A Best Procedure?
With so many procedures, which is best? And, how do we define "best"? It
is especially important, because as we have seen the outcome of an election
depends not only on how the voters vote, but it also depends on which procedure
is used!
Let’s start with an easy task. For two-candidate elections, if
each voter assigns one point to his or her top-ranked candidate and zero points to his or her
bottom-ranked candidate, then one of the candidates will receive a majority
of points, as long as there are an odd number of voters. Such an election
is called majority rule. And, as a procedure, it is ideal – but
only works for elections between two candidates.
A first step in deciding which procedure to use for elections with three or more candidates is to compare how the procedures perform on elections with only two candidates. All the election procedures considered previously (plurality rule, Borda count, single transferable vote/instant runoff, and approval voting) generalize majority rule, as they reduce to majority rule when there are only two candidates and an odd number of voters. Click on this link to see how the aforementioned procedures generalize majority rule, as well as to learn the desirable properties that majority rule satisfies.
Rather than start with the procedure, Kenneth Arrow started backwards. That is, he began by determining a set of properties that any election procedure for three or more candidates should satisfy. Unfortunately, he found that no reasonable election procedure satisfies the seemingly innocuous properties or axioms. His result is known as Arrow’s Impossibility Theorem. And, it is in part why Kenneth Arrow won the Nobel Prize in Economics. To find out more about Arrow’s theorem and its axioms, click on this link.
If there is no best procedure satisfying Arrow’s axioms, then perhaps there are other criteria to use to compare election procedures? Which procedure is easiest to use? Which procedure allows voters to express their true beliefs? Which procedure is less likely to result in voters manipulating their response to influence the outcome? From “impossibility” to possibilities, follow this link for different criteria to compare election procedures.
