A third criterion, however, does differentiate between the two. Neutrality, as this axiom is called, has two components. The first is symmetry, which means that the electoral rules should not favor one candidate over the other. The second requires that the voters’ choice between candidates A and B should not depend on their views about some third candidate C. What would happen in our U.S. example if the Bush voters’ ranking shifted to become Bush, Gore, Buchanan, Nader (instead of Bush, Buchanan, Gore, Nader)? From the standpoint of true majority rule, nothing important would change: the majority still prefer Gore to Bush. But look at what happens under rankorder voting: Gore now receives 348 million points, while Bush’s total remains 346 million. Gore now wins instead of Bush.
Obviously, rank-order voting can violate neutrality. Voters’ preferences between Gore and Buchanan, a candidate who stands no chance of getting elected, determine the choice between Bush and Gore—and the outcome of the election. In contrast, true majority rule always satisfies neutrality. This last assertion may puzzle those readers who recall that in the actual election, discussion abounded about whether votes for Nader would affect the race between Bush and Gore. Indeed, in retrospect it appears that Nader—perhaps with help from the infamous butterfly ballot in Florida and even from Buchanan—may have siphoned off enough Gore votes to tip the election to Bush. But this effect was possible only because the U.S. election system is not actually true majority rule but its own unique system.
Majority Rule and the French Election
LET’S LOOK AT WHAT would happen to the French election of 2002 under true majority rule—which, for simplicity’s sake, we will henceforth refer to as majority rule. Imagine Chirac, Jospin and Le Pen are the only candidates, and the electorate divides into three groups. Everyone in the first group, 30 percent of voters, has the ranking Jospin, Chirac, Le Pen. In the second group, 36 percent of the electorate, the ranking is Chirac, Jospin, Le Pen. In the remaining 34 percent, voters rank Le Pen over Jospin over Chirac. Chirac and Le Pen—with 36 and 34 percent of the vote, respectively—would move forward into a runoff, where Chirac would easily prevail because 66 percent of voters prefer him to Le Pen.
The same outcome would result under yet another system, called instant-runoff voting (IRV), which is practiced in Ireland and Australia and which, like rank-order voting, has been advocated as an alternative to the French and U.S. systems. In IRV, simply put, rankings are used by election officials to successively eliminate the lowest-ranking candidates (and to incorporate their percentages into the voters’ next-ranked choices) until only two candidates remain.
But the French and IRV systems conflict with majority rule. If you examine the configuration of voters’ rankings, you see that Jospin actually commands an enormous majority: 64 percent of the electorate prefer him to Chirac, and 66 percent prefer him to Le Pen. Majority rule dictates that Jospin should win by a landslide.
Recall that under majority rule a voter can make a political statement without harming the chances of any electable candidate. Someone who preferred Jospin to Chirac and knew that Le Pen had no chance of winning but wished to rank him first as a gesture of protest could do so without fear of knocking Jospin out of the race. (Except, of course, in the highly unlikely event that a majority of other voters made the same gesture.) The analogous point can be made about a voter who preferred Gore to Bush but wished to lend symbolic support to Nader. Yet despite these virtues, majority rule has a flaw. It can violate another well-accepted voting principle: transitivity. Transitivity requires that if candidate A is chosen over B, and B is chosen over C, then A should be chosen over C. Now, ignoring Buchanan, pretend that 35 percent of the electorate prefer Gore to Bush to Nader, 33 percent rank Bush above Nader above Gore, and 32 percent go for Nader above Gore above Bush. Sixty- seven percent of voters rank Gore above Bush, 68 percent rank Bush above Nader, and 65 percent rank Nader above Gore. In other words, no matter which candidate is chosen, at least 65 percent of voters prefer somebody else! In this case, majority rule produces no winner.