On the other hand, the American Constitution stipulates that, absent a majority of the electoral votes, the House of Representatives should determine the winner. With a Republican majority in 2000, the House would presumably have gone for Bush. Clearly, having U.S. voters name solely their favorite candidate does not result in an outcome that is obviously right. As in the French election, such ambiguity can be resolved by having voters submit complete rankings. Even though Gore is the favorite of only 49 percent of the electorate, the rankings show that a clear majority of 51 percent—the Gore and Nader voters combined—prefer Gore to either Bush or Buchanan. So Gore is the winner according to an electoral system called true majority rule (or simple majority rule), in which voters submit rankings of all the candidates and the winner is the one who beats each opponent in head-to-head competition based on these rankings.
Rankings can also be used in other electoral systems. Consider, for instance, “rank-order voting”—a procedure often used to elect committee officers that has been proposed to solve the problems inherent in the American and French presidential electoral systems. If four candidates are running, each voter assigns four points to his or her favorite, three to the next favorite, two to the next, and one to the least favorite. The winner is the candidate with the biggest total. The method appears to have been invented by Jean-Charles Borda, an 18th-century French engineer, and is sometimes known as the Borda count. Imagine that 100 million people vote in the U.S. election. Based on our earlier assumptions, we know that 49 million of them will rank Gore first. So Gore will receive 196 million points—that is, 49 million times four points—from the Gore voters. The Nader voters place him second, so he picks up six million points from them. Finally, the Bush and Buchanan voters place him third, for an additional 98 million points. His grand total is 300 million points. If we make the corresponding computations for the others, we find that Nader gets 155 million points and Buchanan 199 million. Strikingly, Bush gets 346 million, even though a majority of the electorate prefer Gore. Only 2 percent of the electorate ranks Bush lower than second place, which is good enough to elect him under rank-order voting.
Thus, true majority rule and rank-order voting result in dramatically different outcomes. Considering this sharp contrast, it may seem hard to say which method is better at capturing the essence of voters’ views. But we propose to do just that. We can evaluate these two systems—and any other—according to some fundamental principles that any electoral method should satisfy. Kenneth J. Arrow of Stanford University originated this axiomatic approach to voting theory in a 1951 monograph, a work that has profoundly shaped the voting literature.
Most voting analysts would agree that any good electoral method ought to satisfy several axioms. One is the consensus principle, often called the Pareto principle after Italian sociologist Vilfredo Pareto. It states that if everyone agrees that candidate A is better than B, then B will not be elected. This axiom does not help discriminate between true majority rule and rank-order voting, however, because both methods satisfy it— that is, both will end up with B losing. Moreover, the principle does not apply very often: in our U.S. election example, there is no unanimous preference for any one candidate over another.
Another important axiom holds that all voters should count equally—the “one-person, one-vote,” or equal-treatment, principle. Voting theorists call it the principle of anonymity: who you are should not determine your influence on the election. True majority rule and rank-order voting also both satisfy anonymity.