“Alternative Vote” is what you get when you slap a ranked ballot on a first-past-the-post system. The defining features of FPTP that lead to issues decried by PR advocates are single-member ridings which form larger chambers, which leads to highly disproportionate results (e.g. if you have an A/B/C split of 40%/30%/30% across 10 ridings, all 10 will elect “A”). leading to a gradual consolidation into two parties, increased polarization, reduced democratic choice, reduced democratic participation (because your voice actually doesn’t matter), etc.
The ranked ballot component of “Alternative Vote” does not meaningfully change any factors of that equation, and can actually exacerbate it – effectively funneling those few non-major party votes back toward major parties as “false choices”. In the all-party special committee on electoral reform in 2016, their report highlights Alternative Vote/Preferential Voting/Instant Run-Off Voting/“Ranked Ballot” (all the same thing) as the single option which would result in even more distorted outcomes than our own First-past-the-post [1]. Australia is the only country to use this at the federal level.
This doesn’t mean that ranking choices / a ranked ballot is fundamentally bad, but that it is a feature of a voting system is neither necessary nor sufficient to fix the problems attached to FPTP. A PR system which leverages ranked ballots to great effect is Single Transferrable Vote, which is basically the same but with multi-member districts rather than single-member, keeping top X winners of the district. That said, there are non-ranked ballot PR options which have been demonstrated to have high degrees of democratic success, so its a bit of a red herring.
[1]: Special Committee on Electoral Reform report 3 (2016): https://www.ourcommons.ca/documentviewer/en/42-1/ERRE/report-3/page-177#50 ERRE report 3 p177. See the diagram under subheading “Proportional Electoral Systems” about the Gallagher index
The most notable attempts of the previous NDP caucus were in Motions 76 and Motions 86.
Motion 76, by Green MP Mike Morrice: https://www.ourcommons.ca/Members/en/mike-morrice(110476)/motions/12180488 This one didn’t come to a vote.
Motion 86, by NDP MP Lisa Marie Barron: https://www.ourcommons.ca/members/en/111023/motions/12517157 This one did come to a vote, but was Negatived (101 Yea / 220 Nay) by the usual suspects.
Unfortunately, both Mike Morrice and Lisa Marie Barron lost their seats in the last election to members of the conservative party due to vote splitting.