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

James Gilmour jgilmour at globalnet.co.uk
Fri Jan 17 11:17:27 PST 2003

Donald wrote (16 Jan)
<CUT to remove the patronising, sadly unamusing remarks.>
> James: "Donald
>  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.

You have chosen to separate three of my sentences that should (obviously) be read
together.  It was clear that my comment above had nothing to do with quotas, Hare,
Droop or any other kind.  You still seem to want to misunderstand the purpose of
an election.  It is about identifying the unique set of candidates who will
satisfy what is, in effect, the criterion you have set out above.  But to identify
that set it is not necessary to use the Hare quota, nor is it necessary to
transfer all the votes to show that if all the other candidates were excluded,
this unique set would have the support of all the voters.  That is not the purpose
of an election.  The purpose is simply to identify the relevant set of candidates.

> 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.

I said nothing about "which candidate is more representative of the voters".  What
I did say was " the purpose of the election is to identify the three candidates
who are most representative of the voters."  The meaning of this should have been
perfectly clear, ie the three candidates out of the (say) ten candidates who were
standing for election.  Once we can identify this unique set of three from among
the ten, the election is over.  Its purpose has been achieved.

> 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
> votes."
> 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.

I have never suggested that any lower number of votes makes anyone more
representative of the voters.  This is totally irrelevant to the purpose of the
election (see above).  The three candidates, each of whom has a Droop quota of
votes, are the members of the unique set.  It is irrelevant whether they have the
support of 75% (+3) of the votes or 95% of the votes.  Support beyond 75% will
make no difference whatsoever to the outcome, ie the election of those three
candidates and the defeat of all the others.

>  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.

This statement is wrong.  There is no limit on the number who can vote for any
candidate.  If three candidates each secures 30% of the first preference votes in
a 3-seat Droop STV-PR election, those three are the three winners and the count is
terminated at the end of the first stage.

> 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.'

This comment is meaningless.  Once we know who the winners are, the whole job is
done.  The purpose of the election has been achieved.

> The final transfer of votes will tell us how `representative of the voters'
> the election really turned out to be,  <CUT>

This may be interesting, but it is totally irrelevant.  We identified the unique
set of winners long ago and so avoided lots of unnecessary paper-shuffling.

> 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.

This analogy is false.  If we consider an IRV (single-seat) election, the count
stops as soon as we can identify one candidate who has secured (at least) 50% plus
1 of the votes.  The count does not go on through further stages until all other
candidates have been excluded just to see how many votes the winner secured out of
the total.  That might be interesting, but it is totally irrelevant to the purpose
of the election.

> James: "In any case, the voters will defeat you, because not all of them
> will mark all possible preferences."
> Donald:  Again, you are wrong -         <CUT>
> 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
> ballots.

Please explain how this comes about.

> 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
> votes??

This statement confirms my comment about your misunderstanding of the arithmetic
of Droop STV-PR elections.  The Droop quota for a 3-seat contest is 1/4 of the
total valid vote plus 1.  If there were 99 valid votes, the Droop quota would be
26 votes (rounding up and ignoring decimals).  If three candidates each got 33
first preference votes, the result sheet show 33 votes against the names of those
three candidates and that would be the end of the election count because those
three had each attained or exceeded the Droop quota.

I do not know where on earth you got the idea "that in a Droop election the
candidates are limited to only 25% +1 of the votes".  It is just not true, and it
is totally irrelevant to the 3 x 33% example.


> 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.

Your position is illogical.  The purpose of the election is to identify the unique
set who are most representative from among all the candidates standing.  The Droop
quota does that with less paper-shuffling, so why do more?  The Droop winners are
also the Hare winners.  The Droop quota gets you to the same place more quickly
and with significantly less work.

> In your entire letter, you did not say what was the purpose of the Droop
> Quota.

I think that purpose is perfectly clear from what I wrote.  The purpose of the
Droop quota is to identify the unique set of candidates who are the most
representative from among the set of all candidates.

> I think you know, you just don't want it to be made public that you
> support the political parties in Droop STV elections.

If you knew me, you would never have written such rubbish.  This assertion is
completely untrue.  I advocate the use of STV-PR because, of all the systems of
PR, STV is the one that minimises the parties' control and maximises the voters'

>  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.

Experience does not confirm this.  If voters want to "vote the party ticket" they
can, but they are equally able to order their preferences in any way they choose.
The "leakage" of transferred votes greatly annoys the party apparatchiks, but it
is an expression of voter power.  It results in the election of both independent
candidates  and candidates from the smaller parties.

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

Not true, if I have understood correctly what you mean by "averaging".  Practical
experience of Droop STV-PR in Northern Ireland has shown that organised
"averaging" of the support over a party's candidates can enhance its chances of
winning the last seat.

> 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.   <CUT>

What figure of speech would you apply to "Davison Quota"?

(See H R Droop, Papers of the Juridical Society, 1896)

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

If it was not clear before, it should be now (see above).

> 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.

I'm afraid there is - as you have well illustrated in your comments above.

I regret I do not understand any of your remaining paragraphs because your
comments about "averaging the votes of factions" do not appear to relate to any
implementation of STV-PR I have ever encountered.  Votes are transferred from
candidate to candidate in accordance with the preferences recorded by the voters.
Parties and organised factions are irrelevant in the counting procedure.  Party PR
will be obtained if the voters vote by party.  But if the voters choose not to
vote by party, then some other PR will be obtained, as determined by the voters.

> 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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