Southern Economic Journal, Vol. 66 No. 1 (July 1999)
Richard F. Potthoff (Duke University)
Review of "On Voting" by G. Tulock.
Writing in a characteristic style that is blunt and outspoken as well as entertaining and satirical, Tullock provides a potpourri of topics and ideas in a small book not just targeted toward specialists in voting theory and public choice but also aimed (successfully, by and large) toward being intelligible to nonspecialists. Woven through the book are a number of themes and subjects for which the author draws on earlier works of his own as well as of others, but his intent is also to cover new material and to stimulate new research. The book is loosely organized. Chapter titles convey only part of what is in a chapter; many topics appear and later reappear, in part because of their interrelations; and, as the author acknowledges, the work is "rather lightly footnoted" (p. 3). Sprinkled throughout the book are interesting tidbis of little-known information, as well as miscellaneous comments sure to generate reader assessments ranging from ingenious to outrageous. My focus will be mainly on describing the more important and provocative aspects of the book and secondarily, on evaluating some of them.
The author maintains that most persons do not understand the complexity of voting systems, do not realize that different systems can produce different outcomes in the same election, and are willing to accept whatever system they are used to just as a matter of tradition and custom. He describes a number of possible election systems, many of them in an Appendix; but some, such as approval voting, receive only limited attention. He points out anomalies of current systems whem more than two candidates vie for one position. Under a plurality (first-past-the-post) system, for example, one such anomaly is strategic voting, in which a voter refrains from "wasting" a vote on a first-choice candidate who seems to be a sure loser.
Another anomaly is that a Condorcet candidate (one who could defeat each opponent in a two-way race with each) may lose. Thus, although in British elections the Liberal Democrats invariably run a poor third (under plurality voting), Tullock reasonably argues that they could typically beat either of the two larger parties in a two-way election and so would be the Condorcet choice. In the 1960 U.S. Presidential election, he contends that Rockefeller could have easily beaten Kennedy and that Johnson could have easily defeated Nixon, thus indicating that neither Kennedy nor Nixon could have been a Condorcet choice. He notes a Louisiana gubernatorial election in which it appears that the candidate who placed third, and who was thus excluded from a subsequent runoff election, was the Condorcet candidate. He thinks that Lincoln would have lost a two-way race to Douglas in 1860.
Concerning systems for electing legislatures, Tullock advances the imaginative idea of a two-house legislature with one chamber elected through proportional representation (PR) and the other through plurality voting in single-member districts. He reasons that electing the two houses in different ways would make it harder to pass new laws (an effect he considers beneficial). If one house is to be elected from single-member districts, though, it would seem that almost any other voting method would be better than plurality voting, but Tullock may have been trying to avoid too sharp a break from the status quo.
The author examines various PR and PR-like systems, criticizing some but not others. He cautions that in those PR systems with a rule denying representation to a party that falls short of a threshold of 5% (say) of the vote, many voters will go unrepresented if there are numerous small parties. His opinion of the Hare PR system (which uses a preferential ballot) is negative.
Earlier, Tullock (1967, Chapter 10) offered a PR system of his own. Arrow (1969) succinctly described it as "an ingenious proposal ... that every elected representative cast as many votes in the legislature as he received in the election" (p. 106). In the pure form of this system, any candidate who receives one or more votes is elected. The system receives only brief mention in the new book. Tullock does add a provision (not in the original version) that voters be allowed to change their representatives at any time, but implementation would appear difficult if a secret ballot is to be retained. Potthoff and Brams (1998) gave his PR system high marks on both representativeness and nonmanipulability, although objections can be raised based on less-mathematical criteria that relate to institutional factors. I was disappointed that the author did not say more about the system and give more of his present thinking concerning it.
A most unusual voting system, which the author thinks worked well, is a ten-stage system once used to elect the top official in Venice. It consisted of five stages that were random draws interspersed with five election stages requiring majorities that ranged from 7/12 to 7/9. The concept of random selection also appears everywhere in the book, as does the concept of requiring large majorities. The author states that many officials in ancient Athens were chosen by lot, mentions the idea of randomly picking either the members of a legislature or the voters who are to elect them, and observes that selection by lot is not such a radical notion when applied to choosing a jury.
Prescribing a majority well above 50% in order to pass a measure is a tenet strongly advocated by the author (and by others as well). He notes the unanimity requirement for juries, observes that the Bill of Rights is intended to protect against possible abuses by simple majorities, and cites situations where approval by more than a simple majority of voters has been required for bond issues and tax increases. He contends that requiring a large majority will result in higher benefit-to-cost ratios of approved projects; less potential for cycling among alternatives; fairer outcomes when a minority has strong feelings but the feelings of the opposing side are less intense; smaller chance that a majority will enact unfair discriminatory measures against a minority, and generally better outcomes where logrolling occurs. A required majority of 2/3 to 3/4 seems to be what he favors. This is a bit higher than the 64% majority requirement advanced by Caplin and Nalebuff (1988).
A number of pages are devoted to logrolling, a topic dealt with extensively in earlier works of the author. He feels that logrolling is both inevitable and largely beneficial, though imperfect. Repeatedly, he argues that logrolling, through tradeoffs, can reduce injury inflicted upon a minority to an extent that would not otherwise be possible. He sees logrolling as a way of taking into account the intensity as well as the direction of people's preferences and as a means for bringing about better compensation for losers.
Arrow's Impossiblity Theorem, spatial voting models, Condorcet cycles, the results of Plott and McKelvey related to cycling, and agenda order and control all achieve Tullock's attention. He presents an impossibility result of his own that he feels is similar to Arrow's but much easier to prove. Generally he does not consider the group of unfavorable mathematical results on cycling and impossibility to be a serious problem at all. He contends that one rarely finds real-world examples of cycling or of constant changes in laws and that cycling in inhibited both by bargaining processes before a vote and by requirements that time elapse between one vote and a later one. On the other hand, he notes a case involving a bond issue in Tucson where he thinks a cycle existed, expresses the view that research on cycles has often been held back partly because of potential negative implications for democracy, and presents a table (p. 42) showing high probabilities of the nonexistence of a Condorcet winner. (He does not mention, though, that the results in the table and other, similar results assume that all n! possible preference rankings of n alternatives are equally likely, an assummption whose concordance with real-world preference distributions can be questioned.)
The author deals with the issue of who should be allowed to votes and discusses restrictions that in various times and places have prevented groups such as females, slaves, blacks, persons who do not own property, persons receiving government pensions, illiterates, and criminals from voting. He is not bashful about expressing unorthodox opinions. Thus, for example, he favors depriving "civil servants and their families" (p. 26) and "people who are dependent upon the government for their livelihood" (p. 103) of the vote. On the other hand, he raises the question of why noncitizens, including nonresident ones, should be prevented from voting, and he ventures that the only reasons for excluding them are selfish ones. He states that the minimum voting age has ranged from 10 (for a tribe in New Guinea) to 25 (in prewar Japan). Although he argues that the voting age has little effect on a voter's total political power over a lifetime, one wonders why he does not try to consider the effect on issues such as the military draft, particularly since an earlier oblique remark seems to refer to his own unpleasant experiences with the draft.
A few scattered comments in the book stand out. The author regard "the Federal Social Security Trust Fund as a fraud and a scandal" (p. 86). He believes it is generally "harder for special interests to get special cartel procedures through referendum than it is to get them through the legislature" (p. 89). He remarks that "in general congressmen know more about what their constituents think about a given bill than about the bill itself" (pp. 89-90). A Florida school board once allowed voters to write in the amount they wanted for an appropriation or a bond issue, he states, with the median preference winning. He reasons that a school board can get a larger amount approved by voters if the alternative is 10% below the status quo than if it is equal to the status quo. He argues that a governor who has a line-item veto will be less effective in reducing expenditures than one who has the broader option (also subject to override) of cutting a fraction of an item. Concerning externalities, the author contends (p. 129) that "the fact that government actions can create externalities, just as well as eliminating them, is almost unknown to many economists," and then goes on to say that recently "a number of citizens in Baghdad ... suddenly discovered that they were suffering from fairly severe externalities from the actions of a democratic government." He calls pre-1968 U.S. ballot barriers against minor parties a "blockade which in essence had been enacted by the two [main] parties as a sort of cartel restriction" (p. 162). He states that corporations once gave one vote per shareholder rather than one vote per share.
The book is unfortunately marred by an enormous number of errors with respect to spelling, capitalization, punctuation, grammar, and, most seriously, omitted words and words that should have been omitted but were not; one wonders where the proofreaders and/or copy editors were. Some small errors on a more substantive level may be noted. The author seems to say that a result of Saari shows that any profile of voter preferences can generate any election outcome, but what Saari actually showed is that there exists a profile that (by the use of different sets of scoring points in a Borda-type system) can generate the fraction (n - 1)/n of the n! possible untied ranked outcomes with n candidates. It is indicated that for a long time, the voting age in the United States was 18 for females and 21 for males, but the 19th Amendment pertained only to sex and the 26th only to age. George McGovern's run for Presidency is placed in 1980, rather than 1972. Quoting poll results that 84% of respondents favored raising the minimum wage but that 78% did not know how much it then was, the author infers that of those who did not know how much the hourly minimum was, at least 62% thought it should be raised; but one can really infer that the figure is at least 79% (that is, 62/78), even higher than 62%. Although he claims (p. 176) to have discussed approval voting "together with strategic methods of cheating on it earlier on in the book," no such discussion exists, and, in fact, approval voting has generally been found to be relatively hard to manipulate (Brams and Fishburn 1983, Chapter 2). In conclusion, I think different readers will find this book useful, provocative, or controversial, or probably a combination of these.
Arrow, Kenneth J. 1969. Tullock and an existence theorem. Public Choice 6:105-11.
Brams, Steven J., and Peter C. Fishburn. 1983. Approval voting. Boston: Birkhauser
Caplin, Andrew, and Barry Nalebuff. 1988. On 64%-majority rule. Econometrica 56:787-814.
Potthoff, Richard F. and Steven J. Brams. 1998. Proportional representation: Broadening the Options. Journal of Theoretical Politics 10: 147-78.
Tullock, Gordon. 1967. Toward a Mathematics of Politics. Ann Arbor, MI: University of Michigan Press.