[EM] Two New STV Features - New to Me
Donald E Davison
donald at mich.com
Sat Sep 25 04:48:49 PDT 1999
Greetings,
I received a letter that contained information on the Northern Ireland
election. This information revealed two STV features which are new to me.
* The first feature is the elimination of some of the lowest candidates
before surplus votes are transferred.
* The second feature is a policy that takes the surplus votes that
would become exhausted, if transferred to the above eliminated candidates,
and gives that share of the surplus to the remaining candidates.
I will now forward, in two parts, the information on the Northern
Ireland election. If you do not understand the text in the parts, have no
fear, I will explain the same in different words and in more detail after
each part.
Donald,
- - - - - - - - Part One Forwarded - - - - - - - - -
Steve wrote:
The election below might be of interest to you. It is the European
Parliamentary Election for 3 MEPs in the Northern Ireland Electoral
Region, held on Thu, 10 Jun 1999.
No. of electors = 1,197,307 Votes Polled = 687,573 (57.71%)
Valid Votes = 678,809 Invalid Votes = 8,764
No. of Representatives to be elected = 3
Electoral [Droop] Quota = 169,703
1st Stage - First Preference Votes: (below)
2nd Stage - Transfer of lowest candidates' votes: (below)
(Anderson, Ervine, McCartney, Neeson)
Total after second stage transfers: (below)
Anderson Natural Law 998 -998 -
Neeson Alliance 14,391 -14,391 -
McCartney UK Union 20,283 -20,283 -
Ervine Progressive Unionist 22,494 -22,494 -
McLaughlin Sinn Féin 117,643 1,709 119,352
Nicholson Ulster Unionist 119,507 43,120 162,627
E2 Hume SDLP 190,731 190,731
E1 Paisley Democratic Unionist 192,762 192,762
Non-transferable 13,337 13,337
------ ------
Totals 678,809 678,809
Anderson, Ervine, McCartney and Neeson were excluded from the election
at the 2nd Stage, before the transfer of Paisley's surplus, because the
total of the two surpluses (23,059 plus Hume 21,028 = 44,087) was less
than the difference between the total votes credited to those candidates
(58,166) and the candidate next above (McLaughlin 117,643), being
59,477. The surpluses were not liable to be transferred first,
therefore, because Anderson, Ervine, McCartney and Neeson would have
continued to be the first four candidates for exclusion. This rule is
designed to simplify and speed up the count.
- - - - - - - end of part one - - - - - - - - - - - -
Donald: I have long argued that it is possible to eliminate more than one
candidate at one time in the run-off routine of election methods like STV
and/or Alternative Vote, as long as the total votes, of the eliminated
candidates, is less than the votes of the next lowest candidate.
It did not occur to me to eliminate candidates before the transfer of
Surplus Votes, but it can be done and it has been done in this real
election.
The math that allows this to be done is as follows:
Lowest Candidates Votes
1st Lowest, Anderson 998
2nd Lowest, Neeson 14,391
3rd Lowest, McCartney 20,283
4th Lowest, Ervine 22,494
Surplus Votes of Hume 21,028
Surplus Votes of Paisley 23,059
--------
Total 102,253
5th Lowest, McLaughlin 117,643
The total of the votes of the four lowest candidates plus the surplus
votes of Hume and Paisley is an amount that is less than the votes of
McLaughlin, the next and 5th lowest candidate.
It is mathematically impossible for any one of the four lowest
candidates to be able to surpass McLaughlin in votes, even if one of the
four were to receive all the votes from the other three plus all the
surplus votes. Therefore, it is acceptable to eliminate these four
candidates before the transfer of surplus votes. Doing so reduces the math
of this election.
We cannot eliminate the fifth lowest candidate, McLaughlin, because
the new total, which includes his votes, is larger than the votes of the
sixth lowest candidate, Nicholson.
Total 102,253
5th Lowest, McLaughlin 117,643
-------
Total 219,896
6th Lowest, Nicholson 119,507
While I accept the eliminations of the four lowest candidates before
the transfer of surplus votes, I cannot accept what happens next.
- - - - - - - - Part Two Forwarded - - - - - - - - - - - -
3rd Stage - Transfer of Paisley's Surplus:
E2 Hume 190,731
McLaughlin 32.90 119,384.90 Runner-up
E3 Nicholson 22,162.56 184,789.56
E1 Paisley -23,059.00 169,703
Non-transferable 863.54 14,200.54
----------
TOTALS 678,809
Northern Ireland rules (manual count)
Count commenced at 0900 hrs on 14 Jun 1999
Count completed at 1930 hrs on 14 Jun 1999
Comment--
The quota is: Valid votes 678,809/(3 + 1 = 4) = 169,702.25 = 169,703.
Rev. Ian Paisley's surplus was transferred at the 3rd Stage as follows:
Surplus of 23,059, divided by the number of first preference
votes he received (192,762) = 0.119624199
The transfer value of his
transferable papers, therefore, was probably 0.12, or 0.13.
Confirmation of Paisley's transfer value:
In fact, the transfer value was 0.14. The surplus of 23,059,
less the non-transferable remainder of the surplus (863.54) =
22,195.46/0.14 = 158,539 transferable papers, of which 158,304
(× 0.14 = 22,162.56) were transferred to Jim Nicholson and 235
(× 0.14 = 32.90) were transferred to Mitchel McLaughlin.
The main reason why the transfer value was higher than
might have been expected, is that 34,223 of Paisley's first preference
votes were non-transferable (compared to 14,762 in 1994), due in part to
the fact that many of them would have passed over second and subsequent
preferences given for the four excluded candidates, to become
non-transferable. The division of the surplus by a lower number of
transferable papers, therefore, produced a higher quotient.
Hope this helps. Regards Steve
- - - - - - - - end of part two - - - - - - - - -
Donald: It took me awhile to understand what is happening in the above
text. If I am in error, I hope someone will correct me.
Again I will explain in different words and in more detail.
The key sentence in the text of the second part is the last sentence,
as follows: "The division of the surplus by a lower number of transferable
papers, therefore, produced a higher quotient."
This sentence tells us that the policy in this election is that the
fractional division is based on only the transferable ballots and not on
all the ballots. Paisley only had 158,539 transferable ballots, therefore
the transfer value under these rules would be 0.1454468 (23,059/158,539).
It appears that the election only used 0.14 of that value. Maybe their
policy is to round down to two places.
If this were a normal STV election, the second order of business after
counting all the first preferences would be to transfer Paisley's surplus
votes. That would be done either by Randon Transfer or Fractional Transfer.
Fractional Transfer has been used in this election. If the fractional part
of 0.1196242 is taken from each of the 192,762 ballots and transferred to
the next preferences of each ballot, then we will have transferred a total
of 23,059 surplus whole votes. Paisley will be left with 169,703 votes, a
full quota.
The division of Paisley's surplus votes, if this were a normal STV
election, would be as follows:
Nicholson 158,304 times 0.1196242 = 18,936.99
McLaughlin 235 times 0.1196242 = 28.11
Non-transferable 34,223 times 0.1196242 = 4,093.90
------- ---------
Paisley & Total 192,762
less quota - 169,703
---------
Surplus Votes 23,059 23,059
The votes that are deemed to be non-transferable are from ballots that
end up on one of the four eliminated candidates or on Hume, who already has
a quota of votes. These 4094 votes would become exhausted, if this were a
normal STV election.
But, this is not a normal STV election. In this election the transfer
value was increased to 0.14, this results in less votes being exhausted and
more votes being transferred.
The mind set of the people in charge of the North Ireland election
seems to be that if votes cannot be transferred to their intended
candidates, then the votes are fair game to be transferred to some other
candidates, even if these other candidates were not preferences on the
ballots in question.
I see this policy as corruption.
The voters of these ballots did not include these two remaining
candidates as one of their preferences, and yet these fractional parts are
being transferred to these two remaining candidates.
If the correct transfer value were used, as would be in a normal STV
election, then candidate McLaughlin would have only received 18,937 whole
votes, a lessor difference of 3000+ votes. This difference would not have
changed this election, but in another election, in which the third and
fourth candidates are closer, this difference could change the results.
This seems to be a policy to give extra votes to the candidates that
receive the most votes in the transfer of surplus votes. This aids
candidates of the larger factions because larger factions will have the
most surplus votes.
STV is a very good election method and many people in the election
reform movement say good things about STV, but what they do not tell us is
that STV has Dirty Little Secrets.
The Droop Quota is one of the Dirty Little Secrets of STV.
This feature of basing the fractional part on only the transferable
votes is another Dirty Little Secret of STV.
Both these Dirty Little Secrets were designed to aid the larger faction
at the expense of the smaller factions, so that maybe, just maybe, the
largest faction will be able to form a government, a task that should not
be expected of a representative body.
The people should elect an executive officer directly and the
representative body should be allowed to merely be a representative body.
Regards,
Donald
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