I’ve built a simple model that predicts the makeup of the House of Commons given the relative votes of the three major parties. The model assumes that the total number of votes cast does not change, that the votes given to all other parties do not change, and that the proportion that a given party achieves in one constituency compared to another doesn’t change.
We then represent the proportion of votes cast as a position in a triangle. The three corners of the triangle represent all major party votes going to one of the three major parties, with the other two getting zero votes. The middle of the triangle represents the three major parties getting exactly equal votes. The inverted triangle in the middle is the region in which no major party gets more votes than the other two put together, and the subdivisions of this middle triangle shows which one got a plurality of the votes (ie more than either of the other two).
The dots represents the Commons our model predicts given this share of the votes: the colour shows which party has a plurality of seats, while a hollow circle indicates a hung parliament and a circle with a white dot shows a 3/5ths supermajority.
So, for example, the middle of the diagram where the three lines meet is under a red hollow circle; this means the model predicts that if all three major parties were to receive an exactly equal share of the votes, the result would be a hung parliament with Labour holding more seats than either of the other two. To be precise, it predicts Labour holding 310 seats, Conservatives with 193 seats, and the Lib Dems having 111.
I’ve marked on there the 2005 elections themselves, which is the only point on the diagram known to be accurate, and what a couple of recent polls would predict according to this model.
You may think that a voting system in which an exactly equal share of the vote for all three parties delivers something very close to an absolute majority to one of them is barking. You may very well think that. I couldn’t possibly comment.