Thursday, May 05, 2011

What if...

As usual, the lobby groups are crying foul over the election results. These groups favour perpetual minority government by requiring a party to get over 50% of the vote to win a majority government. Under our current system, a party that wins a clear pluarilty can form a majority government. No party has won more than 50% of the vote in Canada since Brian Mulroney in 1984 and then it was just barely.

I was asked on Twitter the other day to take a look at what the election results might have looked like under a different electoral system. I've done this before for provincial elections.

It is impossible to give a perfect picture of what might have been for several reasons. First, is there are nearly an infinite number of possible versions of proportional representation that Canada might choose were it to move in that direction. Second, voters might not cast their ballots in the same way if there were a different electoral system presented to them, especially as they would have a ballot specifically for a party seperate from local candidates in almost all iterations.

There are four main types of proportional representation systems that are worth exploring. For reasons of pure logistics, I can only explore three of them.

Mixed Member Proportional

MMP seems to be the most popular model in Canada, in that it has been chosen by electoral reform groups in three provinces (Ontario, New Brunswick and Prince Edward Island) to be put to a referendum. In Ontario and PEI, voters rejected electoral reform, while in New Brunswick a referendum was never held on the proposal.

In an MMP system, there are two tiers of legislators. The first tier continues to be elected from single member districts as they are today. A second tier are selected for multi-member regions (or the jurisdiction as a whole) based on the popular vote for each party (various types of PR can be used to elect this second tier); the second tier legislators are not selected based on the popular votes however, but are used to proportionalize the overall results to bring legislators from both tiers into as close a possible match to the popular vote. For instance, in the 1993 federal election, most of the second tier seats would have gone to the PCs who won 16% of the vote but less than 1% of the seats. An explainer of the Ontario-version of MMP can be found here.

MMP is used to elect the German federal parliament, the New Zealand federal parliament and the devolved assemblies of Wales, Scotland and Northern Ireland in the UK.

For the purposes of my analysis, I will assume that each province gets 25% more members assigned to a province-wide region. This would increase the size of the House of Commons from a 308 member both to a 388 member body. For comparison purposes in the table I present below, I have scaled these results down to a 308 member House of Commons.

Single Transferable Vote

STV is the other proportional representation system given serious consideration in Canada. It has been put to a referendum unsuccessfully in British Comlumbia on two separate occassions. Interestingly, BC voters actually voted in favour of STV in 2005, but the referendum was only to be successful if it received the support of 60% of voters. In a do-over in 2009, support for STV declined from 58% to 39%.

In an STV system, ridings are fused together to larger multi-member districts. Parties may, and ususally do, run as many candidates as there are seats in each district. Voters cast a preferential ballot, ranking all of the candidates of all parties in order. Voters could rank all of the candidates for their prefered party first, or they could mix and match. Candidates are elected when they reach the quota for the riding, which in most cases is 1/(n+1) where n is the number of seats up for election. For instance, in a 7-member riding, candidates would win when they get 1/8th of the vote. When a candidate is elected, his or her second preferences votes are distributed to the other candidates. If no candidate is elected in a given counting round, the candidate with the fewest votes is eliminated and his or her votes are distrbuted to the next preferences. An explainer on BC-STV can be found here.

Ireland and Malta are the only countries to use STV for their national legislative elections, though Australia and India also use it to choose the upper house (i.e. Senate-type body).

Unfortunately, as this system is so radically different than our current system, I cannot think of a proper way to extrapolate the election results onto this system so it will not be included in my analysis.

Party-list proportional representation

This is the purest form of PR; it is a simple matter of people voting for a party, and that party gets the percentage of seats that it got in votes. There are closed-list and open-list models; in the former the party puts forward its list of candidates and if they get 20 seats, the top 20 people on the list get elected. It is this model that was proposed to elect the regional (second tier) MLAs in New Brunswick under the MMP proposal here. The latter gives voters two ballots, where they vote for their party of choice and also to rank the individual candidates (like in STV). Under this model, if a party won 20 seats, the top 20 candidates as ranked by voters would be elected.

Israel is the most well known country to use this system, and it doesn't really make a lot of sense on a national level for a country as diverse as Canada. It could also be applied at the provincial or sub-provincial level. It also usually includes a threshold (commonly 2 or 5%) to screen out "fringe parties."

I will run a provincial and national list PR results using both 2% and 5% thresholds for my analysis.

Additional Member Method

This system is very similar to the MMP system, except that rather than a fixed number of seats permanently enlarging the parliament, as many extra seats as necessary are added to proportionalize the result of the single member constituencies. In some elections, where the results came out proportional anyway, there would be no need to add extra seats. In extreme elections - think BC in 2001, New Brunswick in 1987, etc, many extra seats would need to be added to proportionalize the results.

I ran an analysis of the potential impacts of AMM if the extra seats were added at a provincial or national basis. As adding the seats at a provincial basis can distort the provinces' relative share of seats in parliament, I doubt this system would work in Canada. Therefore, I'll only show the national model below. As with MMP, I've scaled the results to a 308 member House of Commons for comparison purposes.


Additionally, I was asked to examine the possible impact of the "alternate vote." This system, also known as preferntial voting or instant runoff voting, has been used in Australia since 1918 and is the subject of a referendum today in the UK. AV is not a proportional representation system, it is an evolution of our current first-past-the-post system. In AV, people rank the candidates in their single member constituencies rather than simply marking an X for their prefered candidate. Candidates aren't elected until they get 50% + 1 of the vote, ending vote spliting. The UK electoral commission has a video to explain the difference between FPTP and AV.

Using the best data I could find on voters' second choices (which turned out to be this Leger poll), I ran the ridings through until we got majority winners in each riding. There are a number of huge caveats with this - particularly that there are no second perferences for people voting for minor parties and independents, causing all of those votes to become spolied when their first choice dropped out of the balloting. Another big problem is that I couldn't seperate Quebec's second choices from the rest of Canada, meaning second preference choices of and for the BQ are a bit distorted.

However, this should give us a rough picture of how the result would have been with AV and whether or not vote splitting was responsible for the election of a Conservative majority.


Anyway, without further ado, here are the results of the various electoral systems according to my analysis.

Seat comparison

New Democrats1021019599959888123

Proportionality comparison (share of votes vs. share of seats)

 Seat Share
New Democrats30.733.132.830.832.130.831.828.639.9

For all of the data, and most of the calculations used, click here. Some of the calculations were done manually so they are entered directly, while most are the result of spreadsheet-driven calculations.

I'm curious to hear your reactions.


JP said...

It looks like your rescaled the MMP and AMM numbers to add up to 308 seats. I found that a little confusing until I looked at the spreadsheet.

Also, the MMP used for the German Bundestag is a split 299 FPP local seats, and 299+ NPR5 seats (with 323 right now). So just adding 25% extra seats seems pretty conservative to me (and from the chart, not quite large enough to accurately capture the national proportions).

nbpolitico said...

To answer your points, I did scale the MMP and AMM down to 308 to make the table make more sense - and that is explained in the post.

I think you're confusing what I've defined as MMP and AMM. AMM is a form of MMP.

However, the MMP models proposed in Canada have all been of the form of having a fixed number of seats needed or not. These have been in the range of about 25% in the proposals from Ontario, PEI and NB. Thus, this is what I've done for MMP.

The AMM method used in my example could be much higher than 25% if necessary to proportionalize the results, however in this case only about 1/6th extra seats was necessary to do so.

nbpolitico said...

Correction: I see that 25% may have been conservative; the Ontario model suggested 30% non-local seats, while New Brunswick suggested 36% and PEI 37%. However, it still give a good picture.

JP said...

Sorry if I came off as critical, this is a very nice write up and I quite liked it.

Sadly, the recent failure of the UK and less recent failure of Ontario to pass alternative voting schemes makes me pretty pessimistic about ever seeing something other than FPP in Canadian national elections.

nbpolitico said...

My argument has always been that Canada and Britain's democracies were built through evolution rather than revolution and therefore our voting system should evolve the same way.

Under different circumstances, I believe that AV might have passed in the UK. As for Canada, I would suggest a party adopt it as their policy and then implement it when they form government as a natural next step from FPTP. Riding boundaries wouldn't have to change and the layout and number of ballots wouldn't have to change. This approach worked in Australia way back in 1918 and would work here today.

The Pundits' Guide said...

Does the answer to second-choice questions in opinion research parallel actual observed second-choice behaviour in Canadian elections (as found in the Canadian Election Study, for example)?

That assumption could change things a bit.

I guess when you tweeted about "vote-splits" costing Party X a certain number of seats, you were referring to the Alternative Vote scenario?

nbpolitico said...

Pundits Guide - it is indeed impossible to know with absolute certainty how whether people would have voted their first ballot the same way under a different voting system. And there are some weaknesses in my analysis especially in terms of Quebec.

But it is clear that vote splitting, for the most part, hurt the NDP and helped the CPC while having little effect on other parties.

This would be fairly intuitive without an analysis. It is (almost) always the first party that benefits most and second party that suffers most in FPTP.

The Pundits' Guide said...

I agree with your points, but was trying to make a slightly different one in the first case.

You say you used second-choice data from opinion polls to do the AV estimates.

But I've noticed before that actual vote-switching behaviour doesn't always follow those reported second-choice patterns from opinion polls:

A Second Look at Second Choices

I wondered if you had better data on that point.

nbpolitico said...

Indeed, the data is rather wanting. If our media outlets were less cheap/uncooperative we might have exit polls that would provide good data.