Some unusual Condorcet STV methods
Here are some Condorcet/STV hybrids that I thought of while thinking
about proportional representation:
Method one:
- Count first preferences of the (remaining) candidates.
- While any single candidate has more than a Droop quota of first
preference support, elect him and redistribute the surplus. - If all seats are elected, we're done.
- Otherwise, perform a Ranked Pairs election with the whole electorate
and eliminate the loser. - Go to 1.
This is a variant of STV with Condorcet loser elimination, and so the
winners will be biased towards the center of the whole electorate, which
isn't ideal. However, it should be more well-behaved than ordinary STV
because Ranked Pairs passes local IIA. Suppose that there are no
candidates with a Droop quota's worth of first preferences; then the RP
loser will be eliminated, but that won't alter the Ranked Pairs ranking
itself. So the rule above is equivalent to:
- Count first preferences of the (remaining) candidates.
- While any single candidate has more than a Droop quota of first
preference support, elect him and redistribute the surplus. - If all seats are filled, we're done.
- Otherwise, perform a Ranked Pairs election with the whole electorate
and keep eliminating the losers until some candidate has more than a
Droop quota of first preference support. - Go to 1.
It should also be more clone resistant because the Ranked Pairs order
list the clones in sequential order; they're thus also eliminated one
after another. The Ranked Pairs order can still (and probably will)
change after a candidate is elected, however.
The loser elimination method should be one that passes LIIA, so that the
elimination order doesn't change during the elimination itself.
The second one is based on a Hare quota and is a pretty straightforward
port of the idea of clustering. It's sort of a greedy clustering
approach. For simplicity's sake, let's disallow equal rank since it's
going to use coalitions and I don't want to get bogged down in whether
to use acquiescing or solid ones.
- Count the strengths of every solid coalition.
- Among the coalitions with more than a Hare quota's worth of
support, let the one with least number of candidates be the "smallest
strong Hare coalition". Break ties in favor of the coalition with most
votes. - Perform a Condorcet (say Ranked Pairs) election limited to the
ballots that make up the smallest strong Hare coalition. - Elect the winner and eliminate him, and redistribute the surplus.
- If all seats are filled, we're done.
- Otherwise go to 1.
There are no loser eliminations here, so it should be more well-behaved
with respect to monotonicity. But it is Hare-based and so may fail to
find enough winners to begin with.
Going further along this line of reasoning brought me to what I'd call
"expansion methods". But I'll mention them later - no need to clutter up
one post with too many methods :-)
On Sun, Sep 13, 2015 at 10:34:19PM +0200, Kristofer Munsterhjelm wrote:
Here are some Condorcet/STV hybrids that I thought of while thinking
about proportional representation:
Method one:
- Count first preferences of the (remaining) candidates.
- While any single candidate has more than a Droop quota of first
preference support, elect him and redistribute the surplus. - If all seats are elected, we're done.
- Otherwise, perform a Ranked Pairs election with the whole electorate
and eliminate the loser. - Go to 1.
Interestingly enough, I thought about the same approach myself some days
ago, also while pondering about (party-list) PR and the clone issue.
However, I'm not sure if it would be "better" than CPO-STV, so I didn't
pursue the thought any further.
--
Regards,
Vidar Wahlberg
On 09/14/2015 09:52 AM, Vidar Wahlberg wrote:
On Sun, Sep 13, 2015 at 10:34:19PM +0200, Kristofer Munsterhjelm wrote:
Here are some Condorcet/STV hybrids that I thought of while thinking
about proportional representation:
Method one:
- Count first preferences of the (remaining) candidates.
- While any single candidate has more than a Droop quota of first
preference support, elect him and redistribute the surplus. - If all seats are elected, we're done.
- Otherwise, perform a Ranked Pairs election with the whole electorate
and eliminate the loser. - Go to 1.
Interestingly enough, I thought about the same approach myself some days
ago, also while pondering about (party-list) PR and the clone issue.
However, I'm not sure if it would be "better" than CPO-STV, so I didn't
pursue the thought any further.
CPO-STV/Schulze STV would give better results since they wouldn't be
biased towards the center. The two things the above has going for it are
that it's simpler and it scales better: like STV, you can use the method
above with loads and loads of candidates and seats, whereas the number
of comparisons for CPO-STV and Schulze STV increases extremely quickly
as the council grows larger. For the kind of local STV elections where
the voters are supposed to directly rank the candidates, that doesn't
matter, since the voters won't accept having to rank say, 150 candidates
anyway; but if you're doing a party list reduction, that could be quite
important.
It'd be interesting to try to balance the centrist bias by making it
easier for small parties to be elected, e.g. by setting the threshold to
a single seat. But it feels unstable: there's no proof that these will
cancel out in the way we want.
In closed party list, it would also provide an incentive to split
parties if a less centrist faction of a larger party thinks they have a
quota's worth of support on their own; but I imagine that would be the
case with any ranked closed party list method that passes the DPC unless
the party leadership ranks them properly.
(E.g. suppose that party X has two Droop quotas' worth of support, and
X's list as provided by the party is A>B>C. If A and C both have a Droop
quota, i.e. B is the unpopular one, then C has an incentive to split and
form his own party provided that he can retain that Droop quota's worth
of supporters. This is the case because, if Y would be C's new party,
the people who support C could now vote Y>X and be much less concerned
about party Y splitting the vote of party X; either Y wins and C is
elected, or Y isn't and the DPC then lets X benefit.)
To all from one new to this group,
I have been studying election methods for a long time,
including combining Condorcet method with STV.
As I believe I mentioned in my first e-mail, I have invented Binomial STV,
which does not disqualify any candidate before the (averaged) count is
complete.
from Richard Lung.
On 09/15/2015 07:48 PM, Richard Lung wrote:
To all from one new to this group,
I have been studying election methods for a long time,
including combining Condorcet method with STV.
As I believe I mentioned in my first e-mail, I have invented Binomial STV,
which does not disqualify any candidate before the (averaged) count is
complete.
Could you describe your method here? I'd be interested in knowing how it
works, and I imagine the other members of the list would as well.
On 15/09/2015 21:34, Kristofer Munsterhjelm wrote:
On 09/15/2015 07:48 PM, Richard Lung wrote:
To all from one new to this group,
I have been studying election methods for a long time,
including combining Condorcet method with STV.
As I believe I mentioned in my first e-mail, I have invented Binomial STV,
which does not disqualify any candidate before the (averaged) count is
complete.
Could you describe your method here? I'd be interested in knowing how it
works, and I imagine the other members of the list would as well.
Thankyou Kristofer for your interest.
I have evolved a transferable voting method, descriptively called
(preference abstentions-inclusive keep-value averaged) Binomial STV.
Traditional single transferable vote is uninomial: it is just a
preference vote count. Binomial STV also conducts a reverse preference
count. The latter is an exclusion count to do away with the critique,
"premature exclusion" of a trailing candidate, when the transferable
surplus votes happen to run out.
The unfilled preferences or abstentions must also be counted, so that
the relative importance of preference election count and unpreference
exclusion count is conserved.
With Binomial STV, if you returned a blank ballot paper, that would be
equivalent to None Of The Above. But partly unfilled orders of
preference partly count also towards the quota for an unfilled seat.
A preference election and an unpreference exlusion is a first order
Binomial STV count. The result is obtained by inverting the exclusion
keep values and averaging them with the election keep values (using the
geometric mean).
Keep values were introduced by the computer-counted Meek method STV.
However, I extended their use from candidates who are elected with a
surplus of votes, to candidates still in deficit of an elective quota.
This extra information is useful in Binomial STV, because winners are
those who do best on average.
Binomial STV is a preferential data mining system,which can be taken
to indefinitely higher orders of election and exclusion counts.
If preference, p, plus unpreference, u, count is given in binomial
theorem form, (p+u) then the second order count is given by (p+u)^2 = pp
- up + pu + uu. This is the formula for a second order truth table of
four logical possibilities.
The algebra is non-commutative because "up" and "pu" represent two
different operations.
The second order count qualifies the two first order counts with four
counts: "pp" means that the most prefered candidate has votes
re-distributed to next preferences; "up" means the most unprefered
candidate has votes transfered to next preferences. The candidates keep
values for these two counts are averaged for an election count. The
process is repeated, with pu and uu, for an average exclusion count,
which is inverted, and averaged with the average election count, for an
over-all average result.
In turn, a third order count (p+u)^3 may qualify the second order count.
Normally it should not be necessary to determine an election result by
higher order counts. In any case, the system requires an automated
count, extending Meek method (which might be described as a sustained
surpluses count). Binomial STV would not include the Meek method add-on
of reducing the quota, as the preferences run out, because with Binomial
STV, the abstentions are part of the whole preference information.
from
Richard Lung.
,