Vote splitting

There was much talk during the election about vote splitting. Specifically how vote splitting on the left would allow the Tories to take a majority due to a Liberal/NDP vote split. I will look at how much of an effect this splitting had on the results. What seems to be the case is that vote splitting had very little effect on the actual outcome of the election.

That a vote split would have little effect on the past election seems counter-intuitive. The argument goes something like this: The vote on the left is split Liberal/NDP/Green. If all those voters pooled their votes, then the Conservatives would not be government. In fact, during the election there were several web sites devoted to this very premise. I wrote a program to combine the left wing vote. Basically the program took the progressive votes from the third and fourth place finishers and gave them to the highest ranked progressive candidate. If the third or fourth place finisher was a Tory, I gave the votes to the Liberals. So what was the result? The following table shows the actual election night results and what would have happened under the assumptions of this vote de-splitting scheme:

Party	Election Result	De-Split Result
Conservative	143	92
Liberal	76	145
NDP	37	39
Bloc	50	30
Green	0	0
Independent	2	2

As can be seen, we'd be in a Liberal minority situation. Here's the regional breakdown:

Atlantic

Party	Election Result	De-Split Result
Conservative	11	5
Liberal	17	22
NDP	4	5
Bloc	0	0
Green	0	0
Independent	1	1

Quebec

Party	Election Result	De-Split Result
Conservative	10	9
Liberal	13	34
NDP	1	1
Bloc	50	30
Green	0	0
Independent	1	1

Ontario

Party	Election Result	De-Split Result
Conservative	51	22
Liberal	38	72
NDP	17	12
Bloc	0	0
Green	0	0
Independent	0	0

West

Party	Election Result	De-Split Result
Conservative	71	58
Liberal	7	15
NDP	14	19
Bloc	0	0
Green	0	0
Independent	0	0

North

Party	Election Result	De-Split Result
Conservative	1	0
Liberal	1	2
NDP	1	1
Bloc	0	0
Green	0	0
Independent	0	0

So if we use the simplistic view that the left wing is a voting monolith, the Liberals should be very pissed off as they missed their chance to form a minority government. This is the state that the strategic voting sites attempted to get.

There is a problem with the simplistic approach above however. People's second choice voting preference aren't necessarily with the next party over on the spectrum. For example, all NDP voters in a riding won't necessarily vote Liberal as a second choice. This is evident from a Nanos Poll of voter second choices. This would imply that the simple moving of say, all the NDP vote to the Liberals, is an inaccurate reflection of what would actually happen.

Re-coding the program to take this into account, i.e. taking the fourth choice candidate and redistributing the votes based on that party's voters' second choice preferences gives us a different looking scenario. The national and regional tables:

National

Party	Election Result	De-Split Result
Conservative	143	134
Liberal	76	90
NDP	37	38
Bloc	50	44
Green	0	0
Independent	2	2

Atlantic

Party	Election Result	De-Split Result
Conservative	11	8
Liberal	17	20
NDP	4	4
Bloc	0	0
Green	0	0
Independent	1	1

Quebec

Party	Election Result	De-Split Result
Conservative	10	10
Liberal	13	18
NDP	1	2
Bloc	50	44
Green	0	0
Independent	1	1

Ontario

Party	Election Result	De-Split Result
Conservative	51	46
Liberal	38	43
NDP	17	17
Bloc	0	0
Green	0	0
Independent	0	0

West

Party	Election Result	De-Split Result
Conservative	71	71
Liberal	7	7
NDP	14	14
Bloc	0	0
Green	0	0
Independent	0	0

North

Party	Election Result	De-Split Result
Conservative	1	0
Liberal	1	2
NDP	1	1
Bloc	0	0
Green	0	0
Independent	0	0

So it can see that vote splitting likely had little actual effect on the outcome of the election. Apart from a few seats making the close Ontario race even closer, we would still end up with about the same situation in the House of Commons as we have now. This would also imply that vote splitting isn't nearly the problem as it appears to be, with only a handful of seats being affected. Had the election been closer, it may have been a factor, but in this election it would appear that it wasn't a factor at all.

This will come as unwelcome news to the Liberals, who no doubt will blame much of their loss on vote splitting on the left, as would be suggested by the simplistic approach to de-splitting the vote. The actual complexity of voter intent prevents that from being an accurate model to predict seat counts of de-split votes. A model that takes into account voter second choices will more likely reflect what would actually happen if parties on the left were to strategically withdraw candidates across the country to improve chances of electoral success. From the data for the last election, using the Nanos poll, it would seem that there is not much of a change in result at all.