[EM] 01/16/03 - Hey James, Droop Quota is an Oxymoron:

Donald Davison donald at mich.com
Thu Jan 16 00:29:58 PST 2003

01/16/03 - Hey James, Droop Quota is an Oxymoron:

Greetings James and list members.

James, you wrote: "These [Donald's] comments seem to be based on a
misunderstanding of the purpose of elections, on a misunderstanding of the
purpose of the Droop quota, and on a misunderstanding of the arithmetic of
an STV-PR election using the Droop quota."
Date: Tue, 7 Jan 2003, Subject: RE: [EM] 01/05/03 - Two Replies for Olli:

Donald here:  You are the `Pot calling the Kettle Black'.

Instead of me, it is you that appears to have these three
misunderstandings. Anyway, don't dispare, I am here to guide you away from
the Demon Droop and to the light of true understanding and the love of the
Hare quota - Ha Ha.

James: "I'll (eventually) go back to one of Donald's related comments, but
he seems to think the purpose of an election is to allocate voters
perfectly to Hare quota groups.  That is NOT the purpose of an election."

Donald: You wrong me James.  I am well aware and accept the fact that a
candidate can win a seat with less than a quota, any quota.  My position is
that the best method should have an open door which will allow candidates
to receive as many votes as possible up to a number of votes equal to a
proportional share of total votes, a full representative share of the
voters.  The closer the elected candidates come to the Hare quota, the
closer they become the ones who are most representative of the voters.

James: "If it is an election to fill simultaneously, say, three seats, the
purpose of the election is to identify the three candidates who are most
representative of the voters."

Donald:  Yes, we agree on this point, but what is in dispute is what is to
be the measure to tell us which candidate is more representative of the
voters.  While your candidate with 1/4 plus 1 has won a seat, a candidate
with one-third of the votes is more representative of the voters.

James: "If there are three candidates who can each secure a Droop quota of
votes (1/4 plus 1, for a three-seat contest), it follows that these are the
three winners, because no other candidate can then secure a Droop quota of

Donald:  I will agree that these candidates have won the three seats, but
it is not clear how this lower number of votes makes them more
representative of the voters.  Only seventy-five percent of the voters
voted for these three, it would be more representative if ninety to one
hundred percent of the voters voted for these same three.  More would vote
for these three if the method would allow, but Droop method does not allow,
something must be wrong with the Droop method - yes indeed, there is
something wrong.

James: "It is not necessary to continue the transfer of votes until all
votes are allocated perfectly to three Hare quota groups."

Donald:  Wrong!  `The job's not over until the paper work is done.'

The final transfer of votes will tell us how `representative of the voters'
the election really turned out to be, or don't you like bad news with you
morning after `Droop Coffee' (Drip Coffee, Don).

Consider the example of the single-seat election.  A candidate only needs
fifty percent plus one to be the majority winner, but when the votes are
being counted the count is not stopped at fifty percent plus one.  No
indeed, the count continues until the tally is finished, until the paper
work is done.  The same is true for all the multi-seat methods except your
Droop STV (and Meek-Droop-STV).  In the Droop method the math is stopped
before it get too `amusing'.  The results of a Droop election are reported
as: `These are the winners and this is the first runner up.'  In this way
the results don't look too bad, the defect is hidden.

James: "In any case, the voters will defeat you, because not all of them
will mark all possible preferences."

Donald:  Again, you are wrong - you should stop this habit of being wrong?

The voters are not going to defeat me.  I know there are going to be some
exhausted ballots, in any ranked method, but what you don't tell your
readers is that in the Droop method there will be far more excluded ballots
besides the exhausted ballots because the Droop method creates excluded

James: "If there were a 3-seat election in which three candidates each
secured exactly 1/3 of the first preference votes, that is what the STV-PR
result sheet would show.  And it would show the Droop quota as 1/4 of total
valid vote plus 1.  The arithmetic is quite clear - three candidates each
secured (at least) a Droop quota of votes at the first stage of the count,
so they are the three winners.

Donald:  I have already agreed that if three candidates received at least
the Droop number of votes, that these three will be elected, but how can
you say the results sheet would show one third each when we all know that
in a Droop election the candidates are limited to only 25% +1 of the

James: "There would be nothing to hide.  There would be no shame.  There
would be nothing defective."    James

Donald:  `Me thinks you protest too much.'

Now is the time for a reality check of your letter.  You started out
claiming that there were three misunderstandings as follows: `the purpose
of elections' - `the purpose of the Droop quota', and `the arithmetic of a
STV-PR Droop election'.

I agreed with you that the purpose of an election is to identify the
candidates who are most representative of the voters, but we don't agree on
how to measure this representative value.  You want the Droop quota to be
enough representative of the voters. I say we need more, that is, more
votes is more representative.

In your entire letter, you did not say what was the purpose of the Droop
Quota.  I think you know, you just don't want it to be made public that you
support the political parties in Droop STV elections.  Yes, the purpose of
the Droop quota is to benefit political parties over independent
candidates.  In Droop elections the independent candidates will be
eliminated sooner than they would be in a Hare STV election.  This happens
because votes from the higher candidates are transferred to the lower
candidates of the same party.  These extra votes can help a low candidates
avoid a few eliminations, but somebody still must be eliminated.

The Droop Quota also relieves political parties from the ordeal of
averaging their votes on their candidates at the ballot box.

By the way, speaking of the Droop Quota, did you know that the term Droop
Quota is an Oxymoron.  Yep, it sure is.  The word `quota' means `a
proportional part or share of the whole', while Droop is not `a
proportional part or share of the whole'.  These two conflicting words
together form an oxymoron.  I just thought you would like to know that.
That's a juicy bit of information you can drop at your next peer cocktail

Anyway, you still failed to tell us what you think is the purpose of the
Droop quota, give it a shot, take a guess.

Number three, the so called misunderstanding of the arithmetic of Droop
STV.  There is no misunderstanding of the arithmetic of Droop, we both know
the arithmetic.  The dispute is over how far to carry the math.  You want
to stop before it is finished.  I want to continue until the job is done.

In closing, I would like to go on record as saying that I am not opposed to
the averaging of the votes of factions, if a jurisdiction votes in favor of
averaging, but if a jurisdiction votes not to allow averaging of votes by
the rules, like in non-partisan elections, then the method it should use is
Hare Preference Voting, a method in which the rules do not favor the
factions over independent candidates.  The rules of Hare Voting will divide
the total votes into proportional shares.  In the case of three seats, the
shares would be one third - one third - one third.

The results of a Hare STV election can be very proportional, with results
near perfect, perfect being one third of the total votes ending up on each
of three winning candidates.  If your jurisdiction votes not to allow
averaging the votes for the political parties then you should not use the
Droop Quota because the Droop quota is a means of averaging votes.  While
it does a crude job of averaging, it is never-the-less averaging the votes
of political parties.   Besides, the Droop also causes a near quota of
votes to be wasted, which inturn lowers the proportionality of the
election.  In your case of three seats the proportionality will only be 75%
plus three votes.  The balance of 25% less three votes will be wasted votes
of excluded voters.

Other design features of the Hare Preference Voting method should be as follows:
 * Fractional transfer of all surplus votes, original and secondary:
 * Transfer value equal to surplus divided by all the votes of the
candidate with the surplus, not by the number of fractional papers.
 * Transfer both transferable and non-transferrable ballots.
 * Transfer original surplus votes before eliminating any candidates.

On the other hand, if your election is a partisan election, you are going
to find that there will be pressure in your jurisdiction to allow the
averaging of votes.  Political factions want some of the votes of their
higher candidates to be spread onto their lower candidates.  And, being as
all the factions together are a majority of the electorate, it is
understandable that something like the Droop Quota was imposed into
Preference Voting/STV many years ago.  The Droop quota does spread votes
over more candidates, kind of like averaging the votes.

In the event your jurisdiction does approve the averaging of votes, you
should still reject the Droop Quota, there is a better way to average
votes.  The Droop Quota is a crude way to average votes.  It will not do
the best job of averaging the votes for each faction, some candidates can
still be left with lower votes than higher candidates in the same faction.
Besides, don't forget, Droop also creates a near quota of excluded voters
and that lowers the proportionality of the election.

The better way of averaging the votes is a new elimination rule that I have
created.  That rule is as follows: `The candidate to be eliminated shall be
the lowest candidate of the party with the lowest average votes per
candidate.'  This rule will average the votes equally across all the
candidates of each faction, plus it does not exclude any voters, and will
maintain proportionality, and it adjusts for exhausted ballots after every
elimination which inturn makes Meek unnecessary.

My new elimination rule can be added to three methods, SNTV, Bottoms Up,
and Preference Voting/STV.  All three are improved by this new rule, but
Bottoms-Up+rule is the best because it has better proportionality than
SNTV+rule and less math than Preference Voting/STV+rule and with about the
same proportionality.

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