Tuesday, 19 April 2011

AV Voting in Canada?

A recent post in "On Procedure and Politics" pondered the effects of AV voting in Canada.  I was intrigued by the possibility and tried to run a simulation, using data from the '08 election and 2nd choice preferences as stated in a poll as discussed in an article linked in the aforementioned post. 

Using the stated second choice preferences from the survey, I attempted to roughly simulate an AV election in the following way:
  • For each riding result, consider the percentage of vote received, PVR,  of the party with the most votes. If PVR >= 50%, stop and go on to the next party.  If PVR < 50%, move to the next step.
  • Of all the candidates in the riding remaining for consideration, identify the candidate, C, with lowest percentage of votes
  • Redistribute the votes of C according to the poll preferences in the survey.  For example, if the candidate with the fewest votes represents the NDP, we'd give 56% of their votes to the Liberal candidate if the Liberals have a candidate remaining in the riding, because 56% of NDP voters identified the Liberals as their second choice in the poll.  If a particular party in the preference list of C's party has already been removed from the list or didn't run a candidate, redistribute that party's share of C's vote according to the preferences for that party.  For example, if the party/candidate with the lowest total is the NDP, 9% of their votes should go to the BQ. But if there is no BQ candidate or the BQ had been removed from consideration, we redistribute that 9% according to BQ preferences.
  • Remove C from the list of candidates in the riding.
  • Recalculate total votes, T. If 21% of NDP voters don't have a second choice, we remove those votes from the total.
  • Identify the party with the most votes after the redistribution, determine their PVR, given their new vote total and the total votes. If their PVR is >= 50%, we're done, otherwise repeat the aforementioned process but with C removed from the list of candidates.  Continue until we have a party with a PVR >= 50%.
Here are the results under that scenario (in the spreadsheet, ridings in which the AV implementation results in a change in the winning party have a "1" in the "Changed" category).

Original: New:
Cons 143 131
Lib 77 92
BQ 49 42
NDP 37 41
Ind 2 2

Note that the Conservatives lose a number of seats, enough so that a Liberal + BQ or Liberal + NDP coalition exceeds the Conservative seat total.   Also noteworthy, neither the Conservatives nor the BQ pick up seats in this scenario.  This is because relatively few people select them as their second choice.  Here is a list of ridings in which the winning party changed.

Province Riding Winning Party Recalculated Winner
New Brunswick Saint John Cons Lib
Nova Scotia West Nova Cons Lib
Nunavut Nunavut Cons Lib
Ontario Kitchener Centre Cons Lib
Ontario Kitchener--Waterloo Cons Lib
Ontario London West Cons Lib
Ontario Mississauga--Erindale Cons Lib
Ontario Oak Ridges--Markham Cons Lib
PEC Egmont Cons Lib
Quebec Ahuntsic BQ Lib
Quebec Brome--Missisquoi BQ Lib
Quebec Haute-Gaspesie… BQ Lib
Quebec Jeanne-Le Ber BQ Lib
Quebec Laval BQ Lib
Quebec Saint-Lambert BQ Lib
British Columbia Surrey North Cons NDP
Nova Scotia South Shore--St. Margaret's Cons NDP
Quebec Gatineau BQ NDP
Saskatchewan Saskatoon--Rosetown--Biggar Cons NDP

The data can be found at link.  See the "assumption2" tab.  Also, the script is easy to rerun using different assumptions about second choices and the like, so I'd be happy to try other variations in second choices, etc.


Radical Centrist said...

Very intersting! I will try to write up a post on my blog linking back to yours!

mijopo said...

yes, please do, I'd be happy to run some other numbers if that would be useful too.

Anonymous said...

Nothing is so firmly believed as what we least know.

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