CBC Vote Compass and Election Predictions

I’ll come back to the gold standard when I have the time, it ended up being a rather big topic.  I didn’t want March to roll by without a post so instead let us talk about the Canadian Election.

First, here is something you may not have heard of before.  It is something from basic game theory called Hotelling’s Law.  I will not be discussing the validity of the term “law” in this post. I will however give a brief overview of this law when applied to political parties.  In the original game there are two political parties. A and B. We depict the political spectrum as a line that goes from left wing to right wing, pretty standard stuff. In this game voters are evenly distributed across the spectrum and they vote for the party who’s platform is closest to them on the political spectrum.  I will give three examples to clarify.

You be learnin game theory

Ignoring my terrible paint image accuracy we see in the first game that both candidates position themselves exactly in the middle of the spectrum and each player gets 50% of the vote.  This is actually the final equilibrium point and I likely should have drawn it last but I didn’t.  The second game is where each party positions themselves at the extremes of the spectrum.  In this case. both parties still get 50% of the vote but it is NOT in an equilibrium state.  You see, either party can move one step towards the other player and instantly capture more than 50% of the vote and win.  In the third game I don’t know the exact payoff but each player gets all of the votes on the outside of their position and split the votes in between their two positions evenly. For the same reason as game two this is not an equilibrium,  So the point of this is to see that with two parties the only smart move is to move as close to the centre as possible.

Now I understand that there are some major flaws in this idea, mostly to do with the even distribution of voters on a political spectrum and that voters will always vote for the party that is closest to them but it still interesting to work through.

Now lets see how we can use this little bit of game theory and apply it to the current political situation in Canada.  We are in an election and to help everyone make the decision of who they should vote for the CBC has come up with… THE VOTE COMPASS.  It’s so easy!  You answer a few questions and the website tells you which party you are going to vote for.  Just like that, no need to waste your time keeping up to speed on current events.  Here is an example of a vote compass result.

Don’t get too excited, that is not my result, it is just the first hit on Google image search when I searched vote compass.  The positioning of the parties on this grid was determined by “a team of Canadian political scientists, including an advisory panel comprised of the country’s most prominent scholars in the study of electoral politics”(from the FAQ). So you know it is accurate.  I thought to myself I wonder what Hotelling (from 1929) could tell us about this grid. The most obvious answer when you look at the party distribution is that the left is a fragmented mess that shares votes and has no real hope of beating the right unless they ditch some of the parties BUT that would be too trivial an observation for this site and its readers, wouldn’t it?  Instead I will try something totally, legitimately, 100% scientifically proven, really valid.

Yes that is right. I drew a line from one corner of the grid to the other. I then placed a marker on the line in the location for each of the parties. You can see the extreme accuracy of my lines in the picture.  The length of the line is 567 pixels in total and from now on all lengths are in pixels.  The distance between the Conservatives and the far right is 85. The distance between the Conservatives and the Liberals is 259. The distance between the Liberals and the Bloc Quebecois is 94. Everything to the left of the Bloc is 134.  I will get into that area in a bit.

I’ll spare you the math here. Remember that two parties split the distance between them 50/50.  Here are the total number of pixels “voting” for each party.
Conservative: 214 or 37.74%
Liberals: 172 or 29.86%
Bloc, NPD, Green: 181  or 31.92%

Totalling 99.52% which means my crappy MS Paint skills are not 100% accurate surprisingly.  So the issue here is that the Bloc does not run candidates in all the provinces so the uniformity of the voters should go right out the window. Strange thing is that the Bloc is 17 pixels away from the NDP which gives them a total of around 55 total pixels or 9% of the vote.  This leaves 23% for the NDP and Green to fight over.

So there you have it, based on the compass provided by all the latest experts and a very loose interpretation of Hotelling’s Law you have the official Webernet.ca prediction for the election outcome.

This is where it gets a little surprising.  Take a look at these polls. http://www.sfu.ca/~aheard/elections/polls.html

In case the results change and lose the surprise factor of my outcome, here is a small screenshot.


Some of you might say that I rigged the image or something but to be honest, that would take so much more effort that just doing these calculations.

So it appears the only way the Liberals are going to win this election is to move more to the right.  Or of course form some sort of coalit…  nah that is another post entirely.

Hope you enjoyed this one, I did.