A friend writes to me with a very interesting question:

For the municipal election in our ward we are allowed to vote for two of the candidates, our first choice then our second. A friend of our family, who is an old political hand, pointed out that we should vote only for our first choice candidate and ignore a second choice. This is apparently called ‘plunketing’ and gives our chosen candidate a better chance of winning.

I’ve never heard the term before. I did a search on Google and came up with nothing. Is “Plunketing” the correct term? Has anybody else heard of this phenomenon?

It’s important to note that, in my friend’s ward, and in most municipal elections in Canada where it is possible to vote for more than one candidate, your votes aren’t ranked. Your first X for Mr. X counts the same as your second X for Mr. Y. So, what if you choose not to put a second X next to Y, what happens? Let’s look at this mathematically.

Let us assume that there are three choices: Mr. X, Ms. Y and Ms. Z, and let us assume that there are 300 votes up for grabs. Everybody gets two votes. Let us assume that Mr. X has the support of 40% of the population, Ms. Y has the support of 35% of the population and Ms. Z has the support of 25% of the population. Under a single vote situation, X would win, but with two votes, you have to consider what the second choice is. Let us assume that the voters for each candidate favour Y and Z equally as their second choice.

The vote breaks down as follows:

Mr. X 120 votes choice 1
Ms. Y 105 votes choice 1
Ms. Z 75 votes choice 1

Mr. X gets 52 votes choice 2 from Y supporters and 38 votes choice 2 from Z supporters = 90 additional votes

Ms. Y gets 60 votes choice 2 from X supporters and 37 votes choice 2 from Z supporters = 97 additional votes

Ms. Z gets 60 votes choice 2 from X supporters and 53 votes choice 2 from Y supporters = 113 additional votes

Final tally:

Mr. X: 210 votes
Ms. Y: 202 votes
Ms. Z: 188 votes

A much closer contest than public opinion poles would suggest, but roughly corresponding to public opinion.

However, let us assume that Ms. Y and Ms. Z hates Mr. X’s guts, so that 75% of their voters favour each other rather than Mr. X. Let us assume that X voters are split evenly between Y and Z. The tally shifts as follows:

Mr. X - 120X + 26Y + 18Z = 164 votes
Ms. Y - 60X + 105Y + 57Z = 222 votes
Ms. Z - 60X + 75Z + 79Y = 214 votes

Ms. Y and Ms. Z would be the winners even though more voters preferred Mr. X. Now it could be argued that this is still an accurate reflection of the voters’ intent. Ms. Y and Ms. Z may not have been the first choice for most voters, but they were the overwhelming second choice, and thus have the (grudging) support of most of the electorate. However, if X supporters decide to Plunket en masse, the results change as follows:

Mr. X - 120X + 26Y + 18Z = 164 votes
Ms. Y - 105Y + 57Z = 162 votes
Ms. Z - 75Z + 79Y = 154 votes

Mr. X squeaks past Ms. Y for the victory. Ms. Z is shut out. If Ms. Z plunkets:

Mr. X - 120X + 26Y = 146 votes
Ms. Y - 105Y = 105 votes
Ms. Z - 75Z + 79Y = 154 votes

Ms. Z takes the most votes and wins, followed by Mr. X. And if Y plunkets:

Mr. X - 120X = 120 votes
Ms. Y - 105Y = 105 votes
Ms. Z - 75Z = 75 votes

We’re right back where we started. Except that our heads have started to spin.

Ranked voting offers a way around this, but it doesn’t eliminate the problems created by massive strategic voting. However, I think these problems have been somewhat exaggerated. What I think anybody confronted with the prospect of Plunketing should do is this: it’s your vote, use it as you see fit. If you have the option to choose two candidates out of a field, decide which ones deserve your vote. If only one candidate deserves your vote, then vote only for him. If more than two candidates deserve your vote, then decide which two deserves it the most.

The ballot is meant to be a reflection of how you want to mark your ballot, and not how you want the election results to go. That’s a related, but entirely separate issue. Vote with your heart instead of your mind — if only to keep your head from spinning. :-)

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