Did Robocalls Depress Voter Turnout?

Yes, according to this study by SFU Economics professor Anke Kessler, which finds that polling stations with lower Conservative vote shares experienced a larger decrease in voter turnout in robocall ridings than in non-robocall ridings. The study compares polling stations within ridings (rather than simply comparing ridings with and without robocalls). This gets around the problem that robocall ridings were tighter and thus likely to have higher turnout, which would mask the actual effect of robocalls.

Specifically, the study finds that, in non-robocall ridings, a polling station with 10% more opposition support would experience a 0.46% relative decrease in turnout - this is just the result of the left having a bad night and the right having a good night. However, in robocall ridings, a polling station with 10% more opposition support would instead experience a 0.97% relative decrease in turnout. (All '%' denote percentage points.)

In other words, relative to Conservative turnout, non-Conservative turnout decreased by 4.6% in non-robocall ridings, but 9.7% in robocall ridings. The net effect of robocalls is thus measured to be 5.1%. The study notes that the average riding had about 82,000 registered voters and roughly 60% opposition support, so, in an average riding, the results suggest that a robocall campaign would depress opposition turnout by 2,500 votes, over and beyond what it would have been.

Even fully believing in this result (and ignoring that ridings have different sizes and opposition support levels), however, does not imply that the winner would have been different in all robocall ridings where the Conservative margin of victory was below 2,500 votes: the decrease in turnout is spread among all the opposition parties, and not just the one that finished second.

On the other hand, this study looks specifically at the effect of robocalls on turnout. It ignores the fact that people might have still shown up to the polls, but voted for a different party due to robocalls. Thus, the true impact of robocalls could have been significantly larger.