I looked at Single Non-Transferable Voting (SNTV) as if vote tallies per candidate were the same or only slightly modified from the 2021 result.
I am assuming a new MM district that covered three ridings in South Edmonton (Edmonton Mill Woods, Riverbend and Strathcona) plus Sherwood Park-Ft. Sask and Edmonton-Wetaskiwin.
(S. Park, Ft. Sask and Wetaskiwin are actually outside the City of Edmonton - the ridings do not abide by corporate limits of Edmonton as I think they should!)
Findings of effectiveness of SNTV: with votes as cast for individual candidates in 2021 election, and each party running full five-candidate slate, no change in who is elected under SNTV versus FPTP. But with each major party running more considered but still basically arbitrary uniformly-sized three-candidate slates, we see more balanced result simply due to MM district. Two parties - Cons and NDP - elect MPs. but result is more balanced than the single non-Cons MP elected under FPTP. now NDP has two seats and Cons. has only three seats. With each major party running more accurately-sized slate, we see three parties elect MP(s). if Cons run three or four candidates, they elect three MPs. if NDP run three, they elect one. (they might elect two if they run just two!) if Liberals run just two, they elect one. (Running only one candidate will not give them more seats than they win with two candidates!) Three parties is great result for only five seats. much fairer than present almost-total Cons sweep of four out of five seats under FPTP. Three parties represented, just in one half-city district. so I think SNTV. despite its seemingly chancy and vote-wasteful method. actually produces balanced rep. compared to our present FPTP.
But note that to win under SNTV there is no set minimum and many votes are wasted. Each party though generally suffers waste and the system works to ensure that no one party can take all the seats in a district.
Many votes can be wasted and vote-splitting can produce unfair results (but likely more balanced than elections under Block Voting).
Due to these reasons, the portion of votes needed to win a seat under SNTV may be quite small indeed. (Single transferable voting is more scientific, producing less wasted votes. Under STV, the minimum proportion needed to assure victory is the Droop quota, although commonly one or two in each contest are elected with less than that.)
See recent Vanuatu election for results that show this -- https://en.wikipedia.org/wiki/2020_Vanuatuan_general_election
In Ambae, Ngwele won a seat with less than 14 percent of the vote.
In Efate, Ruben won a seat with less than 6 percent of the vote.
In Malekula, Batick won a seat with just a little more than 5 percent of the vote.
and so on.
These are vote totals based on just that candidate's votes. Looking at party tallies, you get more proportionate picture in many cases but some of these successes may have been achieved by a candidate of a party that ran just one candidate so the candidate's tally is the party's tally in the district.
Here's the detailed account of the three thought-experiments of SNTV in five-seat "South Edmonton" district. five-candidate slates with votes as cast for individual candidates in 2021 election. no change in who is elected under SNTV versus FPTP - still four Cons and one NDP. Edmonton Mill Woods 18,392 Uppal Conservative Edmonton Riverbend 26,000 Jeneroux Conservative Edmonton Strathcona 32,000 McPherson NDP Edmonton-Wetaskiwin 48,000 Lake Conservative 18,259 Charles NDP (not elected. if he had received 200 more votes , he would have passed Uppals' total and been elected.) S. Park - Fort Saskatchewan
41,000 Genuis Conservative
But more fairness is produced if each large party runs just three candidates
with each of three large party running just three candidates
(Greens received less than 2000 votes so no chance of getting seat even if they only run one candidate)
three-candidate slates
three Conservatives and two NDP elected.
each party drops two candidates and their vote spread over remaining two candidates (arbitrary equal re-distribution):
drop Cons in
Edm Str 13,000
Edm MW 18,000
total freed votes 31,000 add 10,000 to each remaining candidate
drop Liberal in
Edm Str 4000
S. park 9,000
total freed votes 13,000 add 4000 to remaining candidates
NDP drop
MW 11,000
River bend 14,000
total freed votes 25,000 add 8000 to remaining three candidates
in following, old riding names are continued just for reference. although in reality there would be just one MM district.
Edmonton Mill Woods 18,392 Uppal Conservative (dropped) 16,000 Lib new vote tally 20,000 11,000 NDP dropped Edmonton Riverbend 26,000 Jeneroux Conservative new vote tally 36,000 NDP 14,000 dropped Lib 14,000 new vote tally 18,000 Edmonton Strathcona 32,000 McPherson NDP new vote tally 40,000 Cons dropped Lib dropped Edmonton-Wetaskiwin 48,000 Lake Conservative new vote tally 58,000 18,259 Charles NDP new vote tally 26,000 Liberal 12,000 new vote tally 16,000 S. Park - Fort Saskatchewan 41,000 Genuis Conservative new vote tally 51,000 9,000 Lib (dropped) 15,000 Theroux NDP new vote tally 23,000 candidates by new vote tallies
ELECTED
Wetaskiwin Cons. Lake 58,000
S. Park Cons 51,000
STR NDP McPherson 40,000
Riverbend Cons. 36,000
Wetaskiwin Charles NDP 26,000
NOT ELECTED
S. Park Theroux NDP 23,000
MW Lib 20,000
Riverbend Lib 18,000
Wetaskiwin Lib 16,000.
so three Conservatives and two NDP elected
Various-sized slates
but if Liberal are not likely to win one seat they are not likely to run so many as three candidates
if Conservatives win three when they run just three, perhaps they should run four.
let's see what happens if Conservative run four candidates, NDP three and Liberals two.
Conservatives drop just one
NDP drop two
Liberal drop three
and their votes are spread over remaining candidate(s). (arbitrary equal re-distribution where multiple remaining candidates): drop Cons in Cons Obasan Edm Str 13,000 total freed votes 13,000 add 3,000 to each remaining candidate drop three Liberals Mohamed Edm Str 4000 Holm S. park 9,000 Theiring Wetaskiwin Lib 12,000 total freed votes 25,000 add 12,000 to remaining candidates NDP drop Logan MW 11,000 Gray Riverbend 14,000 total freed votes 25,000 add 8000 to remaining three candidates new vote tallies in following, old riding names are continued just for reference. although in reality there would be just one MM district. Edmonton Mill Woods 18,392 Uppal Conservative new vote tally 21,000 16,000 Henderson Lib new vote tally 28,000 11,000 NDP dropped Edmonton Riverbend 26,000 Jeneroux Conservative new vote tally 29,000 NDP 14,000 dropped Lib 14,000 Chaudary new vote tally 26,000 Edmonton Strathcona 32,000 McPherson NDP new vote tally 40,000 Cons dropped Lib dropped Edmonton-Wetaskiwin 48,000 Lake Conservative new vote tally 51,000 18,259 Charles NDP new vote tally 26,000 Liberal Theiring 12,000 dropped S. Park - Fort Saskatchewan 41,000 Genuis Conservative new vote tally 44,000 9,000 Holm Lib (dropped) 15,000 Theroux NDP new vote tally 23,000 candidates: Cons 4, NDP 3, lib 2 total of 9 candidates New order of popularity of candidates ELECTED Cons. Lake (old Wetaskiwin) 51,000 Cons Genuis (old Sherwood Park) 44,000 NDP McPherson (old STR) 40,000 Cons. Jeneroux (old Riverbend) 29,000 Lib Henderson (old MW) 28,000 NOT ELECTED NDP Charles (old Wetaskiwin) 26,000 Lib Chaudary (old Riverbend ) 26,000 NDP Theroux (old S. Park ) 23,000 Cons Uppal (old MW) 21,000 so three Conservatives, one NDP and one Lib elected. NDP over-estimated their popularity. likely would have taken two seats if had run just two. Conservative did not get extra seat when ran four candidates. they take three seats whether run three or four candidates. NDP had two unsuccessful candidates. if they had run just two, they might have elected both but then Liberals would have suffered two unsuccessful candidates and gotten no rep. not everyone can win. somebody has to lose more than others. But at least all three main parties would have representation in the half-city under SNTV, it seems. (this, especially if duplicated in every major city across country, would do much to reduce artificially created regionalism) So that is how I see result under SNTV. my method is not based on party vote tallies but on votes as cast for individual candidates. obviously STV with transferable votes would produce more dependable results. NDP would win two seats whether they run two or three candidates for example, instead of the one they win under the variable-slate SNTV prediction. Liberals would win one or two seats. under STV, Dave, the result would be much closer to your "largest remainder"-style result, but even without transferable votes, SNTV (at least SNTV with consciously-sized slates) the result is much closer to party-based PR than it is to FPTP.
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