As I was perusing the wikipedia article about the '95 referendum, I came across a fun little conspiracy theory I decided I would investigate. Namely, that the "Oui" side had rigged the vote in their favour, albeit unsuccessfully. Part of this allegation stemmed from a reportedly unusually high level of rejected ballots in predominantly "No" districts.
The first thing I thought to check out is if there was any significant correlation between a district's Oui/No vote margin and the percentage of rejected ballots.
Apologies if this is a confusing graph, but there is almost NO correlation between the number of rejected ballots and whether the district was a Oui/No district. The correlation R^2 of 0.03 is indeed very small, but the significance is in the realm of plausible enough for a Dan Brown novel (P=0.058).
If we treat Chomedy as an outlier and assume that there is something fishy with Chomedy alone, the effect becomes less significant and vanishes (R^2=0.01 and P=0.286).
The next step I decided to check out is whether or not rejected ballots followed a fishy pattern wherein they got rejected more often on the island of Montreal. (mouse over the cartogram to see the rejected ballots cartogram)
Here, Montreal does seem a little lighter than the surrounding areas, but how much of a difference could these spoiled ballots have actually made?
If we assume that the province wide average number of rejected ballots (1.8%) was for legitimate reasons, then for a district like Chomedy with 11.61% rejected ballots, we can assume that 9.8% (11.6%-1.8%) ballots could have been counted there. We should also assume that roughly the same proportion of hypothetically illegitimate ballots voted Oui or No (Chomedy voted 72% No). Multiplying this up together (Total x 0.098 x 0.72) gives us roughly 2935 extra "No" votes in Chomedy. Not a lot!
In fact if we apply the same function to the entire island of Montreal we get approximately 8200 extra "No" votes and 5600 extra "Yes" votes. Not exactly the kind of conspiracy legends are made of...
For reference, the actual margin of victory of No over Oui was 54,288 (2362648 no, 2308360 oui)