be extended through Tyson’s Corner to Dulles International Airport at a cost of a fixed number of billions of dollars. Obviously, voters will differ on their valuation of such a project. In the DRP, all voters are asked to submit their bids indicating by how much they prefer that the project obtain or be scuttled. All bids for and against the project are totaled. If the dollar value of bids favoring the project outweighs the dollar value of bids in opposition, the rail line is built. Any voter whose bid was necessary for the outcome to obtain, however, is charged a Clarke tax equal to the amount of the voter’s bid that proved necessary in changing the outcome. Suppose that I bid $1000 in favor of the project and that the total value of bids supporting the project outweighed the total value of bids against the project by $900. Had I bid any amount lower than $100, the project would not have been undertaken; 2
when my bid was added, the project received net support and was implemented. In this case, I would be charged a tax of $100 – the amount of my bid necessary to changing the outcome. We can see that truthful preference revelation should be optimal in this framework. If I truly value the project at $1000, underrevealing my valuation cannot improve my situation and may lead to cases in which the project is not undertaken but in which I would have been willing to pay the amount required to ensure that the project would obtain. Similarly, overvaluation cannot improve my situation but may lead to situations in which I pay more for the public good than the value I place upon it. The “pivot” mechanism here presented can be extended for choice in continuous space as well; the interested reader is referred back to Tideman and Tullock’s original contribution. The disposition of the taxes collected through the operation of the system has engendered some amount of controversy. In the Tideman and Tullock framework, all collected taxes must be wasted in order to avoid incentive effects that might perturb truthful preference revelation. For example, if all taxes collected are to be used to benefit the local homeless shelter and I value (deplore) the activities undertaken by the homeless shelter, I may overreveal (underreveal) my preferences. Of course, even that waste may not be without incentive consequences; it is certainly plausible that some people oppose waste as such (and that some smaller number prefer waste as such) and will attenuate (accentuate) their votes as a consequence. Tideman and Tullock (1976, 1156) note that the Clarke taxes collected will be quite small, so resource waste will prove minimal. They write: 3
“Thus, if the citizens of the United States were voting on the annual federal budget, the grand total of all the Clarke taxes charged would be in the neighborhood of $2,000, or about one-thousandth of a penny per person.” Bailey (1997) presents a mechanism whereby even this small level of waste can be avoided. While the low level of taxes collected reduces the inefficiencies directly inherent in the use of the DRP, it opens the system to a potentially more damaging critique: when no voter is decisive, all voters are expressive.
III.
Expressive Voting A recurrent problem in the public choice literature centers on the rationality of
voting. Strictly speaking, the expected benefits of voting can never outweigh the costs of doing so. Even if an individual voter truly values the election of Candidate A over Candidate B by a million dollars, the odds that that voter will prove decisive in any reasonably sized electorate approach nil.1 Consequently, any real costs involved in voting make the voting act irrational from the perspective of an income-maximizing voter. Brennan and Lomasky (1993) solve the problem of the rationality of voting but, in doing so, bring forth a much more challenging problem. Because the odds that any individual voter will prove decisive are lower than the odds of winning the lottery, instrumental interests can explain neither the act of voting nor the content of the vote. If we rely on non-instrumental mechanisms to get voters to the polls, we can hardly expect
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Se e M ulligan and Hu nter (2003) fo r d etailed analys is of the fre quency of p ivotal votes . They trenchantly note “Fu ture empirical res earch could als o inves tigate the prevalence of v otes in uncontes ted elections – thes e were omitted from our calculations but are consp icuou s in our data and probably relevant to the theory of v oting.” (51). Expres s ive voting theory readily explains the anomaly.
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them to put on their instrumental thinking cap once they get into the voting booth. Instead, voters engage expressive preferences both in the decision to vote and in the decision of for whom to vote. Expressive voting theory holds that voters maximize utility over both instrumental and non-instrumental factors. Instrumental preferences here refer to positively signed arguments in the utility function that provide an increase in utility if policy X is enacted as legislation. Expressive preferences, by contrast, are those arguments in the utility function that cause an increase in utility simply by the act of voting for policy X, regardless of whether X actually obtains as a result of the election. For example, a worker in the oil industry would see his instrumental interests advanced if arctic drilling restrictions were lifted; if that same worker were also an environmentalist, however, voting against the lifting of drilling restrictions may generate expressive benefits for him. Since any instrumental benefits from voting accrue only with an infinitesimal probability (equal to the probability that the individual voter will be decisive), non-instrumental expressive benefits will surely trump instrumental benefits in the voting calculus. Voters in any reasonably-sized electorate effectively make their electoral choices behind a “veil of insignificance.” 2 Expressive voting severs any tie that might exist between democraticallyapproved policies and efficient outcomes. Indeed, many voters can quite rationally vote for policies that lie directly in opposition to their narrowly instrumental interests if they derive expressive benefits from supporting those policies. As Caplan (2000, 2001)
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Bren nan an d Lomas ky (1993, 124, 224) make first u s e of th e te rm, though Bren nan an d Hamlin (2000) attribute the term to Hartmut Kliemt.
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argues, voters in this context can readily be viewed as rationally irrational. The lack of any decisive connection between the voter’s choice and policy outcomes allows any voter to costlessly entertain whatever biased model of the world they prefer. Caplan specifies that voters have preferences over beliefs about the world. While biased beliefs prove quite costly in an individual’s day-to-day life,3 biased beliefs in the political realm can be entirely costless. It costs the individual voter nothing to believe that tariffs make Americans better off; the individual voter is never decisive in implementing policy. Voters can then rationally hold beliefs that are inconsistent with reality; they are rationally irrational.
IV. Expressive Voting in the Demand Revealing Process Caplan (2003) demonstrates that expressive voting can be the cause of significant political failure in democratic majority voting. Electoral competition pushes candidates to compete in expressive policy space, with the standard median voter result obtaining within that expressive policy space. Biases in expressive voter preferences will lead median voter outcomes to diverge significantly from efficient results. Expressive voters hold preferences over beliefs in policy space that they individually find optimal, but collectively cause serious consequences. While Caplan restricts his analysis to standard majority rule settings, we argue that his critique applies a fortiori within the demand revealing process. Within the majority rule framework, each person can cast but one vote. Within the DRP, each voter 3
Imagine, for ins ta nce , th e c os ts of holding th e b elief that a larg e d os e o f ars en ic is th e a ppropriate cu re fo r a headache. Public opinion on ques tions of economic policy are fre quently as wrong, b ut individuals do not pers onally bear th e co s ts of s uch beliefs as th ey are not d ecisive in s eeing th os e beliefs tu rned int o policy. See Caplan (2002).
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can cast a number of votes that is potentially unbounded. Margolis (1982) hints at this problem, but is prevented from full pursuit of it because Brennan and Lomasky (1993) had not yet been written. Margolis asks whether voters might not be willing to “spend the penny”. He sets up a thought experiment in which voters are asked to reveal their preferences over the level of public expenditure on some public good. The typical voter bidding his marginal valuation will face a Clarke Tax equivalent to 1/100,000 of a penny and will shift the outcome by about $20 towards his desired level of aggregate spending. Margolis argues that a voter in that context should be willing to “spend the penny” – overreveal his preference in order to push the outcome much closer to his desired level of spending, but still (expectationally) incur a Clarke tax of only a penny. In his example, a voter bidding a thousand times more than valuation incurs a huge percentage increase in his Clarke tax; but that tax still amounts to only a penny while the aggregate outcome moves $20,000 closer to his desired level of spending rather than only $20 closer. Margolis’s argument hinges on the low probability that any individual voter will prove decisive or, if decisive, will not have changed the outcome by enough to be liable to a very large tax. This framework is intrinsic to the DRP, as noted in Tideman and Tullock (1976, quoted above). The problem becomes all the greater when we consider expressive voters. Introducing expressive voters into the DRP thoroughly undermines whatever efficiency properties had been claimed for the procedure. Margolis asks if voters might not be willing to “spend the penny”. Voters are willing to incur rather substantial costs to get to the ballot box, costs far in excess of the aforementioned penny. Given the low probability of decisiveness at the DRP ballot box, expressive preferences will be as 7
important in determining the voter’s decision as in majoritarian elections. However, the aggregation of preferences will lead to worse outcomes when policies are measured within intrinsic benefit space. Caplan (2002) shows not only persistent biases in voter beliefs about economics, but that these biases coalesce systematically around expressively-salient foci (antibusiness and anti-foreign, for example). Budge et al (2002) find that party platforms exhibit unidirectionality on many policy dimensions.4 If expressive preferences were normally distributed with an expected value corresponding to the voter’s instrumental interests, there would be little cause for concern; expressive preferences would cancel each other out in that case. Persistent bias in expressive preferences, on the other hand, will lead to biased outcomes under either form of preference aggregation. The DRP will magnify biases in outcomes caused by expressive voting. While the model here presented is narrative rather than formal, it is illustrative. Specify that voters derive expressive benefits that are increasing in the size of their demonstrated commitment to the issue. In majoritarian elections, each voter can only vote once; the voting mechanism ignores the intensity of the expressive preference. Under a demand revealing system, by contrast, voters can use the size of their bids as a means of expressing the intensity of their expressive preferences. Consequently, the voters with
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Bu dge et al code political party manifes tos by the percentage of s tatements falling into each of 56 is s ue categories , mos t of which are unipolar in nature. For example, they code only an “enviro nmental” is s ue category; not “pro” and “con” env ironmental categories. They write “This is becaus e the texts th emselves are one-p os itional. The actual coding categories are theoretically guided but inductively deriv ed – bas ically fo rmed by gro uping related s entences in the text – and s o they reflect the textual practice of o nly endors ing th e ‘o bviou s ’ pos ition on ea ch iss ue – being ag ains t environ menta l des tru ct ion , for example, but a ll for a hard line on law and order. (Laver and Garry 1998, 12) The coding scheme thus directly reflects party as s umpt ion s th at t here is only o ne te nable p olicy on ea ch iss ue.” (Bu dge 2002, 79-81)
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the strongest expressive preferences will have the greatest impact in deciding the outcome of the election. Consider the following example. Voters are asked to determine whether an environmental program should be undertaken. All voters share identical instrumental preferences. Specifically, the program imposes net costs of $10 on all voters measured in instrumental space. Each voter, operating instrumentally, should bid $10 against the project. Forty percent of the voters receive expressive benefits from registering their support for the program. These voters receive $1 in expressive benefits for bidding $100 in favor of the project. Since the electorate is large, no voter is likely to prove decisive. Note that if any voter were decisive, he would vote against the project as the $10 in net intrinsic costs outweighs the $1 in expressive benefits. However, given the veil of insignificance separating voters from the direct consequences of their actions at the ballot box, each of these expressive voters bids the $100 in favor of the project’s implementation. Note that none of these voters will then prove decisive: the project is approved by a wide margin. For any reasonably-sized electorate, the project will be supported by far more than the $100 difference that would require the payment of Clarke taxes. No Clarke taxes are collected, and an inferior result obtains. Expressive benefits of $(0.4*N) are generated at the cost of ($10*N) in instrumental costs.5 Each and every voter in this case, if he were given the choice unilaterally to maintain or scrap the program, would end the program. And, in a majority rule setting, the project would fail.
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No wh ere s hould the arg ument be cons tru ed as implying that expres s ive preferences are not “real” preferences , nor that the utility derived therefrom sh ould be disco unted. Inefficiency s tems from the priso ner’s d ilemma nature of the voting environment, not from any eph emeral nature of express ive utility.
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More realistically, voters enjoy heterogeneous expressive preferences. While expressive preferences are biased in particular directions, individual voters feel more or less strongly about each issue. Under the demand revealing process, voters with the strongest expressive preferences are given the greatest weight. Political failure will be magnified. Indeed, it is not inconceivable that bids could range into the millions of dollars if the probability of decisiveness proves low. While this could be bounded by insisting that voters post a bond against the possibility that their votes prove decisive,6 individual voters presumably could insure against such eventuality given the low probability of decisiveness. The insurance company would then post the bond on behalf of the individual. Absent insurance, we should still expect that expressive preferences will carry greater weight, unless expressive voters face greater financial constraints against bond posting than do instrumental voters. Since expected Clarke taxes remain quite low, the bonding requirement only restricts the magnitude of the bid to an amount dictated by one’s personal wealth and risk aversion.
V. Conclusion The demand revealing process provides an interesting and relatively new mechanism for aggregating preferences and arriving at optimal policy outcomes, when that process is restricted in application to matters utterly bereft of expressive content. For example, it might enjoy productive use for decision making within a corporate board of directors.7 As a method of making social choices, however, the procedure is quite 6
Nicolaus Tideman, perso nal corresp ond ence. Note, however, Attiyeh et al (2000), who find the mechanism fails to work und er the s implest exp erimen tal co nd itio ns . 7
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undesirable if voters are expressive. Margolis’s (1982) worry that voters might “spend the penny” to magnify the effect of their vote becomes quite troubling when those same voters might “spend the dollar” to gain larger expressive benefits from their vote. Restricted in application to small group settings where the probability of decisiveness remains high, or to settings where expressive preferences are unlikely to come into play, the DRP may prove greatly beneficial. In more normal voting environments, majority rule remains preferable.
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VI. Bibliography Attiyeh, Greg, Robert Franciosi, and R. Mark Isaac. 2000. “Experiments with the pivot process for providing public goods.” Public Choice 102 (95-114). Bailey, Martin J. 1997. “The demand revealing process: To distribute the surplus.” Public Choice 91 (107-126). Brennan, Geoffrey and Loren Lomasky. 1993. Democracy & Decision: The Pure Theory of Electoral Preference. Cambridge: Cambridge University Press. Budge, Ian. 2002. “Theory and Measurement of Party Policy Positions.” pp. 75-90 in Budge, Ian, Hans-Dieter Klingemann, et al., Mapping Policy Preferences: Estimates for Parties, Electors, and Governments, 1945-1998. Oxford: Oxford University Press. Caplan, Bryan. 2000. “Rational Irrationality: A Framework for the NeoclassicalBehavioral Debate.” Eastern Economic Journal (26) 191-211. Caplan, Bryan. 2001. “Rational Ignorance vs. Rational Irrationality.” Kyklos (54) 3-26. Caplan, Bryan. 2002. “Systematically Biased Beliefs about Economics: Robust Evidence of Judgmental Anomalies from the Survey of Americans and Economists on the Economy.” Economic Journal (112) 433-58. Caplan, Bryan. 2003. “The Logic of Collective Belief.” Rationality and Society (forthcoming). Clarke, E.H. 1971. “Multipart Pricing of Public Goods.” Public Choice (11) 17-33. Green, J. and J. Laffont. 1976. “Characterization of satisfactory mechanisms for the revelation of preferences for public goods.” Econometrica (45) Margolis, Howard. 1982. “A thought experiment on demand-revealing mechanisms.” Public Choice (38) 87-91. Margolis, Howard. 1983. “A note on demand-revealing.” Public Choice (40) 217-25. Mulligan, Casey B. and Charles G. Hunter. 2003. “The empirical frequency of a pivotal vote.” Public Choice (116) 31-54. Tideman, Nicolaus and Gordon Tullock. 1976. “A New and Superior Process for Making Social Choices.” Journal of Political Economy (84) 1145-59. Tullock, Gordon. 1982 “More thought about demand revealing.” Public Choice (38) 167-70. 12
