Keith Edmonds wanted opinions about DMP,
which is a suggested voting method for BC (British Columbia) Canada,
The acronym perhaps is a bit unfortunate -- "Dump Canada" !?
But never mind that :)
I had earlier discussed the history of voting-reform attempts
in Canada here
The DMP page says PEI in 2016 adopted MMP (Mixed member proportional),
along the way considering other systems including DMP -- which I did
not know -- my Canada history
evidently is out of date and only knew about an earlier 2005 failed
PEI voting reform attempt.
The DMP page says DMP was invented by Sean Graham in 2013.
The web pages
identify a PhD botanist named "Sean W. Graham" at the University of Alberta,
but it is not clear to me whether that Sean Graham has anything to do with the
Sean Graham who invented DMP.
1. DMP uses simple FPTP-style ballots.
Each riding (i.e. district) elects 2 MPs (not 1) and hence
will be twice its old population. (Exactly twice, if number of old
ridings was even.
Otherwise approximately twice. I presume it is intended that all ridings be
equipopulous, or very nearly, although the DMP page did not
actually say so explicitly.)
2. In each district, each party can run either 1 or 2 candidates,
in the latter case as a conjoined team containing one
"senior" and one "junior." (The "senior" is the one listed first.
These ordered teams act like a micro-sized version of a "party list.")
Apparently "independent" is for this purpose regarded as a pseudo-party,
and the DMP description unfortunately did not say what to do if 2 or more
independents wanted to enter the race.
3. Each voter marks a single "X" on the ballot for the candidate, or
conjoined team (presumably the one they "support most," albeit exactly
should mean to them is not tremendously obvious).
4. Whichever candidate or 2-team gets the most X's, wins that riding's
(for the team's senior, if it is a team).
5. We then go to a second counting round. In it, all junior members
of teams are eliminated and their votes transfer to their teammate, EXCEPT
that if the first seat was won by a team, then that team's junior stays
in the race, and with a vote count equal to half of his team's count.
[Now at this point, you might naively have expected the DMP rules to
elect the guy with the most votes to the 2nd seat, and you might have
criticized DMP by claiming that according to some STV-like philosophy,
the junior member of the first-seat-winning team should NOT have gotten
half its votes, but rather, e.g, his team's number of votes MINUS the 2nd-top
vote count? But no: that all is NOT how DMP works, so forget that.]
6. Next, DMP eliminates anybody with fewer than 5% of the then-remaining votes.
[And I presume if everybody got below 5%, then everybody besides the
top vote-getter is
eliminated (?), but the DMP rules did not actually say that explicitly.]
7. Next, DMP elects the top independent if he got the most, or 2nd-most votes.
Note, this rule is asymmetric and "unfair" in the sense it treats independents
differently than party-candidates. That is a highly unusual innovation.
Even more unusually, this unfairness actually favors the independents.
(Usually, unfair election systems have disfavored independents.)
While the DMP system as a whole may not actually help independents --
see the very
next rule -- certainly this particular DMP rule does.
8. Otherwise, DMP eliminates all independents. (And this rule unfairly hurts
9. Next, DMP eliminates everybody besides the top 3 vote-getters in that riding.
10. Now, the entire province, or perhaps even country, is considered.
Each party has some already-attained seat-count in that province,
i.e. considering the first-seats only.
Each party also has some province-wide vote-count.
Based on the party vote-counts, we work out its "ideal" seat counts
(intended to yield the same proportion of party-seats, as votes, where
seats I mean the seats not already claimed by independents).
When computing these ideal seat counts, the DMP page seems
to indicate that in some manner these are rounded off to integers.
The DMP rules I saw left this rounding off method unspecified -- but
would need to actually specify something! The DMP page does not
specify it, but pretends it has.
11. That party's ideal seat count MINUS its actual seat count elected so far,
is its "seat deficit."
[I presume, although the DMP page does not actually say so explicitly,
that negative seat deficits -- for parties who already won more
than their ideal seat count -- are changed to zero?]
12. Next, comes the final stage.
At this point the DMP rule description suddenly gets incredibly vague
At the final crux stage, DMP wants to elect the 2nd seats in each district
(aside from districts where that 2nd seat already was won by an independent)
in some way that
(1) makes parties with bigger deficits more likely to win (so we
get PR = proportional representation, or anyhow get closer to PR), and also
(2) makes candidates with bigger vote counts more likely to win.
Those are both good goals, and there are plenty of ways to try to
satisfy those two goals, but you have to CHOOSE a precise method.
Instead, the DMP page just acts as though those goals ARE a method,
which is bullshit.
There are goals, and there are methods to achieve those goals. You
actually have to specify the method. DMP does not, then pretends it has.
OK, so what do I think of the DMP idea?
Well, first of all, most obviously, it is a lie and a cheat -- it is
pretending to be a voting method, but is not and will not really be
one until the unspecified rules are actually specified.
Therefore let me invent some suggestions to fill the gap and thereby convert DMP
into a genuine voting method so that we can actually have something concrete
to think about. My suggestions below may or may not be the best
possible ones, and may or may not be what Sean Graham would
have wanted -- but at least they are something concrete.
WDS GAP-FILL #1:
Any number of independents are allowed to enter the race, and they
also are allowed to enter as 2-man teams if both agree to be a team.
An alternative idea would be
1': Same, but forbid team-hood for independents.
WDS GAP-FILL #2:
There is no "rounding off" and no deficit-zeroing either.
That is, the ideal seat count for a party, and
also consequently its seat-deficit, are allowed to be fractions (and
seat-deficits are allowed to be negative), and are not
demanded to be whole numbers.
Note however that (as a lemma) the sum of all the deficits is always
going to be nonnegative. Also note that by having negative and
fractional values we enable
seeking the best still-attainable approximation to PR.
WDS GAP-FILL #3:
The open seats are filled as follows.
A. find the still-alive candidate (in all ridings) with the most votes.
If his party has a positive deficit, then elect him (and decrease that
deficit by 1).
B. take him off the "live" list.
C. keep going until all open seats are filled.
3': Here a different possible gap-fill (not equivalent) would be
A. find the party with the greatest deficit.
B. Among its still-live candidates, find the one with the most votes.
C. elect him (and decrease that party-deficit by 1,
and take him off the "live" list).
D. keep going until all open seats are filled.
3'': Yet another possible gap-fill (not equivalent) would be
A. find the still-alive candidate (in all ridings) with the most
his top rival. If his party has a positive deficit, then elect him (and
decrease that deficit by 1).
B. take him off the "live" list.
C. keep going until all open seats are filled.
3''': there are other ideas possible too...
OK, so now what do we think of DMP (with gaps filled)?
Well, I consider it "ad hoc" and something of a "kludge" rather
than systematically constructed. That is, it includes some
unfair and goofy rules, plus some arbitrary thresholds like "5%"
and "top 3" which hopefully were chosen near-optimally for Canada, but
it is hard to know that -- perhaps actually the best values are quite different
from what Graham thinks they are -- and also perhaps the optimum
values for Canada are not the same as the optimum values for Pakistan.
This ad hockery is not necessarily a bad thing. In particular the value "2"
for the number of MPs in a district, might be best possible.
The DMP page claims these advantages (slightly edited):
* Keeps the simple ballot design of Canada’s Single Member Plurality
* Eliminates the need for long party lists,
* Retains a degree of local representation and accountability,
* Accommodates rural communities by providing the benefits of
proportional representation without creating enormous districts.
Those all sound plausible to me. I also think
* DMP looks like it could have a pretty high level of immunity
to something I call "targeted killing" strategic voting.
On the other hand:
* DMP by insisting on "mark one X" ballots sacrifices the greater
with ratings-style ballots (e.g. for range voting).
* DMP's asymmetric treatments of independents versus parties is
it still might be better than many rival schemes in practice.
* The 5% threshold causes a party that gets 5% of the countrywide vote,
possibly to get zero seats, thus killing small parties (that otherwise
might have been
able to grow and prosper over many years) in infancy.
* Meanwhile the "religious cult wacko" party which happens to have its
cult headquarters in Bethlehem, wins Bethlehem's seat (but cannot win any other
seats in the country) even though only getting 1% nationwide. This contrast
is intended to illustrate the notion that DMP may unfairly hurt
parties like the Greens which have widely distributed fairly uniform support,
by comparison to parties like a religious cult that have less support, but it is
It would be possible to eliminate much of DMP's ad hockery and unfairness
by regarding the independents as a pseudo-party province-wide and/or
then treating them the same as any other party. This might seem a bit odd since
some independents will be very different from others (much more unlike
than same-party members usually are) but does that necessarily matter?
Well, I think this alternative would have both advantages and
suspect the advantages would outweigh the disadvantages.
Disadvantage: some popular independent could "drag" some
wacko ones up via his "coat tails."
Advantages: superior simplicity, superior(?) fairness, less apparent-randomness,
and that coattail-dragging helps to cancel out unfair problems
inherently suffered by all independents in Canada.
The following page by me is relevant to Canada...:
Warren D. Smith
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