The results of the Quebec provincial election were stunning enough, as we have been discussing in the previous planting. No one saw the strong showing of the ADQ coming. The fall of the ruling PLQ to minority status was expected, but there was quite a late swing away from the PQ. A few days before the election, it looked as if a PQ minority government was possible, but the party wound up in third place.

In this entry, I want to look not at the shifts in voter sentiment, but rather at how the electoral system took those actual votes and turned them into seats. This is a politically relevant question for Quebec given that the province: (1) has never before had an election result in a minority situation, and (2) has had a recent electoral-system review process. The minority government might be seen as a sign of the “failure” of the FPTP system just at a time when there has been discussion of replacing FPTP with some form of PR.

The seat-vote result is striking in being almost proportional:

PLQ, 33.1% votes, 38.4% seats
ADQ, 30.8% votes, 32.8% seats
PQ, 28.3% votes, 28.8% seats

We certainly do not normally expect such close correspondence of votes and seats percentages in FPTP systems.

To get an idea of whether this aspect of the election is a “surprise” or not, I turned to one of my favorite tools, the seat-vote equation (originally devised by Rein Taagepera). If you are unfamiliar with the seat-vote equation, I suggest clicking on those words at the top of this planting and scrolling back in time–especially to the first planting in that orchard block (an estimation of seats in the then-upcoming Canadian federal election). But the short version is that the seat-vote equation allows us to estimate a “normal” seats distribution based on the following inputs (and only these inputs):

The votes shares of the leading parties
The total number of votes cast
The number of seats in the legislature
The number of electoral districts

Naturally, in FPTP systems, those last two are the same quantity.

The s-v equation does not incorporate any information about the geographic distribution of the parties’ supporters, notwithstanding the obvious importance of such distribution to the actual outcome. Parties win seats in FPTP systems solely based on where their votes are–no district-level plurality, no seat–rather than as a function of their jurisdiction-wide votes shares.

So, how did the equation perform in this election? Asking this question is really another way of asking a more politically relevant question: How did the electoral system perform? The latter question assumes that there is some “expected” relationship between jurisdiction-wide party support and their legislative support. Deviations from the s-v equation estimates would suggest that the electoral system is not translating votes into seats in a predictable manner. Again, we should not necessarily expect such a predictable translation when the system is FPTP, because of the dependence of parties on local pluralities rather than on jurisdiction-wide support in order to win seats.

Following are the (rounded) predictions of the seat-vote equation, based on the known values of the input variables indicated above:

PLQ, 51
ADQ, 42
PQ, 32

These hardly differ from the actual result (48, 41, 36). The s-v equation expects the largest party to get a bigger bonus than it actually got and the third party to get slightly more punished than it actually was. But it tells us that, in a jurisdiction with FPTP and the number of seats and voters that Quebec has, an election so close among the top three parties in votes should produce a fairly close correspondence of seats and votes. The predicted advantage ratio for the PLQ was 1.23; its actual ratio was 1.16. Even FPTP with three-way competition can produce moderate deviations from proportionality and Quebec’s 2007 result was one where moderate deviations were both expected and actually materialized.

As for the impact of this outcome on the electoral system review, I am not in a position to predict the political consequences of this outcome on that review, but I would conclude that the outcome has not made the objective case for PR stronger. None of the formal review processes in FPTP jurisdictions in the last four decades stemmed from a minority situation, and Quebec’s result was not even disproportional. The existing electoral system gave Quebec voters pretty much what they voted for.

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Postscript:

Paul Wells and his readers have been having fun figuring out the smallest shifts of votes that could have produced a very different seats result–a reminder that s-v correspondence in FPTP systems does sometimes rest on knife’s edge results.

Mr Wells also offers a great video link on the PQ, 1976. Ah, those were the days…