Usher Political Economy (Blackwell, 2003)

Ham

Figure 9.1 A directed graph of the outcomes of pair-wise votes between ham, cheese, and tuna. The arrow from, for example, cheese to ham, means that cheese beats ham in a pair-wise vote.

The capriciousness of voting

Voting becomes capricious when the outcome depends more upon the intricacies of the voting rules or upon side deals among voters than upon the preferences of the voters themselves. To show how the outcome of voting depends on voting rules, we construct an example with three options in a community composed of three groups of voters where preferences among the options are identical within each group but different from one group to another. Suppose once again that the class must choose one and only one type of sandwich for everybody, but that now there are three types of sandwiches to choose from: ham, tuna and cheese. With these three options, there can be six preference orderings: “ham preferred to cheese preferred to tuna,” “ham preferred to tuna preferred to cheese,” “cheese preferred to ham preferred to tuna,” “cheese preferred to tuna preferred to ham,” “tuna preferred to cheese preferred to ham,” and “tuna preferred to ham preferred to cheese.” Every student’s preference ordering must be one of the six, though not every possible ordering need be represented among students’ preferences. Suppose all students have one of the three preference orderings in table 9.1, so that outcomes of all pair-wise votes are as shown in figure 9.1. In a class of 100 students, there are 35 students (called group I) who prefer ham to tuna to cheese as shown in the first row of table 9.1, 33 students (called group II) who prefer tuna to cheese to ham as shown in the second row, and 32 students (called group III) who prefer cheese to tuna to ham as shown in the third row. To emphasize how public choice may be affected by the voting mechanism, the preferences are chosen so that ham has more first preferences than either cheese or tuna, but ham loses to both cheese and tuna in a pair-wise vote. This constellation of preferences is odd but by no means impossible. The voting methods to be compared are first-past-the-post, sequential voting, the single transferable vote, the Borda method, and proportional representation.

First-past-the-post

Each person votes for one of the three sandwiches, and the sandwich with the most votes wins. Ham gets 35 votes; tuna gets 32 votes; cheese gets 33 votes. With first- past-the-post voting and with tastes as shown in table 9.1, ham wins because it gets the largest number of votes. If sandwiches were political parties, if the entire country were

divided into constituencies each electing one Member of Parliament, and if preferences of voters in each constituency were as shown in table 9.1, the ham party would win every seat in Parliament, even though it commands no more than 35 percent of the total vote.

First-past-the-post voting is especially susceptible to vote-splitting. Think of the ham party as “right wing” and of the cheese and tuna parties as “left wing”. The situation in table 9.1 is where the left is split between two parties, both of which could beat the right-wing party in a straight pair-wise vote, but both of which lose to the right-wing party when neither is prepared to abandon the field to the other. Ambition, jealousy, minor differences in political views, or mere inertia may keep both candidates in the running though they each know they will both lose the election. In Canada today, the “conservative” vote is split between the Progressive Conservative Party and the Alliance Party, and it is at least conceivable that a combined conservative party could defeat the Liberals, though the Liberals would always emerge victorious in a three-way contest.

Supporters of first-past-the-post argue in its defense that vote-splitting is less important in practice than extreme and fanciful examples might suggest because recognition of the possibility of vote-splitting provokes parties with similar programs to fuse before the election and because the really important consideration in societies where voters are not too diverse is that voting yields a majority party in Parliament with the ability to govern the country. Recognition of the possibility of vote splitting pressures political parties with similar programs to coalesce before the election. Typically, though by no means invariably, elections are contested by two major parties with platforms hammered out as a compromise among their supporters before the election. The very terms left wing and right wing are a reflection of this possibility.

Yet there is something peculiar about the implicit assumption that people’s views on all political issues can be categorized as left or right, so that a person who holds a left view on one issue can be expected to hold a left view on the rest. One would like to think that people are more independent than that. The original reference of these terms was to the French National Assembly of 1789 where the seating arrangement was a reflection of how nasty one was prepared to be to King Louis XVI. It is hard to imagine a correspondence between that seating arrangement and anything of importance today. The only sense I can make of these terms is as convenient labels for broad coalitions

of politicians seeking office, with perhaps some reference to the extent of government influence over the economy.

First-past-the-post rules can have dangerous consequences for a society that is deeply divided by language, race, or religion and where the division is within constituencies, not among them. First-past-the-post voting rules would simply not be respected in a society where religion is divisive and where, for example, 51 percent of each constituency is Muslim and the remaining 49 percent is Hindu, or vice versa. Some other political accommodation would have to be devised.

Sequential voting

Though ham wins in first-past-the-post voting, it must necessarily lose to tuna in sequential voting because tuna is preferred to either of the other sandwiches in a pairwise vote. Frequently, the outcome of sequential voting depends on the order of the sequence, but not in this case.

The single transferrable vote

Voters are instructed to list all candidates in order of preference, so that, for example, a voter in group 1 of table 1 would write, “ham, tuna, cheese.” If any option has more than 50 percent of the first-place votes, that option wins. Otherwise, the option with the lowest number of first places is deleted from everybody’s list, and the votes are recounted. Once again, if any option has more than 50 percent of the first-place votes, that option wins. The process is repeated as many times as is necessary for one of the options to emerge with over 50 percent of the first-place votes. The process must eventually supply a winner because one candidate must have over 50 percent of the vote when the number of contenders is reduced to two and because a tie is virtually impossible when there are millions of voters. In our example, no option gets 50 percent of the vote on the first round, tuna is deleted from the contest because it has the smallest number (32) of first places, and then cheese gets 65 out of 100 votes in the contest with ham. Though ham wins under first-past-the-post and tuna wins in sequential voting, cheese wins in the single transferrable vote.

The Borda method

Voters are instructed to list all candidates in order of preference. With three options, an option gets 2 points for each first place, 1 point for each second, and 0 points for each third place. With 35 first places and no seconds, ham gets 70 points [35 × 2]. With 32 first places and 68 second places, tuna gets 132 points [(32 × 2) + 68]. With 33 first places and 32 seconds, cheese gets 101 points [(33 × 2) + 32]. With voting by the Borda method and with tastes as shown in table 1, tuna wins.

All three sandwiches are chosen in at least one of these four methods of voting. Voting is capricious, in the sense that the outcome is dependent on the method of

voting, when there is no single overwhelming winner with enough support in the electorate to prevail in all of the methods of voting we have examined.

Proportional representation

Members of Parliament may be selected not in one constituency at a time but altogether. Think of ham, tuna, and cheese as names of political parties (no sillier than donkeys and elephants) rather than as names of sandwiches. Think of the numbers in the second column of table 1 as percentages of the electorate, and suppose 100 Members of Parliament have to be chosen. Under proportional representation, seats in parliament are proportional to votes in the nation, 35 seats for the ham party, 32 for the tuna party and 33 for the cheese party. Legislators in Germany and Israel are chosen by proportional representation.

Another aspect of the capriciousness of voting is that the outcome may depend upon deals among voters when two or more matters have to be resolved together. Suppose that 10 percent of the population favors the support by the state of the “one true religion,” and that the 90 percent of the population who oppose support by the state of the one true religion are divided equally between liberals and conservatives, distinguished, for example, by their preferences about state control of industry. If those in favor of the state support of the one true religion do not care one way or another about the control of industry, or if their concern about industry is entirely subordinate to their concern about religion, then the religious group can ally itself, and form a majority, with either the liberals or the conservatives. A majority coalition of the religious folk and the conservatives would implement a platform of conservative economic policy and state support of the one true religion. A majority coalition of the religious folk and the liberals would implement a platform of liberal economic policy and state support of the one true religion. There is no basis for predicting which of the two alliances will be formed. We will return to this problem in the discussion of bargaining at the end of this chapter.

The paradox of voting

The constellation of preferences in table 9.1 and figure 9.1 has been chosen so that tuna beats either cheese or ham in a pair-wise vote. From this fact alone, one might be inclined to say that tuna is the right choice for the class and that the outcome of first- past-the-post voting is an aberration. The inference would be that sequential voting is preferable because tuna emerges victorious in any sequence of votes. Suppose, for example, that the sequence is tuna against cheese in the first round of voting, followed by the winner against ham in the second. Tuna is “elected” because it wins both rounds, and would continue to do so in any other sequence. Unfortunately, sequential voting has its own equally troublesome problems.

Consider a slight modification of the constellation of preference orderings in table 9.1. Preferences in table 9.2 are the same as in table 9.1 except for a reversal of the second and last preferences of group III, as shown in the bottom row. Once

Ham

Figure 9.2 A directed graph of the paradox of voting.

again, ham wins in a three-way contest, though a slight change in proportions of voters would alter that. However, with this pattern of preferences, sequential voting turns perverse, giving rise to what is called a “paradox of voting.” One can see immediately from table 9.2 that ham beats tuna and that tuna beats cheese. Both wins are substantial. Ham beats tuna with 68 percent of the votes, and tuna beats cheese with 67 percent of the votes. If the outcome of the vote can be thought of as representing the preferences of society, then, to be consistent, society would have to prefer ham to cheese as well. One would naturally expect ham to beat cheese in any pair-wise vote. The essence of rationality is consistency. If a person tells you that he prefers ham to tuna and that he prefers tuna to cheese, but that, nevertheless, he prefers cheese to ham, it would be hard to escape the conclusion that this person is irrational, even insane. Collective decisions by majority rule voting may be just like that! With the constellation of individual preferences in table 9.2 and with collective decision-making by voting, cheese is preferred to ham – by a vote of 66 percent – despite the fact that ham is collectively preferred to tuna and tuna is collectively preferred to cheese. Depending on the pattern of preferences, a community of people may vote inconsistently without any individual being inconsistent or insane. The paradox of voting is that though each voter is rational, the community as expressed by voting need not be. For the pattern of preferences in table 9.2, the outcomes of all pair-wise votes are shown in the directed graph in figure 9.2.

An immediate consequence of this potential irrationality is that the “agenda setter” can sometimes determine the outcome of voting through his authority to choose the sequence of votes. With three options to choose from, there are three possible sequences of pair-wise votes: (1) ham against tuna, followed by the winner against cheese, (2) ham against cheese, followed by the winner against tuna, and (3) cheese

against tuna, followed by the winner against ham. The agenda setter is the person who chooses among these sequences. When preference orderings are as shown in table 9.1, the agenda setter is powerless because tuna wins regardless. But when preference orderings are as shown in table 9.2, the agenda setter can rig the outcome of the vote in his choice among the three possible sequences. The trick is that, with the preference orderings in table 9.2, the option introduced in the last vote always wins. If the agenda setter wants ham to win, he need only choose the third of the three sequences above.

The agenda setter can be foiled by sophisticated, as distinct from sincere voting. Voting is said to be sincere when, for example, I always vote for ham over cheese if I really prefer ham to cheese and regardless of what I expect to be the outcome of a sequence of votes to be. Voting is said to be sophisticated when I vote against my preferences now in order to get a better outcome in the end. Suppose the agenda setter favours ham, and consider the strategy of the third group of students whose preferences, as shown in the bottom row of table 2, are for tuna, cheese and ham in that order. Hoping to maneuver students to vote for ham, the agenda setter arranges a first round of voting between tuna and cheese, anticipating that tuna wins the first round and is then beaten by ham in the second. That is exactly what happens if everybody votes sincerely. The agenda setter gets his way at the expense of the third group of students for whom ham is the least desirable sandwich. Understanding this, these students may vote for cheese rather than tuna in the first round, anticipating that cheese beats ham in the second. These students would prefer tuna, but they cannot get it. The best they can do is to vote against their first preference, tuna, to obtain cheese which is at least preferable in their estimation to ham. The moral of the story is that voting is unpredictable and dependent on the strategies of the voters.

The poor dispossess the rich

A classic argument against democratic government runs more or less as follows: With universal franchise, there is nothing to stop the poor from employing the power of the vote to expropriate the rich. As nobody’s wealth would be safe from predation by voting, it would be in nobody’s interest to work hard, to educate himself or to invest in order to become rich. Enterprise would cease. Society would sink into poverty until such time as majority-rule voting with universal franchise is replaced by some other form of government. Perhaps society could get by with a property qualification for voting, as favored by the classical economists and as was the practice in most democratic countries until the end of the nineteenth century. Otherwise monarchy or dictatorship would seem to be required.

The argument that the voting allows the poor to dispossess the rich can be framed with reference to the choice of a rate for a negative income tax. A negative income tax is a universal lump sum transfer of income financed by a proportional income tax. Suppose for convenience of exposition that the government undertakes no expenditure other than the transfer of income. The government levies proportional income tax at a rate t to pay for a transfer of T dollars per person. Thus, if a person’s gross (pre-tax-and-transfer) income is yG, his net (post-tax-and-transfer) income

becomes yN where

Suppose also that tax collection is costless in two respects: (1) There is no administration cost to tax collection, no tax inspectors to be paid, no tax evasion and no need for police to detect and prosecute tax fraud. (2) There is no inefficiency or wastage of resources as people rearrange their affairs to reduce their tax bills, switching expenditure from taxed to untaxed goods or from taxed work to untaxed leisure and do-it-yourself activities. Thus, regardless of the tax rate, the national income remains invariant. With no administrative cost or wastage of resources in taxation, the government balances its budget as shown in equation (2).

where N is the total population of tax-payers, yiG is the gross income of person i, the left-hand side of the equation is total public expenditure, and the right-hand side of the equation is total public revenue. Substituting the government’s budget constraint, equation (2), into equation (1), we see immediately that each person’s net income, yiN, is connected to his gross income, yiG, as follows

A natural interpretation of equation (3) is that a person’s net income is a tax-weighted average of his gross income and the average income in the population as a whole. The higher the tax rate, the closer to the average does each person’s net income become. Thus, an increase in the transfer per head financed by an increase in the tax rate is beneficial to everybody with a gross income below the average, and is detrimental to everybody with a gross income above the average.

The tax rate is determined by voting. Since everybody seeks to maximize his net income, it follows from equation (3) that everybody with below-average pretax income favors maximal redistribution, while everybody with above-average pre-tax income opposes redistribution altogether. The one group wants t = 100 percent. The other group wants t = 0 percent. In a vote, the option of setting t = 100 percent wins if more than half the voters have below-average pre-tax incomes, and the option of setting t = 0 wins otherwise. In fact, all electorates have majorities with less than average incomes. At virtually every time and place where the income distribution has been observed, there have been more people with below-average incomes than with above-average incomes, reflecting a skewed distribution of income with a few exceptionally wealthy folk and a great clustering of ordinary folk with incomes somewhat below the mean. For example, in a community of five people whose incomes are $1, $2, $3, $5, and $9, the average income per head is $4 but three out of the five people have incomes below $4. A majority of three of these five people votes for a tax rate of

100 percent. On our assumptions so far, a majority would always vote for a tax rate of 100 percent in a one-to-one contest with any other rate. All income is confiscated and redistributed equally among all citizens. The incentives to work and save are wiped out completely. Whether the assumptions required to derive this gloomy prognosis are reasonable, and what becomes of the proposition when the assumptions are modified, will be discussed below.

The exploitation problem

Seven people sit around a table. On the table is $700,000 which is theirs as soon as they can decide how to allocate the money among themselves. All decisions are by majority-rule voting. What happens? Whatever the outcome, it can be represented as a platform {y1, y2, y3, y4, y5, y6, y7} where y1 is the allocation to the first person, y2 is the allocation to the second person, and so on, and where the sum of the seven allocations has to be $700,000.

The obvious procedure is to divide the money equally, $100,000 per person. The platform would be {100, 100, 100, 100, 100, 100, 100} where the numbers refer to thousands of dollars. If people are considerate, that is how the sum might be divided. But economics is the calculus of greed, and greedy people might hit upon a more advantageous allocation. Suppose four of the seven are men and the remaining three are women. The four men might strike a deal to take the entire sum for themselves, excluding the women altogether. They might agree to vote for the platform {175, 175, 175, 175, 0, 0, 0} which provides $175,000 for each man and nothing for any of the women. This greedy platform defeats the original platform {100, 100, 100, 100, 100, 100, 100} in a pair-wise vote. Nor is it essential to this example that people differ by gender. The seven people may differ by race. Four blue people might form a coalition to dispossess three green people. Four western people might form a coalition to dispossess three eastern people. Majority rule voting allows any four people to establish a coalition to exploit the remaining three.

The allocation of $175,000 to each of four people is not an electoral equilibrium in the sense that it can defeat every other allocation in a pair-wise vote. Though it can beat the platform {100, 100, 100, 100, 100, 100, 100}, the platform {175, 175, 175, 175, 0, 0, 0} cannot beat every other platform. It is beaten by the platform {200, 200, 200, 0, 100, 0, 0} which could emerge as follows: The first woman (person 5) might propose to the first three men that they join her in a coalition where they each get $200 thousand, she gets $100 thousand and the fourth man is displaced altogether. Everybody in the new coalition is better off than in the old coalition, and the first three men would be inclined to accept the proposal if they could be certain that the coalition would hold. But the new coalition is no more stable than its predecessor. For example, the second woman might offer to accept $25 thousand in a new coalition excluding the second man and providing an extra $25 thousand to each of the three remaining members of the old coalition. That platform could be defeated by yet another platform, and so on, ad infinitum. There is no electoral equilibrium at all. There is no platform that cannot be defeated by some other platform in a pair-wise vote.

The nice platform {100, 100, 100, 100, 100, 100, 100} may be especially vulnerable and unstable as a consequence of mistrust. I may be prepared to accept my fair share, $100,000, of the income as long as I am confident of your good faith. But, if I begin to doubt you, if I begin to fear you may be about to form a coalition behind my back and from which I am excluded, then I may begin negotiations of my own, and you, in turn, may be provoked to act more aggressively than if you trusted me. The nasty platform {175, 175, 175, 175, 0, 0, 0}, while not a full electoral equilibrium, may be more stable in practice than the nice platform because each beneficiary, each of the four men in this example, knows that he has more to lose in the end – 175 rather than 100 – if the nasty platform is overturned.

The exploitation of minorities by majorities and the dispossession of the rich by the poor, as discussed in the preceding section, are similar in that one group suffers at the hands of another, but they differ in the manner and consequences of discrimination. In the exploitation example, there are no prior rights to shares of the $700,000. There is no generally accepted rule for the voters to follow. (Equality might constitute such a rule in some societies, but not in societies with market-based economies where incomes differ markedly from one person to the next.) In the dispossession of the rich by the poor, there are two rules which conflict to some extent. There is a prior allocation of income (or, equivalently, of property rights), and there is a prior agreement not to reassign people’s incomes arbitrarily – so much for you, so much for me depending on how favorable a deal each of us can make within the majority coalition. There is one tax rate for everybody, and the vote is confined to determining what that tax rate is to be.

An important moral can be drawn. Democracy – by which I mean no more than that major public decisions are taken by majority rule voting – works best in societies not too sharply divided between identifiable groups with opposing interests. Current rhetoric notwithstanding, democracy is hardly threatened by the division of mankind into men and women because men and women have too many interests in common, not least of which is their common concern for their children of both genders. Language is potentially more divisive. Most bilingual or multilingual countries establish federal governments with constitutionally protected powers for states or provinces where minority languages are geographically concentrated. Church and state are rigidly separated in democratic countries for fear that religion may become politically significant. Hindu and Muslim coexisted peacefully enough within greater India as long as India was a colony, but ceased to coexist on the establishment of democratic government after independence. Location, social class, or industry will do as a basis for expropriation when nothing better is available.

The argument is not that different languages, races or religions are incompatible in themselves, but that they supply people with the badges that facilitate exploitation by voting. How do you know in practice who belongs to the majority coalition and who is to be exploited? You know because people are identifiable by language, religion, or race. The sharper the division in society, the more stable a majority coalition is likely to be. Exploitation by language, religion, or race originates in the pathology of democratic politics rather than in the pathology of language, religion, or race.

THE DEFENSES OF DEMOCRACY

Defenses of democracy can be classified under three headings which might be called natural, procedural, and institutional. Natural defenses are circumstances where majority rule voting works very well and the diseases of democracy do not threaten at all. Voting about some topics gives rise to a paradox of voting or the expropriation of minorities by majorities. Voting about other topics is free of these defects. Procedural defenses are subsidiary voting rules, imposed regardless of what people vote about. People do not just vote, on and on, with amendment after amendment ad infinitum as our exposition of the exploitation problem might suggest. Voting is framed by subsidiary procedures that supply a degree of determinacy which might otherwise be absent. Institutional defenses are man-made constraints upon the content of voting. Matters that would otherwise prove divisive are removed from the domain of voting and consigned instead to the domains of non-political institutions, to markets with private property, and to civil rights. These three defenses of democracy will be discussed in turn. As we proceed, the reader should bear in mind that the world of voting is more various and complex than the models we employ to describe it. Models can be useful as guideposts without at the same time describing the terrain completely or marking each and every pitfall along the way.

Natural defenses

Two kinds of natural defenses may be distinguished. The first might be called matters of common concern, among them the choice of executives and administrators, foreign affairs, monetary policy, fiscal policy, measures to reduce unemployment of labor, administration of the police, transport, and communication. Citizens differ in their opinions about these matters, but the great majority of citizens gain or lose together according to whether policy is chosen and administered well. Other things being equal, most people are better off when a country is at peace with its neighbors, when alliances are formed judiciously and when the crime rate is low Though there is no bright line separating matters of common concern from matters giving rise to conflict of interest among voters – as when high-paid and low-paid workers differ about the appropriate weighting of employment and price stability as objectives of financial policy – there may be enough of a distinction to explain why voting can sometimes proceed without much bitterness or controversy.

The second natural defense is that people’s preferences – however different they may be – can sometimes be lined up on a common scale. Interests may differ markedly, but the constellation of preferences may nevertheless be such that an electoral equilibrium does arise. The essence of the paradox of voting, exemplified by the vote about ham, cheese and tuna sandwiches as discussed above, is the absence of an electoral equilibrium comparable to the equilibrium in competitive markets. Not all divergences among preferences are like that.

Imagine a less peaceful university than the university to which you are accustomed, a university where the different classes fight one another with spears. Consider a class