With voters’ rankings belonging to this two-element class, rank-order voting satisfies its nemesis: the principle of neutrality (because voters’ views on Nader do not affect whether Bush or Gore wins a rank-order election). Yet majority rule also works well here, because it satisfies its nemesis, transitivity. But rank-order voting no longer works well if the situation becomes slightly more complicated. If we add a third ranking— Gore, Nader, Bush—majority rule is still transitive. These three rankings together do not constitute a Condorcet cycle. Rankorder voting, however, no longer satisfies neutrality. Suppose 51 percent rank Bush above Gore above Nader. If the remaining 49 percent rank Gore above Nader above Bush, Gore will win. If the remainder instead have the ranking Gore, Bush, Nader, however, then Bush wins—even though this group of 49 percent has the same ranking of Gore and Bush in either case.
Majority rule still fails to work well sometimes, as the Condorcet paradox shows, though less often than other voting rules do. And in such cases, it has to be modified to identify a winner. There are many ways this can be done. Perhaps the simplest modification is as follows: If no one obtains a majority against all opponents, then among those candidates who defeat the most opponents in head-to-head comparisons, select as winner the one with the highest rank-order score.
Improving Future Elections
THE WAY most countries pick their presidents is faulty. Both the 2000 U.S. and 2002 French presidential elections were appreciably affected—perhaps decisively—by candidates who had no realistic chance of winning. These candidates were able to wield influence because, in each case, only a voter’s top-ranked candidate was counted.
We believe that when more than two choices present themselves, voters should submit a ranking of candidates and that majority rule—as we have discussed it—should determine the winner. Such a method would not be perfect; no method is. But as the majority dominance theorem shows, it would come closer to an accurate representation of the voters’ wishes than any other system does.
This story was originally published with the title "The Fairest Vote of All"