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Who Will Win this Election?

By       Message Paul Cohen     Permalink
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Waiting to vote
Waiting to vote
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In earlier articles of this series, quite a few different voting systems of voting have been described and considered. But the series has developed over more than two years and readers may well have forgotten or never even read some of those earlier articles so it seems worth offering a review -- and that is our purpose in this article. Here we will first describe the circumstances of a hypothetical election and then go through each of the electoral systems in turn to see how that election might might turn out under that system.

The election we will consider is between three candidates. The voters are strongly focused on a single issue and it does not matter much what that issue is. Two of the candidates, Isfor and Isagien, represent the two different sides of that issue and the voters split pretty evenly between them. Nearly every voter prefers either Isfor or Isagien but opposes the other of those two. The third candidate, Benute has managed to remain neutral on the issue of the day, saying that it is best to wait to see how matters evolve and make a decision in the future. Both Isfor and Isagien ridicule Benute for just kicking the can down the road, but Benute seems seems well liked by nearly all voters and is the second choice for essentially all of the voters.

You are encouraged now give some thought about which of the three candidates you think should win the election - not on the basis of any choice of electoral system but on the basis of having a good democracy.

If the election were held using plurality voting, most voters would probably realize that Benute really has no chance and so they would vote for either Isfor or Isagien. One or the other would win by a slim margin and no doubt half of the voters would feel cheated and unhappy about the outcome.

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On the other hand, if the election were held using balanced plurality voting, (where a voter can choose to vote for or against one candidate) then some fraction of the voters would likely choose to vote against whichever of Isfor or Isagien they oppose and only a negligible handful of voters would choose to mention Benute on their ballot. Voters would feel forced to make a decision, for example to vote against Isfor rather than for Isagien. The decision would seem to depend on whether it was more important to the voter that Isagien win or that Isfor not win election, but there is another way to think of that decision. Voters would mostly be aware that the choice would not make any difference in the contest between Isfor and Isagien but rather, the choice would only make a difference to Benute's competitiveness in the election. Votes against either candidate would help Benute remain competitive. If at least half of the voters on each side were more concerned about, from their viewpoint, the wrong candidate being elected then both Isfor and Isagien would have a negative vote-count so Benute would win with a vote-count of (essentially) zero. That is one possible outcome, but with balanced plurality voting it would be quite possible for any of the three candidates to win.

With approval voting, there is no such ambiguity. Recall that this is the system where a voter is asked to indicate approval of each candidate the voter chooses. In this particular election, roughly half of the voters would show approval for each of Isfor and Isagien while essentially all voters would indicate approval for Benute. This would make Benute the winner.

With balanced approval voting, (where the voter is asked to indicate approval or disapproval -- or neither - for each of the candidates) the outcome is much the same as with approval voting. It is likely that half of the voters would cast a vote for Isfor and Benute and against Isagien, while the other half would cast a vote for Isagien and Benute but against Isfor. The election would clearly go to Benute with 100% approval while Isagien and Isfor would each net only 0% approval.

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In this election there are few enough candidates that there would would really be little motivation for using balanced ration voting, but for the sake of providing an example we can consider it nonetheless. Each voter would be handed three (it could be more or less than that, but three seems reasonable with just three candidates) balanced plurality ballots.

A smart way for an voter who prefers Isagien would be to cast one ballot for Isagien and two ballots against Isfor; after all, the most important priority of such a voter is that Isfor not to win but to give Isagien an advantage. Then again, casting two ballots for Isagien and one against Isfor is also a smart approach for such a voter but it gives Isagien even more of an advantage.

If all voters cast one ballot in favor of Isfor or Isagain two against the other then those two candidates both have negative net scores and Benute would win with a net score of zero. At the other extreme, if all voters cast two ballots for and one against then the result is a tie or near tie between Isfor and Isagain.

But of course there are many possibilities between these so that any of the three candidates could come out the winner. However, it seems likely that the voters would be educated on the consequences of their votes and that they would realize that a vote against the candidate they opposed would help their second-choice candidate, Benute, to remain competitive in the election. It seems likely then that many of the votes would be cast in the negative and that Benute would have a good chance to be the winner.

This article is now getting quite close to the thousand-words that OEN suggests as a maximum length, but we still have IRV and IRBV to consider. The reader is encouraged to give some thought about what might happen given these other systems of voting. I do plan to write a follow-up article addressing these two other systems, however.

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A concerned citizen and former mathematician/engineer now retired and living in rural Maine.

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