Saturday, March 3, 2012


Voting is important.

When your country/province/city/university/bridge club holds an election, they are asking for you to determine who is going to be representing you for the next term. The Governors at the Board are going to be told that the two undergraduates that the U of A student body sends to them were elected from the masses to represent the masses, and so it's important that you vote for the two that best reflect your opinions.

However, in the Students' Union, we don't use a first past the post system. Instead of saying, "I like candidate A!", you get the option of deciding your second favourite, third favourite, and so on. At some point, you can even rank None of the Above as if they were a candidate! The options are limitless!

The long-lasting problem with systems like this, though, is that most people simply will not understand how their vote is counted. It's a fact that all voting systems can be played strategically, and really die-hard supporters will want to know the ins and outs of how best to vote in order to guarantee their candidate's success.

Unfortunately, to most people the process works something like this:
It doesn't.

I'm going to talk about four different methods of determining the winner of elections. This post is about to get super fun! Before I do that, though, I want to quickly mention a few of my favorite electoral system criteria that "expert political scientists" have come up with:

Absolute Winner: May seem obvious, but if one candidate gets more than 50% of the votes on the first round, they should win.

Independence of Clones: The election outcome should remain following the addition of an identical candidate with an equal chance of winning.

Condorcet Winner: If a candidate wins a head-to-head competition against every other candidate, that candidate must win the election.

First Past the Post

This one is pretty easy:

Everyone votes.

The person with the most votes wins.

Pros: Dead easy.

Cons: It kinda sucks in terms of figuring out the best candidate. If five people run, you could expect a candidate to win with only slightly more than 20% of the popular vote. Also, it only examines the first choices of voters.

As a voting system, it only satisfies the absolute winner criteria. It fails the independence of clones criteria as vote splitting is a very common issue amongst similar candidates, and it fails the Condorcet criteria because it doesn't even consider the subsequent choices of voters.

Borda Count

Second easiest:

Everyone votes.

Each candidate gets a number of points for each first place vote, a smaller number of points for each second place vote, an even smaller number of points for each third place vote, etc. The candidate with the most votes wins!

Pros: Still pretty easy. It also takes into account the subsequent ranking of candidates by voters, and tends to give a winner that most people are generally ok with (as opposed to FPTP where a majority is likely to have never voted for a winner).

Cons: Fails pretty much every other test in the book. You could have 50.1% of first place votes and still lose if another candidate has a VERY strong second place showing.

Instant Runoff Voting

A little bit more complicated:

20% of students vote (sad fact).

All first-ranked votes are examined. If someone has more than 50%, they win! If they don't, the last-ranked candidate gets kicked off the island, and their second-ranked votes are redistributed to the remaining candidates. This process continues until, at the end of the day, someone finally has more than 50% of the votes (often through borrowed votes from other people).

Pros: Vote-splitting doesn't happen in this method: if one candidate pushing for a waterslide in Quad is expected to get 60%, and another candidate comes forward with the same promise, we're still going to get a waterslide in Quad. This assumes, of course, that people would rank both candidates numbers 1 and 2 on their ballot if they really want that slide. By the time that a winner has been determined, more than half the voters will have indicated in some way that they support that candidate more than anyone else who's left, so a majority will be (begrudgingly, at least) satisfied with the results.

Cons: It can be complicated. If you didn't understand the SU's system before reading this post, you weren't alone. If you don't understand it after reading this post, please tell me and I'll try to make it clearer.

This method satisfies all the above criteria apart form the...

Condorcet Method

Way more complicated:

Everyone votes.

For every possible pair of candidates (that's 10 if there are five candidates in a race), the candidate who is ranked higher more often is declared the winner in that head-to-head contest. If one candidate wins against all the other candidates, then they win the election. If there's a tie in the number of victorious head-to-head contests, then a complicated method based on vote differentials is used to determine the winner.

Pros: It's awesome. It's actually by a mile the coolest way to count votes.

Cons: It takes a while to explain to people, and for large races it basically can't be done by hand.

Now you know! The SU uses an Instant Runoff Voting system for its executive, and a variant iterative IRV system for its council elections. What's especially fun about electoral systems, though, is that different systems often change the results of an election. Take a look at this example:

42 Voters: A, B, C, D
26 Voters: B, C, D, A
15 Voters: C, D, B, A
17 Voters: D, C, B, A
Total voters: 100

What's really fun (and I'll let you do the math) is that the winner of this election depends on the method. First past the post simply says that A should win. A Borda Count or the Condorcet Method would let B win, and an Instant-Runoff Vote would elect candidate D. Go figure, right?

At the end of the day, what I'm trying to say is that the order in which you rank your candidates in this election really does matter.

Stay tuned for an analysis of the election results after they're revealed!

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