CSDC/CÉCD 2018 Quebec Election

2018 Quebec Election

These forecasts were created by Eric Guntermann (UC Berkeley, Political Science) and Benjamin Forest (McGill, Geography). Both are members of the Centre for the Study of Democratic Citizenship.

If you have questions, please contact Dr. Guntermann (English or French) or Prof. Forest (English).


For each party, we calculated the proportional increase or decrease in votes since the last election. In other words, we divided their current projected vote share (based on the latest poll) by the proportion of votes the parties received in the 2014 election.

We then multiplied each party's previous vote share in each district by the proportional increase (or decrease) and derived their predicted vote share from a truncated normal distribution (from 0 to infinity) with a standard deviation based on polling errors from the last election. We determined the standard deviation by calculating the absolute difference between the actual result for each party in each riding and the final poll result from each firm in 2014. That way, our estimate of the swing in favour of or against each party in a riding is based on how good we know each polling firm is at estimating that party's support in that riding.

There is one complication though. In 2018, a new firm, Mainstreet Research, has been running polls in Quebec. Since it did not run polls in 2014, we have no direct way of knowing how informative their polls are about swings in individual ridings. We deal with this problem by calculating the gap between the 2014 result and the average final poll for all other firms. This tells us how good polling firms are in general at predicting the result in each riding. We then add a firm-specific correction by calculating the difference between the average result in the most recent poll from each of the other firms and the result from the Mainstreet poll of interest. We then add the two to get the standard deviation for the swing distribution in that riding.

This whole procedure simulates an actual election.

In each district, we determined the winning party by identifying the one that received the most votes. We then counted the number of seats each party won in Quebec as a whole.

We repeated the simulated election 1000 times. The estimated seat share for each party is the median number of seats from these simulations. We also calculated 95% confidence intervals. The lower bound is the value that is higher than 2.5% of simulated seat shares. The upper bound is the value that is lower than 2.5% of simulated seat shares.


Quebec adopted new election districts (riding) boundaries in 2017, so we could not simply use the district-level results of the 2014 election as our starting point. Rather, we needed to transpose the 2014 results into the constituencies to be used for the 2018 election. This means that we began with geographically detailed election results.

Élections Québec provides the results of the 2014 election by section de vote or SDV. SDV are very small geographic units that correspond to polling stations. (In a few cases, there are two or more polling stations in one SDV. In these cases, results from the multiple stations are added together to obtain the vote totals for the SDV.) The SDV results reflect votes cast in-person on election day, and thus provide detailed information on the spatial pattern of the vote.

A substantial number of ballots were not cast at polling stations, however. These include advanced ballots cast before election day, mail-in ballots, ballots cast at mobile polling stations, ballots cast by prisoners, and other situations. Such votes cannot be definitively tied to a specific location within districts but are not necessarily similar to votes cast at SDVs. For example, in Abitibi-Ouest the Liberal candidate received 33% support from SDV votes, but nearly 40% support from non-SDV votes.

This means that the non-SDV votes must be allocated to specific locations. While it is impossible to know precisely where such votes were cast, we assume that the geographic pattern of these votes is similar to the geographic pattern of SDV ones. Thus, we allocate the non-SDV votes according to the spatial pattern of SDV votes. For example, if an SDV accounts for 12% of all Liberal SDV votes in a district, we allocate 12% of the non-SDV Liberal votes to that same SDV. See Table 1.

Table 1


Total SDV Liberal votes

Proportion of total SDV Liberal votes

Total non-SDV Liberal votes in district

SDV proportion x total Liberal non-SDV votes

Aggregate Total Liberal votes (SDV + non-SDV)
































By transposing the 2014 votes (both SDV and non-SDV), we can find what the election results would have been using the 2017 boundaries.

To do so, we allocated each 2014 SDV to the 2017 districts by overlaying their boundaries with each other using a Geographic Information System (GIS). Where a 2014 SDV falls entirely within a 2017 district, the allocation is easy. There are cases, however, where a 2014 SDV is split between two 2017 districts, and we must assign the SDV votes to one constituency or the other. We adopted a simple method known as centroid allocation.

First, we use the GIS to calculate the centroid of each SDV. (A centroid is the equivalent of the centre of a geometric shape like a circle or square but can be determined for irregular shapes. For practical purposes, it can be considered the centre point of an SDV.) We then allocate each SDV to a district by the location of its centroid. This approximates the partisan composition of the new 2017 districts. See Map 1.

Map 1

On Map 1, the thick black line is the boundary of two 2017 districts; the red lines are the 2014 SDV boundaries; and the green dots are the centroids of the 2014 SDVs. In the middle of the map, several SDVs overlap with the two districts, but their centroids lie clearly within one or the other constituency.

Transposing the 2014 results to the 2017 boundaries gives the PQ a plurality in one additional district at the expense of the PLQ.

Interested researchers can download the 2014 election results by district using the 2017 boundaries in CSV, Excel and STATA 12 formats by clicking on the appropriate links below.