These are big numbers. Could have changed the outcome.
It’d be very interesting to maybe simulate whether or not some of these voters could’ve elected some of the 3rd parties they preferred if they had had Approval Voting.
Single winner reform in Canada would probably not help smaller parties win more seats. It would mostly help the Liberals, who are the most affected by vote splitting. Single-winner reform without a spoiler problem might hurt the Liberals if it allows for a rival party to emerge that is largely aligned on a left-right scale, but speaks out against some of the shady things that Trudeau has done. But the NDP, Greens, and BQ are probably better off under FPTP than a non-PR system with less vote splitting.
I would think the NDP are hurt most by people voting for the Liberals to beat the conservatives. In the last election polling showed that Mulcair would have beat Trudeau if not for favorite betrayal. In a case for vote splitting people tend to vote for who is going to win so there is a weird accumulating effect driven by polling and propaganda.
OK, after looking at this article (note: this person really should have separated their model by province, or at least separated Quebec; the model is flawed, but the preference data contains useful information), I have to agree. The selective way that IRV mitigates vote splitting seems like it would be most likely to help the LPC, since they can still use the strategic voting argument while benefiting from NDP transfers in ridings where the first preferences lean Conservative. While it also might help the NDP by reducing strategic voting (and according to the article also help the NDP win Conservative ridings because the Liberal second preferences lean NDP, which would probably be Condorcet failure elections in IRV), I would have thought it would endanger seats the NDP holds by allowing Conservative transfers to help the Liberals (which was why I made my first post). However, according to the article, a lot of Conservatives wouldn’t indicate a second preference, so the LPC only benefits a little from their transfers, so it didn’t hurt the NDP as much as I would have expected. I think this strongly suggests that a lot of Conservative voters would bullet vote in Approval elections, so Approval would also not endanger NDP-held seats much.
Some ridings where the Conservatives lead in first preference might be won by the Liberals in Approval and the NDP (or the Conservatives) in IRV because of center-squeeze. However, some might still be won by the NDP in both IRV and Approval, since strategic Liberal voters in plurality (and eventually some non-strategic ones) would probably approve the NDP, possibly moving the NDP candidate ahead of the Conservative.
Lowering strategic voting could also endanger some Liberal seats. In IRV these might be picked up by the NDP or the Conservatives. The Conservatives would probably not make such pick-ups in Approval, though the NDP might.
The conservatives had a lot of vote splitting with the PPC. I have seen estimates that the existence of the newly formed PPC cost the conservatives 6 seats.
In the end it is very hard to know what would happen with Approval voting. The game is changed so the parties would even change their platform. There is less incentive to campaign negatively and also there is an effect where platforms become more moderate.
Is it possible to figure out how nationwide PR would’ve looked by adjusting the actual vote tally with the number of voters who said they would’ve honestly voted for someone different?