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SOME THOUGHTS ON THE PROBLEMS OF DEMOCRACY Gordon Tullock March 15, 2002
Democracy is frequently referred to as a system of majority voting. Granted, the last election in the United States the opposing candidate received more popular votes than the winner, and neither received a majority of popular votes because of the existence of other candidates, it is surprising that our system is called that." Of course the winner did get a majority both in the Supreme Court and in the electoral college. The loser got a majority in the Florida Supreme Court.1Why do we call it "majority voting" when . . . The failure to get a majority in the popular vote is not particularly uncommon. Lincoln, for example, got only 35 percent of the popular vote and if one of the three of his opponents in the election, Douglas, had met him in a 2 candidate election, he would have won. The 1912 election, once again, had a winner who received less than half the popular votes. In Wilson's case he had two opponents, either one of which could have beaten him if the other had not been present. The current government in Canada received less than half the popular vote and, except in wartime, no British government has been elected by more half the voters since 1920. In both of these cases, of course, the winner had more than half of the representatives in Parliament. During its long reign in India, the Congress party never received a majority of the popular vote. Normally it received less than 45 percent. Another and interesting case is the election of 1960. Nixon had more popular votes than Kennedy but lost in the electoral college. The fact that Nixon had more popular votes, although not a majority of all votes, is almost a secret2. 1The Florida Supreme Court, solidly Democratic, voted 4 to 3 for Gore. Seven of the United States Supreme Court voted to overturn the Florida Supreme Court decision, but two of them wanted to send it back to Florida for further consideration. Hence the common newspaper reference to decision as 5 to 4. 2For an explanation of the actual situation see my letter to the editor of The New York Review of Books; Nov. 10, 1988 "Did Nixon Beat Kennedy? and the "Reply" by Francis Russell whose article I was criticizing. He accepted my criticism.
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The election of 1960 is interesting and here I foreshadow the major part of this article in that the two strongest candidates for the final election were eliminated in the selection processes of the two parties. It is reasonably certain that Johnson could have beaten Nixon in both popular and electoral votes and that Rockefeller could have beaten Kennedy . All of this does not indicate the system is inferior, but it does suggest that we stop calling it majority voting. The problem of more than two alternatives As on my readers will know, there are two general types of democracy, one originating in England long ago in which the voters directly select individual candidates. The other, which originated on the continent in the 19thcentury, is called proportional representation and I will to a large extent leave it out of the discussion below. Actually, I rather prefer proportional representation, but it is a different subject and requires different analysis. But to return to my main subject, the reader will have noticed that in each of the cases with a winner who did not have a majority of the votes, more than two alternatives were presented to the voters. With only two candidates or proposals before the voters these problems do not occur. Unfortunately, there are many people who would like to be the president and many ways which the government income could be spent. In the real world, it is likely that the system is confronted with more than two alternatives and it must either cut them down to two by some means or be willing to accept a candidate or proposition chosen by less than a majority. Of course it may happen that although there are three candidates or proposals one of him gets more than half of the votes. But we should not have a system which depends on that chance. The paradox: from Condorcet to Black and Arrow This problem has been known for a very long time and procedures to either simply take the one that has the most votes or reduce the number of alternatives to two and then vote on the those two are orthodox. Unfortunately, none of these procedures really overcome the problem. Shortly before the French Revolution two French aristocrats, Condorcet and Borda, looked into the problem and Condorcet found what is now known as Condorcet Paradox while Borda produced system which avoided that Paradox but introduced another. This was of course the period of the great expansion of democracy and, perhaps as a result of the enthusiasm for democracy, the problem was largely forgotten although some mathematicians seem to have known about it. In the mid-19thcentury, Lewis Carroll rediscovered the paradox and did considerable work on it without finding a solution. He too was largely forgotten and the problem was rediscovered by Black who also discovered that he had predecessors lost in the obscurity of minor mathematical publications. Black succeeded in reviving interest in the issue which is a little paradoxical since it is obvious he did not like the idea of democracy having paradoxes. Working with Newing he produced a proof that this paradox could not the avoided if there were more
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than two alternatives.3Notably he did not put out his work as a criticism of democracy because he was a firm believer in democracy. Nevertheless careful reading of his book with Newing shows the impossibility of avoiding the Paradox except in special cases. While Black and Newing were working, Arrow produced a general proof that the paradox cannot be avoided in the general case.4This was his famous general impossibility theorem. Notably it was only a remarkably long delay in the refereeing process which prevented the Black and Newing paper from being published before Arrow. In the early days of research in public choice, papers dealing with the paradox were a major component of papers submitted to me as editor of the journal. I think that most of these papers were inspired by desire to avoid the paradox or at least to minimize it. If this was the inspiration, it failed. The paradox continues and indeed I have invented a much simpler although less elegant proof.5After considerable delay I discovered a proof that the problem was not nonexistent, but of less importance than had been thought. If the voting preceded in the usual way of legislatures with anyone free to introduce an amendment is, it would precede to an outcome very close to the center of the cloud of individual optima. A dictatorial chairman, however, could lead the votes to almost anywhere he wished. Since the usual procedure is not involving a dictatorial chairman, this meant that the voting normally would lead to a more or less satisfactory outcome. Professor Arrow, in a very kind letter, accepted in the bulk of my reasoning but pointed out that the latter part was not really mathematically strict. He was right, but the reasoning was very strong even if not perfect, mathematicians standpoint.6What are fans of democracy to do? The end result of all of this work is most disappointing for proponents of democracy. Since the author and all of the readers of this paper are such proponents of democracy we should all the unhappy about it. As far as I can see, however, the usual response is not to be sad, but to sweep the problem under the rug. Psychologically this is no doubt an optimal response, but it seems to me that scholars should busily search for some better way of dealing with the paradox. I frankly admit I have not found one, but the point of this article is to attempt to interest other scholars in a revival of voting problem, so important in the early days of Public Choice, but normally today not even mentioned in the average issue or, indeed, in the average 10 issues. 3Black, Duncan and R.A. Newing. Theory of Committees and Elections. [2d Edition] Boston: Klewer Academic Publishers (1998). 4Arrow, Kenneth J. Social Choice and Individual Values. [2d Edition] New York: Wiley (1963). 5See" Some Simple But Confusing Mathematics" in my On Voting Edward Elgar, 1998 Cheltenham, UK, paperback, Locke Institute, Fairfax Va, 2001. 6 Tullock, Gordon. "The General Irrelevance of the General Impossibility Theorem". The Quarterly Journal of Economics Vol81, Issue 2 (May 1967) p.256-270
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This is particularly surprising granted that intellectuals are currently vigorously producing arguments for democratic governments, and hence would be one would think particularly interested in eliminating paradoxes in democracy. The new arguments for majority voting, and the authors normally refer to majority voting rather than simply democracy fall into two categories. The first is the allegation that democracy's tend to produce capitalistic economies and hence are prosperous. Dictatorships are allegedly less efficient in the economic field. Democracy and economic progress In the first place, economists have long known for (or at least many of them have) that a capitalistic system is a better method and of producing prosperity than a centrally directed one. In the last few years most intellectuals have adopted this idea. Note however, that except for a certain number of "reactionary" economists this idea was not popular among intellectuals 50 years ago. Warren Nutter undertook a major research project in communist statistics and decided that the rate of growth of the Soviet Union was not in any way remarkable. Indeed it was about that of United States and markedly lower than that of Japan. As a result he was practically drummed out of the economic profession. Note that efforts to duplicate his research turned out to be surprisingly similar although the CIA which funded them never overtly admitted that. It was however not just the CIA which disagreed. To repeat, Nutter's career was more or less terminated in the economic profession. The University of Virginia did not give him significant pay raises and moved him to an inconvenient office. He could not go anywhere else because other universities also thought that he was following his ideology and not his science. This was a personal tragedy for Nutter and a policy tragedy for many governments. The view that economic progress required central control by someone not hampered by democratic mechanisms was widely held. Many of the people who felt this way remained in favor of democracy for reasons other than its economic effects. Nevertheless, the recent view sweeping intellectuals that democracy works better in economics than a communist dictatorship is recent. Further, as far as I can see, like the earlier enthusiasm for communist dictatorships in the economic field, it was based on nothing more than one of the waves of enthusiasm that tend to sweep the intellectual classes, although the collapse of the old order in Russia undoubtedly contributed If we look at the real world, Japan, Germany, France, and India are all democracies and doing very badly in their economies while Singapore and Hong Kong continue to be prosperous with dictatorships and China, a clear-cut dictatorship and a rather impressive one, currently claims the highest rate of growth of any significant country. Speaking for myself, I tend to distrust communist statistics, but observation on a recent trip to China indicates it is very much better off than it was not too long ago, at the end of the great proletarian cultural revolution. Democracy and peace Another recent argument for democracy is that democracies are relatively peaceful. This began with view that democracies did not engage in aggressive wars.
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Apparently, after a while, some intellectuals read the history of 19th-century in which democracy's conquered much of the world, and the claim was reduced to one in which democracy's do not fight other democracies. The original claim was particularly surprising since many of the intellectuals who made it were American citizens and therefore should have been aware that United States had seized is present geographic area by a series of minor but certainly aggressive wars. Consider the reduced claim that democracies rarely fight other democracies. During a rather long period in which democracies were rare and hence had little opportunity to fight each other this was undoubtedly true. Still it should be kept in mind that in 1914 it could easily have been argued that both England and Imperial Germany were democracies, indeed the major undemocratic country in the war was Russia. Of course at that time all the monarchies were moving toward democracy and England and Germany were much farther along than Russia. The end product of the war was that what progress Russia had made towards democracy was canceled and one of the world's worst autocracies put in its place. The dissolution of Austria-Hungary was disastrous by any standard. The history of the fragments was complicated, but on the whole a setback for democracy. Since shortly after the war Italy became a dictatorship, albeit a rather mild one as compared to Russia, it is not very obvious that the allied victory expanded democracy. World War II had a very nasty dictatorship, the Soviet Union, on the same side with United States and England. Indeed it did most of the fighting. Japan had an elected legislature and the Emperor's powers were very modest. It seems likely that they should be regarded as a constitutional monarchy rather than as a dictatorship. The end product of the war was of course the great expansion of the Soviet dictatorship so that Europe in 1945 was less democratic than it had been in 1930. Once again to refer to the war as a war for democracy is misleading Better alternatives? I have been presenting all of this material which could be regarded as an attack on democracy, not in order to run down democracy but indicate that the enthusiasm for democracy in the last 10 years and for communist dictatorship in the early '50s were simply examples of the instability of intellectual opinion. Personally I prefer democracies, but I must admit that the arguments for a democratic state are much weaker than those for a capitalistic economy. Further, when you look around the world you realize that Prince Bismarck's invention, the welfare state is largely dominant in democracies. Since the long run prospects of that system are poor, this could be an argument against democracy. It is however quite possible to feel as I do that in spite of its defects, democracy is better than the currently known alternatives. So far this paper has not had any dominant theme except that it shows little enthusiasm for democratic methods of government. I have to admit that I am not enthusiastic about democracy. Like Churchill, I favor it over its current competitors, but it seems to me that we should be looking for something better. The purpose of this note is first to deal with certain popular arguments for democracy, which I think are false, as a preliminary to encouraging my listeners to look for new forms of government.
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I find when talking to people about improvements in government the first response with respect to any idea is to ask, "Is it more democratic than our present methods?" If it were it would have the same defects. It could be, however, that there is another form of government which has all of the advantages of our democracy but adds something on to it. I have no suggestions at the moment but I believe that seeking a better form of government then democracy is sensible policy. It may be of course that the better form is a modification of our present democracy. If we look around the world we observe some democratic governments that are more successful than others. In my opinion the Swiss government is not only the best democratic government in the world but also the best government. Thus copying it would be an improvement even though I am great admirer of our Constitution. Melding the two might be an excellent idea. But I hope that the public choice scholars can do better. But let me return to my main theme which is problems with our present democracy. I will begin by once again turning to either the Arrow theorem, or the Black Newing proof that the voting process has paradoxes. Back to the voting paradox Roughly speaking, simple majority voting works very well if they're only two alternatives. When there are more the outcome may be close to random. In general, in democracies there are more than two people who would like given job and they're more than two policy suggestions for any given problem. In most functioning democracies these multiple choices are winnowed down to two which are then voted on. It is not obvious that one of the alternatives eliminated in the winnowing down process could not get a majority over whoever wins in the election limited to the two survivors. Of course the winnowing down process does not always get the final choice pattern down to two alternatives. I above mentioned cases in the American system in which no one got a majority because there were more than 2 alternatives which attracted significant votes. If one looks at policy choices we once again find a number of alternatives offered which are then winnowed down to two by successive votes in accord with the procedural rules in use in that particular voting body. Granted the prospect of paradox, it is by no means obvious that one of the other alternatives which lost earlier could not be the winner selected by the operation of the rules of order. To take a simple and artificial set of choices, suppose that the various alternatives actually offered as amendments in the Senate are: A, B, C, D, E, and F. Note that these are only a set of amendments offered on the floor of the Senate. If we considered those offered in committee, the set of amendments to the House version and what was done in the conference committee, probably at least 25 or 30 possible variants are proposed at one or another stage in the process. One of these numerous alternatives could be capable getting majority against the winner in the formal vote. Suppose for example that the votes are taken F against E, the winner against D. and so forth. This leads to B winning, but that B as never been offered against E, so it's perfectly possible that E could beat B but not beat D. This is simply an example of the standard possibility of circular majorities. We
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have no real measure of how often it happens. The first effort to find out how often was a joint article by Colin Campbell and myself which generated random preferences for a large body of synthetic voters in the computer memory and then tested them for cycles. The method is obviously crude but the only improvements on our design have been based on the same method but with larger collections of random numbers assigned to voters. Obviously, we need improvements but it is clear that the cycles are reasonably common. In this paper, I will make no effort to find out how common they are. I simply assume that they sometimes happen, and when they do, the outcome is not one we should respect. Of course, if they were rare we could regard the possibility as a minor defect, and go ahead. If they were common they would not be a minor but a major defect. Unfortunately we do not know. The effect of the paradox on Congressional elections But let us go on to the candidates selected by election. In addition to the paradoxes mentioned above, in the United States there is another very serious problem. In the 2000 election year, 31 members of the House of Representatives chose not to run -- presumably mainly in order to retire. Of the remaining to 394, all but 11 were re-elected. It is sometimes said that the security of tenure held by members of the House of Representatives is greater than that held by members of the House of Lords. The basic reason for this security is that the members of the House are able to get the federal government to expend great resources for their re-election. They have large staffs, considerable free travel, access to a free television studio in the basement of the capital, and many other advantages. There doesn't seem to be any exact accounting for this money, but I asked a professional lobbyist how much he thought it was worth and he gave a figure of two and half million per congressman per election. It's obvious why they are so secure and obvious why they want to restrict campaign expenditures by potential opponents. Senators do not have as firm a grasp on their offices as the members of the House and a President probably even less. In the case of the President resources spent by the federal government to get him re-elected are immense. It is probably true that resource expenditures have the highest payoff when there is little other information. Thus, the value of these large government expenditures would be highest for the House. It should be noted that in the 19th century when these expenditures were not as large congressman normally served only one term. This leads us perform a mental experiment. There must be several thousand people who would like to be President and who think at least a little bit of running. Most of them drop the idea almost immediately, but some will give it further consideration and talk to people about the possibilities. At this stage we're down to something like the 50 possible candidates. They "test the water." There was a senator unknown to me who recently visited Washington to a give a speech to an organization which he thought might support him. The Washington Post reported him as " testing the water" and said he received an enthusiastic response. This put him a bit above many of the above 50, perhaps in the top 10 or 20.
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At this point he would begin trying harder to get support from one of the parties, from special-interest groups, etc. he would also begin trying to raise money. Eventually he would either be nominated or not. Whether he became President would depend on who else was nominated and, in particular, how many were nominated. The prospect that somebody who could beat the eventual winning candidate was eliminated early in the game is certainly good. In other words the paradox exists here as well as in the choice of issues. Indeed it appears to even stronger here. Some suggestions for improvement This rather lengthy essay has raised a number of difficulties of a fundamental nature with democracy. They do not prove that democracy is inferior to any other given system, but they do indicate that we should substitute hard research for enthusiasm. In recent years there's been very little effort to solve these problems. I would like to encourage my audience to go back to the fundamentals. As a sort of study aid for people looking for improvements in the structure of government I should like to list some suggestions that already been made. This is not intended to be a complete list of possible changes, but only a set which have been made but have received little or no attention. I think they should be given more attention by students in this field, but I hope that someone will invent even better ones. I begin with Clarke's demand revealing process. This has had more attention than the others including a complete issue of public choice devoted to it. As the reader may know, I have done some work in this area and am an enthusiast for the system. It permits the voter to express not only which alternative he prefers, but also how much he prefers it. The outcome might lead to a minority of intense voters defeating a majority of near indifferent voter. My second proposal is Earl Thompson's suggestion to put individual policy changes up, in essence, to a bid. Among other things this permits compensation of the losers. The third proposal is Hanson's betting procedure in which the voter may be rewarded for favoring a decision for certain proposals if ex post an impartial commission finds that it adds to the national welfare. All three of these methods are radically different from our current voting procedures. Indeed, it could be argued that they're not really voting at all. Nevertheless they are a start. Note that all three permits a minority to win over a majority. Also, all three of these suggestions are subject to the Arrow, Newing and Black problem. If there are more than two alternatives, the order in which they are taken up may lead to different outcomes. Voting on all alternatives at the same time may also lead to different outcomes. As in other cases where these problems arise, voting on the order of taking them up to also leads to paradoxes. Still these are a start in investigating radically different ways of making decisions, and they're not monarchical. Alternative voting procedures These are variants on the actual voting procedure. Other possible changes involve the problem of who can vote. Dennis Mueller suggested that voters to given a short
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examination before being permitted to vote. The intent, of course, is to restrict the voting to people who at least know some elementary facts about the government. I, myself, perhaps influenced by my knowledge of China, have suggested an examination for the candidates. Following the Chinese precedent the examination for different offices would be of different degrees of difficulty. A man who would fail the president's exam might well pass that for alderman. Again following the Chinese precedent the examination would leave several candidates for each office to be selected by the voters. They would remain in control but the number of alternatives would be reduced. If the examination were well-designed the alternatives would also be improved. It is not obvious that one man one vote is ideal. Corporations give different people different votes depending on how many shares they own. As an aside, this system was originated by Lord Clive. He not only started the British Empire in India by his victory at Plassey, but he also, in an unsuccessful effort to control the Honorable Company, caused changes from one man one vote to one share one vote. It's not at all obvious which is the best system. I find, however, that most people are strongly opposed to, let us say, the one vote for every dollar in taxes paid. Whether this is merely opposition to a new idea or a rational position, I do not know. When I talk to people about it their objections normally are not well reasoned. Indeed they normally offer no reason at, all, merely opposition. There are other proposals for giving different people to different numbers of votes. Nevil Schute wrote a whole novel, In the Wet, devoted to this idea, and one of the richest men in United States Hunt -- also produced a book on it. The additional votes could be distributed in terms of payment for services. For a modest example, suppose any war veteran who actually got shot at gets an extra vote. Another radical idea is to permit people to hold their votes in abeyance. I could, for example, decide not to vote for president in 2004 and then cast two votes in 2008. Or perhaps I could have credit, testing two votes in 2004 and none in 2008. Perhaps to charge interest, I might be prohibited from casting votes for Senators in 2008. Undemocratic governments and conclusion But let us consider some undemocratic ideas. Gibbon thought the period of the adoptive Emperor's in Rome was the happiest in human history. Mexico used a somewhat similar system from 1931 to 1987. It also had a reasonably good government by the rather moderate standards of Mexican government's. For a list of other governments which are not democratic, I suggest my forthcoming "Undemocratic Governments". The reader should keep in mind that it is not necessary for the government form to be suitable for a nation state. It may be suitable only for use in individual governments which form only a part of the nation. If these were undemocratic, they would nevertheless be subject to popular control because of the possibility of moving. Note that some government functions cannot conveniently be broken up. In military matters economies of scale require large government units. There are other areas where breaking up government is unlikely to be successful. As an obvious example consider the regulation of the electromagnetic spectrum. No doubt the reader can think of many others. Nevertheless, pre-1870 Germany seems to have been pretty well governed
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although none of the constituent monarchies were democratic. I do not claim that any of the alternative governments I have listed is ideal. Nevertheless, I think they should receive careful study. Further, I think we should look for other forms of government. There is no natural law which says we cannot invent new forms of government which are better than the current sample. It is to encourage the reader to engage in such radical thought that this essay is dedicated. 3301 N. Fairfax Drive, Suite 450 ~ Arlington, Virginia 22201 703-993-4930 ~ www.mercatus.org ~ mercatus@gmu.edu
SOME THOUGHTS ON THE PROBLEMS OF DEMOCRACY Gordon Tullock March 15, 2002
Democracy is frequently referred to as a system of majority voting. Granted, the last election in the United States the opposing candidate received more popular votes than the winner, and neither received a majority of popular votes because of the existence of other candidates, it is surprising that our system is called that." Of course the winner did get a majority both in the Supreme Court and in the electoral college. The loser got a majority in the Florida Supreme Court.1Why do we call it "majority voting" when . . . The failure to get a majority in the popular vote is not particularly uncommon. Lincoln, for example, got only 35 percent of the popular vote and if one of the three of his opponents in the election, Douglas, had met him in a 2 candidate election, he would have won. The 1912 election, once again, had a winner who received less than half the popular votes. In Wilson's case he had two opponents, either one of which could have beaten him if the other had not been present. The current government in Canada received less than half the popular vote and, except in wartime, no British government has been elected by more half the voters since 1920. In both of these cases, of course, the winner had more than half of the representatives in Parliament. During its long reign in India, the Congress party never received a majority of the popular vote. Normally it received less than 45 percent. Another and interesting case is the election of 1960. Nixon had more popular votes than Kennedy but lost in the electoral college. The fact that Nixon had more popular votes, although not a majority of all votes, is almost a secret2. 1The Florida Supreme Court, solidly Democratic, voted 4 to 3 for Gore. Seven of the United States Supreme Court voted to overturn the Florida Supreme Court decision, but two of them wanted to send it back to Florida for further consideration. Hence the common newspaper reference to decision as 5 to 4. 2For an explanation of the actual situation see my letter to the editor of The New York Review of Books; Nov. 10, 1988 "Did Nixon Beat Kennedy? and the "Reply" by Francis Russell whose article I was criticizing. He accepted my criticism.
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The election of 1960 is interesting and here I foreshadow the major part of this article in that the two strongest candidates for the final election were eliminated in the selection processes of the two parties. It is reasonably certain that Johnson could have beaten Nixon in both popular and electoral votes and that Rockefeller could have beaten Kennedy . All of this does not indicate the system is inferior, but it does suggest that we stop calling it majority voting. The problem of more than two alternatives As on my readers will know, there are two general types of democracy, one originating in England long ago in which the voters directly select individual candidates. The other, which originated on the continent in the 19thcentury, is called proportional representation and I will to a large extent leave it out of the discussion below. Actually, I rather prefer proportional representation, but it is a different subject and requires different analysis. But to return to my main subject, the reader will have noticed that in each of the cases with a winner who did not have a majority of the votes, more than two alternatives were presented to the voters. With only two candidates or proposals before the voters these problems do not occur. Unfortunately, there are many people who would like to be the president and many ways which the government income could be spent. In the real world, it is likely that the system is confronted with more than two alternatives and it must either cut them down to two by some means or be willing to accept a candidate or proposition chosen by less than a majority. Of course it may happen that although there are three candidates or proposals one of him gets more than half of the votes. But we should not have a system which depends on that chance. The paradox: from Condorcet to Black and Arrow This problem has been known for a very long time and procedures to either simply take the one that has the most votes or reduce the number of alternatives to two and then vote on the those two are orthodox. Unfortunately, none of these procedures really overcome the problem. Shortly before the French Revolution two French aristocrats, Condorcet and Borda, looked into the problem and Condorcet found what is now known as Condorcet Paradox while Borda produced system which avoided that Paradox but introduced another. This was of course the period of the great expansion of democracy and, perhaps as a result of the enthusiasm for democracy, the problem was largely forgotten although some mathematicians seem to have known about it. In the mid-19thcentury, Lewis Carroll rediscovered the paradox and did considerable work on it without finding a solution. He too was largely forgotten and the problem was rediscovered by Black who also discovered that he had predecessors lost in the obscurity of minor mathematical publications. Black succeeded in reviving interest in the issue which is a little paradoxical since it is obvious he did not like the idea of democracy having paradoxes. Working with Newing he produced a proof that this paradox could not the avoided if there were more
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than two alternatives.3Notably he did not put out his work as a criticism of democracy because he was a firm believer in democracy. Nevertheless careful reading of his book with Newing shows the impossibility of avoiding the Paradox except in special cases. While Black and Newing were working, Arrow produced a general proof that the paradox cannot be avoided in the general case.4This was his famous general impossibility theorem. Notably it was only a remarkably long delay in the refereeing process which prevented the Black and Newing paper from being published before Arrow. In the early days of research in public choice, papers dealing with the paradox were a major component of papers submitted to me as editor of the journal. I think that most of these papers were inspired by desire to avoid the paradox or at least to minimize it. If this was the inspiration, it failed. The paradox continues and indeed I have invented a much simpler although less elegant proof.5After considerable delay I discovered a proof that the problem was not nonexistent, but of less importance than had been thought. If the voting preceded in the usual way of legislatures with anyone free to introduce an amendment is, it would precede to an outcome very close to the center of the cloud of individual optima. A dictatorial chairman, however, could lead the votes to almost anywhere he wished. Since the usual procedure is not involving a dictatorial chairman, this meant that the voting normally would lead to a more or less satisfactory outcome. Professor Arrow, in a very kind letter, accepted in the bulk of my reasoning but pointed out that the latter part was not really mathematically strict. He was right, but the reasoning was very strong even if not perfect, mathematicians standpoint.6What are fans of democracy to do? The end result of all of this work is most disappointing for proponents of democracy. Since the author and all of the readers of this paper are such proponents of democracy we should all the unhappy about it. As far as I can see, however, the usual response is not to be sad, but to sweep the problem under the rug. Psychologically this is no doubt an optimal response, but it seems to me that scholars should busily search for some better way of dealing with the paradox. I frankly admit I have not found one, but the point of this article is to attempt to interest other scholars in a revival of voting problem, so important in the early days of Public Choice, but normally today not even mentioned in the average issue or, indeed, in the average 10 issues. 3Black, Duncan and R.A. Newing. Theory of Committees and Elections. [2d Edition] Boston: Klewer Academic Publishers (1998). 4Arrow, Kenneth J. Social Choice and Individual Values. [2d Edition] New York: Wiley (1963). 5See" Some Simple But Confusing Mathematics" in my On Voting Edward Elgar, 1998 Cheltenham, UK, paperback, Locke Institute, Fairfax Va, 2001. 6 Tullock, Gordon. "The General Irrelevance of the General Impossibility Theorem". The Quarterly Journal of Economics Vol81, Issue 2 (May 1967) p.256-270
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This is particularly surprising granted that intellectuals are currently vigorously producing arguments for democratic governments, and hence would be one would think particularly interested in eliminating paradoxes in democracy. The new arguments for majority voting, and the authors normally refer to majority voting rather than simply democracy fall into two categories. The first is the allegation that democracy's tend to produce capitalistic economies and hence are prosperous. Dictatorships are allegedly less efficient in the economic field. Democracy and economic progress In the first place, economists have long known for (or at least many of them have) that a capitalistic system is a better method and of producing prosperity than a centrally directed one. In the last few years most intellectuals have adopted this idea. Note however, that except for a certain number of "reactionary" economists this idea was not popular among intellectuals 50 years ago. Warren Nutter undertook a major research project in communist statistics and decided that the rate of growth of the Soviet Union was not in any way remarkable. Indeed it was about that of United States and markedly lower than that of Japan. As a result he was practically drummed out of the economic profession. Note that efforts to duplicate his research turned out to be surprisingly similar although the CIA which funded them never overtly admitted that. It was however not just the CIA which disagreed. To repeat, Nutter's career was more or less terminated in the economic profession. The University of Virginia did not give him significant pay raises and moved him to an inconvenient office. He could not go anywhere else because other universities also thought that he was following his ideology and not his science. This was a personal tragedy for Nutter and a policy tragedy for many governments. The view that economic progress required central control by someone not hampered by democratic mechanisms was widely held. Many of the people who felt this way remained in favor of democracy for reasons other than its economic effects. Nevertheless, the recent view sweeping intellectuals that democracy works better in economics than a communist dictatorship is recent. Further, as far as I can see, like the earlier enthusiasm for communist dictatorships in the economic field, it was based on nothing more than one of the waves of enthusiasm that tend to sweep the intellectual classes, although the collapse of the old order in Russia undoubtedly contributed If we look at the real world, Japan, Germany, France, and India are all democracies and doing very badly in their economies while Singapore and Hong Kong continue to be prosperous with dictatorships and China, a clear-cut dictatorship and a rather impressive one, currently claims the highest rate of growth of any significant country. Speaking for myself, I tend to distrust communist statistics, but observation on a recent trip to China indicates it is very much better off than it was not too long ago, at the end of the great proletarian cultural revolution. Democracy and peace Another recent argument for democracy is that democracies are relatively peaceful. This began with view that democracies did not engage in aggressive wars.
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Apparently, after a while, some intellectuals read the history of 19th-century in which democracy's conquered much of the world, and the claim was reduced to one in which democracy's do not fight other democracies. The original claim was particularly surprising since many of the intellectuals who made it were American citizens and therefore should have been aware that United States had seized is present geographic area by a series of minor but certainly aggressive wars. Consider the reduced claim that democracies rarely fight other democracies. During a rather long period in which democracies were rare and hence had little opportunity to fight each other this was undoubtedly true. Still it should be kept in mind that in 1914 it could easily have been argued that both England and Imperial Germany were democracies, indeed the major undemocratic country in the war was Russia. Of course at that time all the monarchies were moving toward democracy and England and Germany were much farther along than Russia. The end product of the war was that what progress Russia had made towards democracy was canceled and one of the world's worst autocracies put in its place. The dissolution of Austria-Hungary was disastrous by any standard. The history of the fragments was complicated, but on the whole a setback for democracy. Since shortly after the war Italy became a dictatorship, albeit a rather mild one as compared to Russia, it is not very obvious that the allied victory expanded democracy. World War II had a very nasty dictatorship, the Soviet Union, on the same side with United States and England. Indeed it did most of the fighting. Japan had an elected legislature and the Emperor's powers were very modest. It seems likely that they should be regarded as a constitutional monarchy rather than as a dictatorship. The end product of the war was of course the great expansion of the Soviet dictatorship so that Europe in 1945 was less democratic than it had been in 1930. Once again to refer to the war as a war for democracy is misleading Better alternatives? I have been presenting all of this material which could be regarded as an attack on democracy, not in order to run down democracy but indicate that the enthusiasm for democracy in the last 10 years and for communist dictatorship in the early '50s were simply examples of the instability of intellectual opinion. Personally I prefer democracies, but I must admit that the arguments for a democratic state are much weaker than those for a capitalistic economy. Further, when you look around the world you realize that Prince Bismarck's invention, the welfare state is largely dominant in democracies. Since the long run prospects of that system are poor, this could be an argument against democracy. It is however quite possible to feel as I do that in spite of its defects, democracy is better than the currently known alternatives. So far this paper has not had any dominant theme except that it shows little enthusiasm for democratic methods of government. I have to admit that I am not enthusiastic about democracy. Like Churchill, I favor it over its current competitors, but it seems to me that we should be looking for something better. The purpose of this note is first to deal with certain popular arguments for democracy, which I think are false, as a preliminary to encouraging my listeners to look for new forms of government.
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I find when talking to people about improvements in government the first response with respect to any idea is to ask, "Is it more democratic than our present methods?" If it were it would have the same defects. It could be, however, that there is another form of government which has all of the advantages of our democracy but adds something on to it. I have no suggestions at the moment but I believe that seeking a better form of government then democracy is sensible policy. It may be of course that the better form is a modification of our present democracy. If we look around the world we observe some democratic governments that are more successful than others. In my opinion the Swiss government is not only the best democratic government in the world but also the best government. Thus copying it would be an improvement even though I am great admirer of our Constitution. Melding the two might be an excellent idea. But I hope that the public choice scholars can do better. But let me return to my main theme which is problems with our present democracy. I will begin by once again turning to either the Arrow theorem, or the Black Newing proof that the voting process has paradoxes. Back to the voting paradox Roughly speaking, simple majority voting works very well if they're only two alternatives. When there are more the outcome may be close to random. In general, in democracies there are more than two people who would like given job and they're more than two policy suggestions for any given problem. In most functioning democracies these multiple choices are winnowed down to two which are then voted on. It is not obvious that one of the alternatives eliminated in the winnowing down process could not get a majority over whoever wins in the election limited to the two survivors. Of course the winnowing down process does not always get the final choice pattern down to two alternatives. I above mentioned cases in the American system in which no one got a majority because there were more than 2 alternatives which attracted significant votes. If one looks at policy choices we once again find a number of alternatives offered which are then winnowed down to two by successive votes in accord with the procedural rules in use in that particular voting body. Granted the prospect of paradox, it is by no means obvious that one of the other alternatives which lost earlier could not be the winner selected by the operation of the rules of order. To take a simple and artificial set of choices, suppose that the various alternatives actually offered as amendments in the Senate are: A, B, C, D, E, and F. Note that these are only a set of amendments offered on the floor of the Senate. If we considered those offered in committee, the set of amendments to the House version and what was done in the conference committee, probably at least 25 or 30 possible variants are proposed at one or another stage in the process. One of these numerous alternatives could be capable getting majority against the winner in the formal vote. Suppose for example that the votes are taken F against E, the winner against D. and so forth. This leads to B winning, but that B as never been offered against E, so it's perfectly possible that E could beat B but not beat D. This is simply an example of the standard possibility of circular majorities. We
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have no real measure of how often it happens. The first effort to find out how often was a joint article by Colin Campbell and myself which generated random preferences for a large body of synthetic voters in the computer memory and then tested them for cycles. The method is obviously crude but the only improvements on our design have been based on the same method but with larger collections of random numbers assigned to voters. Obviously, we need improvements but it is clear that the cycles are reasonably common. In this paper, I will make no effort to find out how common they are. I simply assume that they sometimes happen, and when they do, the outcome is not one we should respect. Of course, if they were rare we could regard the possibility as a minor defect, and go ahead. If they were common they would not be a minor but a major defect. Unfortunately we do not know. The effect of the paradox on Congressional elections But let us go on to the candidates selected by election. In addition to the paradoxes mentioned above, in the United States there is another very serious problem. In the 2000 election year, 31 members of the House of Representatives chose not to run -- presumably mainly in order to retire. Of the remaining to 394, all but 11 were re-elected. It is sometimes said that the security of tenure held by members of the House of Representatives is greater than that held by members of the House of Lords. The basic reason for this security is that the members of the House are able to get the federal government to expend great resources for their re-election. They have large staffs, considerable free travel, access to a free television studio in the basement of the capital, and many other advantages. There doesn't seem to be any exact accounting for this money, but I asked a professional lobbyist how much he thought it was worth and he gave a figure of two and half million per congressman per election. It's obvious why they are so secure and obvious why they want to restrict campaign expenditures by potential opponents. Senators do not have as firm a grasp on their offices as the members of the House and a President probably even less. In the case of the President resources spent by the federal government to get him re-elected are immense. It is probably true that resource expenditures have the highest payoff when there is little other information. Thus, the value of these large government expenditures would be highest for the House. It should be noted that in the 19th century when these expenditures were not as large congressman normally served only one term. This leads us perform a mental experiment. There must be several thousand people who would like to be President and who think at least a little bit of running. Most of them drop the idea almost immediately, but some will give it further consideration and talk to people about the possibilities. At this stage we're down to something like the 50 possible candidates. They "test the water." There was a senator unknown to me who recently visited Washington to a give a speech to an organization which he thought might support him. The Washington Post reported him as " testing the water" and said he received an enthusiastic response. This put him a bit above many of the above 50, perhaps in the top 10 or 20.
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At this point he would begin trying harder to get support from one of the parties, from special-interest groups, etc. he would also begin trying to raise money. Eventually he would either be nominated or not. Whether he became President would depend on who else was nominated and, in particular, how many were nominated. The prospect that somebody who could beat the eventual winning candidate was eliminated early in the game is certainly good. In other words the paradox exists here as well as in the choice of issues. Indeed it appears to even stronger here. Some suggestions for improvement This rather lengthy essay has raised a number of difficulties of a fundamental nature with democracy. They do not prove that democracy is inferior to any other given system, but they do indicate that we should substitute hard research for enthusiasm. In recent years there's been very little effort to solve these problems. I would like to encourage my audience to go back to the fundamentals. As a sort of study aid for people looking for improvements in the structure of government I should like to list some suggestions that already been made. This is not intended to be a complete list of possible changes, but only a set which have been made but have received little or no attention. I think they should be given more attention by students in this field, but I hope that someone will invent even better ones. I begin with Clarke's demand revealing process. This has had more attention than the others including a complete issue of public choice devoted to it. As the reader may know, I have done some work in this area and am an enthusiast for the system. It permits the voter to express not only which alternative he prefers, but also how much he prefers it. The outcome might lead to a minority of intense voters defeating a majority of near indifferent voter. My second proposal is Earl Thompson's suggestion to put individual policy changes up, in essence, to a bid. Among other things this permits compensation of the losers. The third proposal is Hanson's betting procedure in which the voter may be rewarded for favoring a decision for certain proposals if ex post an impartial commission finds that it adds to the national welfare. All three of these methods are radically different from our current voting procedures. Indeed, it could be argued that they're not really voting at all. Nevertheless they are a start. Note that all three permits a minority to win over a majority. Also, all three of these suggestions are subject to the Arrow, Newing and Black problem. If there are more than two alternatives, the order in which they are taken up may lead to different outcomes. Voting on all alternatives at the same time may also lead to different outcomes. As in other cases where these problems arise, voting on the order of taking them up to also leads to paradoxes. Still these are a start in investigating radically different ways of making decisions, and they're not monarchical. Alternative voting procedures These are variants on the actual voting procedure. Other possible changes involve the problem of who can vote. Dennis Mueller suggested that voters to given a short
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examination before being permitted to vote. The intent, of course, is to restrict the voting to people who at least know some elementary facts about the government. I, myself, perhaps influenced by my knowledge of China, have suggested an examination for the candidates. Following the Chinese precedent the examination for different offices would be of different degrees of difficulty. A man who would fail the president's exam might well pass that for alderman. Again following the Chinese precedent the examination would leave several candidates for each office to be selected by the voters. They would remain in control but the number of alternatives would be reduced. If the examination were well-designed the alternatives would also be improved. It is not obvious that one man one vote is ideal. Corporations give different people different votes depending on how many shares they own. As an aside, this system was originated by Lord Clive. He not only started the British Empire in India by his victory at Plassey, but he also, in an unsuccessful effort to control the Honorable Company, caused changes from one man one vote to one share one vote. It's not at all obvious which is the best system. I find, however, that most people are strongly opposed to, let us say, the one vote for every dollar in taxes paid. Whether this is merely opposition to a new idea or a rational position, I do not know. When I talk to people about it their objections normally are not well reasoned. Indeed they normally offer no reason at, all, merely opposition. There are other proposals for giving different people to different numbers of votes. Nevil Schute wrote a whole novel, In the Wet, devoted to this idea, and one of the richest men in United States Hunt -- also produced a book on it. The additional votes could be distributed in terms of payment for services. For a modest example, suppose any war veteran who actually got shot at gets an extra vote. Another radical idea is to permit people to hold their votes in abeyance. I could, for example, decide not to vote for president in 2004 and then cast two votes in 2008. Or perhaps I could have credit, testing two votes in 2004 and none in 2008. Perhaps to charge interest, I might be prohibited from casting votes for Senators in 2008. Undemocratic governments and conclusion But let us consider some undemocratic ideas. Gibbon thought the period of the adoptive Emperor's in Rome was the happiest in human history. Mexico used a somewhat similar system from 1931 to 1987. It also had a reasonably good government by the rather moderate standards of Mexican government's. For a list of other governments which are not democratic, I suggest my forthcoming "Undemocratic Governments". The reader should keep in mind that it is not necessary for the government form to be suitable for a nation state. It may be suitable only for use in individual governments which form only a part of the nation. If these were undemocratic, they would nevertheless be subject to popular control because of the possibility of moving. Note that some government functions cannot conveniently be broken up. In military matters economies of scale require large government units. There are other areas where breaking up government is unlikely to be successful. As an obvious example consider the regulation of the electromagnetic spectrum. No doubt the reader can think of many others. Nevertheless, pre-1870 Germany seems to have been pretty well governed
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although none of the constituent monarchies were democratic. I do not claim that any of the alternative governments I have listed is ideal. Nevertheless, I think they should receive careful study. Further, I think we should look for other forms of government. There is no natural law which says we cannot invent new forms of government which are better than the current sample. It is to encourage the reader to engage in such radical thought that this essay is dedicated. 3301 N. Fairfax Drive, Suite 450 ~ Arlington, Virginia 22201 703-993-4930 ~ www.mercatus.org ~ mercatus@gmu.edu