[EM] Droop fails the Markus Schulze Rule

[Tom Round]

Donald, look, I thought I had explained my argument about this clearly
enough yesterday, but I'll put it another way ...

There are still votes wasted even if you use a Hare quota.

[1] Firstly, because (to use the five-seat example with Hare quota 20% and
Droop quota 16.67%), the last one in does not really need a full 20%. Under
either quota, s/he needs only half of the votes remaining. If s/he has that.
s/he is "home and hosed" even if every single other vote goes against her or
becomes exhausted once the last runner-up is eliminated.

*       Under Droop, "half  of the votes remaining" translates to half of
33.34%, or 16.67% -- the same quota as the first 4 to reach quota.

*       Under Hare, "half  of the votes remaining" translates to half of
20%, ie 10.01% -- only half of the quota as the first 4 to reach quota. The
other 9.99% are still effectively wasted even if one continues with the
cosmetic exercise of transferring them to the only candidate remaining.
(Shades of the Eastern Bloc -- "Candidate Stopoff received 100% of the votes
cast!" but only because there were no others left to vote for.)

[2] Secondly, because the first four winners would still (as a matter of
mathematical proof) be safe from defeat had they only polled an exact 16.67%
each and gained not one vote extra after that, requiring them to reach 20%
instead of 16.67% before you start distributing their surplus preferences
means each of them is wasting 3.33% 

Thus, under the Droop quota, up to 16.66% of the votes may be wasted --
those that end up with the last runner-up, ie, with the candidate that could
not reach the quota of 16.67%.

Under Hare, the maximum wasted votes are actually higher. First there is the
13.33% locked away as surplus votes for the first four winners (ie, 3.33%
for each). Then there is the 9.99% who may barrack for the last runner-up
against the last winner. I make this a 23.33% vote-wastage rate. That's
almost half as much again, under Hare as under Droop, who could have stayed
at home or voted a blank ballot without having any less effect on who is
elected.

Sorry, but "ye kinna change the laws of physics" ...

It's cheating to deem the votes for the last-eliminated runner-up to
"really" favour the last-elected winner, to give him/her a full quota.
(Especially not if, like Donald, you object to other exhausted votes being
deemed credited equally to the remaining candidates to avoid the need to
re-calculate a reducing quota at each stage.) One might as well say that
under Instant Runoff (ie, Alternative Vote as used widely in Australia),
every winning candidate has 100% approval in his/her electoral district
because, after the last runner-up is excluded, s/he is left with 100% of the
votes (or of the votes remaining, if you have optional preferences and any
votes are exhausted). This does not change the iron law of psephology that
the winner only _needs_ a quota of 50.00000001% to be certain of winning.

I am curious as to the empirical evidence for the claims that, in Cambridge,
Massachusetts, "ideological slates and constituencies of higher
socioeconomic status receive an advantage with the Droop Quota", and that
"independent candidates and working class people (who inevitably vote
shorter ballots) are disadvantaged by Droop." 

I should mention that, in Australia, where we have used Single Transferable
Vote for dozens of multi-seat elections in the past century, I have never
once heard or come across any complaint from any candidate -- big-party,
small-party, micro-party or independent -- that the use of the Droop quota
is discriminatory. Complaints about seat numbers per district, yes, or about
optional versus compulsory preferences, or about party-ticket-voting
options, or about proposals to exclude candidates or parties below a certain
"threshold" of first-preference votes ... but never, from any practising
politician who would have a meaningful stake in raising objections, about
the Droop quota compared to the Hare quota.

At 20:07 15-10-99 -0400, you wrote:
>Greetings,
>
>Markus Schulze wrote:
>     "I think, that the aim of proportional representation is to minimize
>the number of the wasted votes."
>
>Donald:  I liked this statement so much that I decided to make it a rule -
>I call it The Markus Schulze Rule.
>
>     This statement is another real truism of the proportional
>representation movement.
>
>     Now, the question is: How well will Hare STV and Droop STV live up to
>the Markus Schulze Rule?
>     It is best to use Ideal Conditions when we compare the two. Ideal
>Conditions are when there are enough informed choices made by the voters so
>that no ballot becomes exhausted.
>     This may never happen in a real election, but it is mathematically
>possible.
>
>     Anyway, the Hare STV election will not have any wasted votes. Every
>ballot will end up on one or another of the winning candidates. Each
>elected member will have received the same number of votes - an equal part
>of the total votes.
>     The Droop STV election will not fare as well. The Droop will produce
>one quota of wasted ballots.
>
>        <B> Droop fails the Markus Schulze Rule. </B>
>
>     Also, while the elected members will all have the same number of
>votes, the amount will not be an equal part of the total votes.
>     Now, I am not suggesting that the last Droop quota be transferred - no
>way am I saying that.
>     I am saying that the Droop is a fraud and should be discarded before
>we even start the count.
>
>Regards,
>Donald
>
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