Sunday, May 15, 2011

Districts of Different Sizes: Who Benefits?

It is well-known that the size of electoral districts (whether measured by population, electorate, or votes) varies wildly, not only across provinces, but also within provinces. When we put everything together, which party benefited from these discrepancies in 2011?

One measure of this would be to compare a party's actual voting share to what I'll call its effective voting share, defined as the average of that party's share of votes in each riding.

For example, suppose that a country has two electoral districts, with 40 votes in district A, and 60 votes in the district B. A party gets 50% of the vote in A, and 30% in B. Clearly, that party is favoured because it's doing well in a less populated district. Its actual national vote share is 38% (38 votes out of 100), but because the districts have equal weight, the party's effective voting share is 40% (average of 50% and 30%).

For each of the major parties, below is its effective voting share, with its actual voting share in parentheses:

CON: 39.7% (39.6%)
LIB: 19.3% (18.9%)
NDP: 30.8% (30.6%)
BQ: 5.6% (6.0%)
GRN: 3.7% (3.9%)

CON: 39.9% (39.8%) in 307 ridings with candidates
BQ: 23.2% (23.4%) in Québec
GRN: 3.8% (4.0%) in 304 ridings with candidates

We immediately notice that all three main parties modestly benefit from some votes being more important than others. This may be slightly surprising in the case of the Tories, whose support is concentrated in underrepresented BC, Ontario and Alberta. However, this is more than countered by Conservative support being concentrated in rural ridings, which tend to be less populated, and by Albertans voting less than other Canadians.

The Bloc and the Greens, on the other hand, are hurt. The Bloc is disadvantaged mainly because Québec votes are worth less than the average vote elsewhere due to a larger number of electors per district, while the Greens' support is concentrated in underrepresented BC.

The lesson I take from this exercise is that this distortion is rather minimal: no party's effective voice is changed by more than 0.4% (1 seat if we had a proportional system). So while the variation of district sizes may be unfair to certain constituencies, it does not significantly affect party representation in the Commons.

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