Roger D. Congleton
Professor of Economics
Center for Study of Public Choice
George Mason University
Fairfax, VA 22030
09 10 06
Universitet Aarhus
Aarhus, DK

Ia. Voter Ignorance and Public Policy
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 or the about policies that the candidate promise to deliver if in office
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A great body of survey evidence, as well as introspection, and our own direct experience with others clearly proves this to be the case.
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Economists often spend much of a lifetime attempting to master a single area of public policy, and still have unanswered questions.

Ib. Voter Ignorance and Public Policy
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Based on what we know about voter knowledge, we should expect democratic polities to be a disaster, as was widely anticipated by critiques of popular suffrage.
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(Even after the success of the United States in the nineteenth century this was, in fact, a widely predicted consequence of democratic governance throughout Europe.)
Yet, the twentieth century has demonstrated that democratic governments do better rather than worse than other governmental forms.
Democracies are richer, safer, and more stable than their rivals, and have been for more than a century.
How is this possible?

Ic. Voter Ignorance and Public Policy
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Perhaps, voting doesn’t really matter and we are just fortunate in having the right “political leaders” who guide us to peace and prosperity.
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(Yet, these leaders are chosen by voters.)
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Perhaps voters known more than they reveal to pollsters or perhaps little is necessary to pick the “right” leaders
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Perhaps, public policy doesn’t matter very much, so it doesn’t matter whether voters make mistakes or not.
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(This approach is occasionally used by economists.)

IIc. Voter Ignorance and Public Policy
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It may well be the case that majority rule, itself, organizes voter information in a manner that allows
far better policy decisions to be chosen via elections than would be possible if policies were chosen directly by a "typical" voter.
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The first part of this paper uses Monte Carlo analysis of elections to demonstrate that this is possible.
However, as also demonstrated below, there are limits to the information aggregating ability of majority rule, which in turn limit the scope of effective democratic policy.

IIa. Majority Rule as an Information Aggregation Process
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There is a theorem named after an 18 th century French philosopher and mathematician named Condorcet.
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In 1785, Condorcet argued that jury trials tend to achieve better results than would be associated with any single member of the jury, because the “middle opinion” is less likely to be wrong than others.
About a hundred years later a statistician named Galton noticed that “median estimates” at weight-guessing contests at county fairs were remarkably accurate.
About a hundred years later, a few contemporary political scientists began to apply this “jury theorem” to large scale elections.

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The jury theorem and the statistical properties of medians combined with electoral competition between political parties implies that voters may not need very much information for democracy to yield "correct" policy outcomes.
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McLennan (1998) argues that the information aggregating ability of majority rule can be extremely powerful in the limit.
These papers suggest that the policy choices made by majority rule tend to be far more accurate than one would expect based on survey evidence on voter knowledge.
On the other hand, another series of theoretical papers suggests that the Jury Theorem may not operate at all.
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For example, Austin-Smith and Banks (1996) argue that the result of majority rule may be no more informed than is the typical voter, because they may not use their own information when voting, because of perceived advantages of information cascades.
Yet if this is true, there is again the puzzle of how democracies can work so well on average.

IIb. Majority Rule as an Information Aggregation Process
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This Paper explores some of the strengths and weaknesses of majority rule as an information aggregation (or sorting) technique.
One of the best known results from deterministic voting theory is the median voter theorem—discovered by Duncan Black in the late 1940s.
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His result and numerous extensions of that result by other theorists suggest that if there is an equilibrium in representative democracies it occurs when the median voter gets his or her favorite politician and favorite policies.
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That is to say, in cases where two candidates or two parties compete for elective office, the candidate whose policies are closest to the median voter’s ideal will be elected to office.
The Jury Theorem implies that Democracy can choose the “right” policies or the “right” candidates because there are circumstances in which democratic outcomes are very similar to median estimates.

IIc. Majority Rule as an Information Aggregation
Process
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The median voter theorem implies that in electoral contests between two candidates or two coalitions there is a strong tendency for platforms to converge to positions that are approximately equal to the median voter’s most preferred policies.
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Although, candidate positions are never identical in practice, we do observe a great deal of convergence. The policy differences of mainstream candidates are generally very small relative to the range of policies that we can imagine.
This is not because voters all agree about what good policy look like, but simply a consequence of efforts to maximize votes or vote shares.
(Many voters are disappointed with the available policy options and candidate choices available in a typical election.)

IIIa. On the Quality of Median Voter Estimates
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In limiting cases, in which candidate platforms converge to essentially identical positions, the voter decisions about which candidate to vote for can only be based on differences in the
perceived quality of the candidates.
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In this case, voter assessments can be thought of as estimates of candidate quality.
Disagreements over candidates or coalitions, in such cases, arise only because voters have different estimates of candidate quality, estimates.
The median of these estimates, as demonstrated below, can be
amazingly accurate estimates of candidate and policy quality.
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However, median assessments of candidate quality are not always inaccurate or even biased.
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These limitations are also explored below.

IIIb. On the Quality of Median Voter Estimates
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Whether the median voter results are accurate or not depends on the manner in which voters collect information about candidates.
Economic theory implies that voters will not collect and analyze every bit of information that might possibly be useful, but only collect and analyze data which are expected to have benefits that are anticipated to be greater than their costs.
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Rational voters will economize on political information in the same way that they economize on other sorts of information.
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However, there are two quite different methods of doing so: they may economize by choosing a small sample of “complete” data points, or they may focus on a small subset of variables or policies and ignore the others.
The latter is what I refer to RATIONAL IGNORANCE,
although the former is sometimes confused with the latter.
The simulations demonstrate that the finite sample and partial sample method of economizing have quite different implications for the jury theorem.

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As a point of departure, assume that two candidates
(or parties) compete for elective office and that their platforms have completely converged to the median voter's ideal point.
The voters, consequently, attempt to estimate the relative quality of the two candidates for high office: a more or less familiar incumbent and a less familiar challenger.

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Suppose that the quality of candidate i is well known to be a linear function of one observable characteristic, E i
, (perhaps experience or intelligence) and one unobservable characteristic, H
 candidates. Assume that: i
, (perhaps honesty).
Suppose also that E and H are randomly distributed among
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E is distributed uniformly, U(E L ,E H ) with E L = - E H , and that
 unobservable characteristic H is also uniformly distributed with mean a and variation u i
~ U(h L , h H ) with h L = -h H .
Candidate i’s quality is thus: Q i
= a + bE i
+ u i
(1)
Given particular values for their reference politicians, the resulting estimates can be quite different.

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Consider the case in which reference candidates are drawn randomly from a distribution in which the observable characteristic is uniformly distributed:
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E ~ U(-10, 10) and the stochastic component of the unobservable characteristic, u, is uniformly distributed, u ~ U(-2, 2),
 with H = -4 + u, and Q = H + (0.4)E.
The true underlying candidate function is, thus,
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Q o
= -4.0 + 0.4 E o
+ u o
In this special case, a = -4.0 and B = 0.4
.

:
Estimated Candidate Quality Functions
0.80
0.60
0.40
0.20
-0.00
-0.20
-0.40
-0.60
-8 -6 -4 -2 0 2 4

:
Estimated Challenger Quality
45
40
35
30
25
20
15
10
5
0
-5 -4 -3 -2 -1 0 1 2

Table 1: Estimates of Candidate Quality as the
Electorate Varies in Size
Electorate
11
Ave
Qchal
-4.114
Med. Est.
Qchal
-4.068
St. Error of Est.
2.68
Electoral
Mistakes
13
101
501
1001
2001
-3.808
-3.884
-3.964
-4.07
-3.975
-3.827
-3.979
-4.093
2.77
2.63
2.34
2.31
14
14
13
10
4001 -3.787
-3.746
2.43
13
100 elections are simulated for each community of voters. The incumbents, reference candidates, and challengers are drawn from the same distribution, and vary in each election.

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First , voters may completely understand the underlying quality of candidate relationship, but decide to economize on information by gathering no information about the observable candidate quality characteristic, E.
Second , voters may decide to economize on information by ignoring the effect of the unobservable variable, H, and
focusing all of their attention on the observable variable, B.
Third , voters may decide to remain rationally ignorant (or be naturally ignorant) about both determinants of quality, Q and
E.

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The simulations below explore the case in which the population of voters is composed of all four types : the poorly informed voters used in our first series of simulations and the three types of ignorant voters.
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In order to distinguish the mistakes induced by rational ignorance from those associated with irreducible uncertainty on mistaken electoral outcomes, voting outcomes for five ranges of the unobserved variable, u, are simulated.
Two population mixes of slightly informed and rationally ignorant voters are simulated. In the first case, the slightly informed group is about equal in size to the ignorant group.
In the second, the slightly informed group is assumed to be a small minority.

Table 2: Electoral Mistakes:
Choosing the Inferior Candidate
Simulations: 100 elections, 205 voters: 202 slightly informed voters, and 35 of each type of rationally ignorant voter
Range of u Slightly
Informed
+/- 0.1
+/- 1.0
+/- 2.0
+/- 4.0
0
5
13
28
Ignorant of E
27
28
17
31
Ignorant of H
35
34
33
37
Ignorant of both
40
55
48
45
Overall
Electorate
0
5
14
23

Table 3: Electoral Mistakes with relatively more
Ignorant voters
Simulations: 100 elections, 204 voters: 51 slightly informed voters, and 51 of each type of the rationally ignorant voter.
Range of u
Informed group
Ignorant of E
Ignorant of H
Ignorant of both
Overall
Electorate
+/- 0.1
+/- 1.0
+/- 2.0
15
+/- 4.0
21
1
5
25
19
27
24
54
34
49
36
49
55
43
51
28
24
38
32

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Note that the effects of rational ignorance are more important than the difficulty of the estimation problem faced!
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(There is a systematic increase in mistake rates for the electorate as a whole as the variance of u increases, but there is an even greater increase in mistakes as the proportion of rationally ignorant voters increases.)
Note also that even in the case where the range of u and the electorate composition are the least favorable to democratic decision making, majority rule still ameliorates the problem of rational ignorance to some extent.
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The final outcome is less error prone than two of the three rationally ignorant subpopulations, although far more error prone than is the group that collects a small, but complete, data set.

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It bears noting that an expert of panel of experts does not necessarily do better than an uninformed electorate.
Table 3 : Expert vs. Median Voter Estimates
Sample size Expert
Estimate of A
Expert
Estimate of B
Est. Challenger
Quality
N=10
N=50
N=100
Actual Values
Median Voter*
-4.34
-4.19
-4.19
-4
-3.79
0.33
0.42
0.42
0.4
0.35
-2.39
Standard Error of Estimate
-3.02
-2.51
1.48
1.09
-2.51
1.14
-2.4 = -4.0 4(4)
0.968
*Median Voter estimates are the sample average and standard error from 10 elections with
1001 person electorates each voter with one independent observation and the incumbent.

The simulation results suggest that the information
“aggregating” ability of majority rule is jointly determined by (1) the underlying uncertainty of the phenomena being estimated (candidate quality), and (2) the extent of voter ignorance.
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In cases where just a bit of complete information is available to voters and median voter results obtain, majority rule will make remarkably accurate policy decisions even in cases in which voters have very little information. This explains why democracy may work as a form of governance.
On the other hand, in cases, or policy areas, in which voter information is bounded in the sense that relevant details are completely missing from voter information sets, democracy will be mistake prone. This explains why democratic governance may fail even in otherwise favorable circumstances.

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In either case, informational limits bound the effectiveness of democratic policy (in the sense that public policies may more or less systematically advance the true interests of the median voter).
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The results of the simulations, suggest that good public policy decisions are mostly likely to be made in areas where voters have at least a bit of direct knowledge about the public policy issues under review.
In other areas of policy, biases and mistakes tend to be commonplace.
Thus, one policy implication of this line of research is that it would be wise to restrict public policy to policy areas--public goods and uniformly provided services--where voters have at least a bit of information.

A second policy implication , is that to the extent that policy ignorance can be reduced, it will systematically improve public policy in a democracy.
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For example, such policies as:
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Publicly financed education
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The publication of policy information and data sources
Protections for a free and competitive press
Freedom of information acts and legal protections for “whistle blowers”
And, perhaps, subsidies for social science and policy analysis
All reduce ignorance, and thereby promote more effective policy formation within representative democracies.

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Third , constitutional designs can also reduce ignorance by increasing transparency, and promoting the dissemination of policy relevant information.
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In the US, we accomplish these goals with Federalism,
Bicameralism, Referenda, and our bill of rights.
Most other countries do not do this as well as we do this, and doubtless we could do better as well.
Errors can be reduced by restricting public policy to areas in which voters have at least a bit of information.
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It is striking how many of the policies adopted by wellfunctioning democracies promote the dissemination of policy relevant information—and how little of this is done in dictatorships and democracies that perform poorly.

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Finally, it bears noting that information-based mistakes may determine the ultimate limit of democratic public policy.
This is not because imperfect information is the only problem faced by democratic polities.
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A broad strand of the public choice, political economy, and political science literature indicates that there are a variety of agency and decision problems associated with political decision making.
However, imperfect information is a more fundamental problem.
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Given perfect information, competitive elections, and a symmetric distribution of voter interests; most agency problems can be solved democratically, as voters demand and candidates compete to deliver appropriate institutional reforms.
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Without a relatively broad information base, however, these institutional solutions are not likely to be adopted, either because they are neglected by rationally ignorant voters or because of errors in judgment about their need or effectiveness.