In many of the articles in this series have presented arguments to explain why one voting system should be preferred over another or sometimes why one system is particularly faulty. The faults of plurality voting are quite widely understood, so plurality voting is particularly vulnerable to such criticism. But those faults are not so apparent when an election is between only two candidates. I even have claimed that it would not be possible to improve on plurality voting for elections with only two candidates. But through examples, we will see here how that is not true.
Let us construct five similar stories, each about an election in a city with 156,000 registered voters, but each election using a different voting system. This city's elections have always used plurality voting and typically about 100,000 voters take part in these elections.
The city incorporates a geographic area that includes portions of several different counties. In this special election, there are only two candidates (having initials RP and DM) and the only issue on the ballot is to determine which will become the next mayor.
City voters invariably have strong opinions about RP; nearly everyone in the city feels they know everything they want or need to know about him; no one is on the fence about him. He is strongly favored by 45,000 voters but just as strongly opposed by all the other voters. DM, the other candidate, is very popular, but only in the county where she lives. In the remainder of the city voters do not know much about her. In the city there are 35,000 voters, mostly from her home county, who particularly favor her election. All the same, she has little or no actual opposition from voters.
Before reading on, I urge you to spend a moment considering which candidate deserves to win the election.
This first version of our election story, is to consider what would happen if the election were held as such elections always have, using plurality voting. RP has the votes of the 45,000 voters who support him but no others. The voting for DM is less predictable, but certainly DM will get at least 35,000 votes, mostly from her home county; she may also pick up support from, let us say, another 8,000 voters. A portion of these 8,000 voters have recently learned enough about her record to support her on that basis, but it seems likely that more of the 8,000 votes are from voters who still know little about DM but who feel that just about anyone else would surely be better choice than RP. But a bit of arithmetic makes it clear that RP wins the election with 45,000 votes against the 43,000 votes for DM.
The media characterizes the 68,000 registered voters who failed to vote as apathetic and probably uninformed citizens who simply did not care who would win; no doubt that shoe will fit some of them. But among those missing voters, there may be a few who did take the trouble to visit the polling station but submitted a blank ballot. And a great many other missing voters no doubt suffer from what we might call an excess of honesty; for these voters, voting for someone they know little about seems too much like a lie; and these voters are obsessive about being truthful, at least in this context. Having discussed their reasons with friends, they may have also influenced others not to vote.
Can we blame plurality voting for all the low-voter-turnout elections? There surely are other factors that come into play, but plurality voting would seem to share a significant portion of the blame.
The second ending of this story involves another popular voting system is called Approval Voting. It differs from plurality voting in that it removes the limitation of voting for just one candidate; it allows a voter to cast a vote in favor of any number of candidates. This could be significant in an election with more candidates, but in this case, with only two candidates, there seems to be nothing to be gained; it merely allows a voter to vote for both candidates; whatever the psychological effect, the effect on the election outcome is identical to voting for neither. Still, perhaps a few voters might do this instead of not voting at all. The election outcome is the same as in the plurality example, however.
Ranked-choice voting (a.k.a. Instant Runoff Voting) has been aggressively promoted and it has been adopted here and there. Rather than being asked whether they support one candidate or another, voters are asked to rank the candidates in order of preference. With many candidates, constructing this list could become a challenge for voters, but with merely two is quite easy, at least for voters who do favor one of the candidates. Each voter's list must be shorter than the number of candidates so with only two candidates, these voter lists can rank only a single candidate. So, in an election with only two candidates, the outcome will be no different than for a plurality election. As with the two previous examples, RP wins with 45,000 votes against the 43,000 votes for DM.
BPV (balanced plurality voting) is much like plurality voting but it asks a voter to specify either support or opposition to the single candidate that the voter chooses. For the vote tally, the number of opposition votes for a candidate is subtracted from the number of support votes for that candidate to obtain that candidate's net vote. In a two-candidate election, a vote of support for one candidate has the same effect on the election outcome as if that were a vote of opposition for the other candidate. From that point of view, the outcome for a BPV election should be identical with the outcome of a plurality election. However, remember that in the plurality election there are those excessively honest voters who chose to stay home or to turn in a blank ballot rather than to fib about whom they support. No doubt in this mayoral election there were another 3,000 voters than voted in the plurality election.
100 voters who had voted for RP in the plurality election instead vote in opposition to DM; no doubt that them feel more honest but there is no effect on the election outcome. More important is that the 3,000 new voters joined forces with 8,000 of the voters who had voted for RP in the plurality election, to provide RP with 11,000 votes of opposition. The result is a win by DM, a different outcome than we have seen previously. The opportunity that BPV introduces to cast an opposition vote is what made the outcome different.
But the outcome was very close, with only a 1,000-net-vote margin. A little vote suppression such as long lines at the polling stations or a couple bad traffic jams in just one county could have made the outcome match the common outcome of the plurality, ranked choice or approval elections.
For the final version of our election story, we consider what would happen in the case of a BAV election. With BAV, voters can specify, for each candidate, either no preference at all, support or opposition. As with BPV, the vote tally for each candidate is obtained by subtracting the count of opposition votes from the number of support votes. In the example election, the vote tally for RP will be negative (making a clear statement that DP has more opposition than support). While RP tallies 44,900 - 48,000 = -3,100 net votes, the tally for DM would be 34,650 = 35000-350 net votes. DM wins this election, but this time using BAV, in a landslide. As a bonus, voters feel they were able to express adequately what outcome they want.
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