[EM] Two New STV Features - New to Me; Exhausted votes
Craig Carey
research at ijs.co.nz
Sun Nov 21 21:44:32 PST 1999
Mr Donald Davison wrote this towards Mr Catchpole, referring to STV:
At 02:54 21.11.99 , Donald E Davison wrote:
...
>David Catchpole wrote: "That's Droop with the addition of districts-
...
> You are in error, ... It is not Hare that can do the same, it is
>the exhausted ballots that can cause candidates to be elected with less
>than a quota in either Hare or a Droop election.
>
> The only proper way to compare Hare to Droop is to conduct any test
>without exhausted ballots.
The following message attempts to uncover the idea of an "exhausted ballot".
----------------------------------------
In a 26 September 1999 Mr Davison sent in a message replying to
"Steve". The message, reproduced in full below, comments on a what
happened in the third stage of the "European Parliamentary Election for
3 MEPs in the Northern Ireland Electoral Region, held on
Thu, 10 Jun 1999".
I attempt in this message to show what Mr Donald Davison means by the
words "exausted ballots", and why they are bad and why voters need to
fill in a full paper rather than STV being amended or improved, or a
better version being selected.
The September 1999 message by Mr Donaldson, is about how the transfer
values that are calculated by this formula:
the surplus divided by the number of transferable votes
It is more common in STV methods, for the transfer value to be calculated
by this:
the surplus divided the voting papers.
The message being replied to is about the transfer in the 3rd stage
of the votes owned by Ian Paisley.
Ian Paisley's surplus was stated to be 23,059; the first preference
votes were said to be 192,762; and the transferrable votes were
said to be 158,539. There were therefore 34,223 non-transferable votes.
The transfer was noted to be 0.14. Note that
(23,059/158,539) = 0.145446.
The transfer value ought be nearer 1 unless it were an aim to reduce the
power of votes to affect outcomes during transfers.
Mr Davison wrote this:
> If this were a normal STV election, the second order of business after
... the transfer value would equal 0.1196242 ...
> 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.
Mr Davison might have been writing about a STV system that is used
somewhere else. In Northern Ireland, are transferred to the candidates
marked on the papers. That implies that no allegation of a "mind set"
was successfully made about leaders of Northern Ireland.
Hopefully the "European Parliamentary Election" in Northern Ireland, clips
the transfer value down to 1.
This is what can go wrong when the transfer value is not clipped down
to 1. Some papers get too much influence [influence can be said to be their
ability to counter papers with no 2nd preference]:
STV, two winners, three candidates, A and C win:
A 670
AC 10
B 320
Total = 1000
Quota = 333.33 (approx)
The surplus for A = (680-333.33) = 346.67
Transferable votes = 10
Transfer value = (Surplus divided by Transferable votes) = 34.667
The AC papers then are made to have the weight 346.67.
The transfer occurs
B 320
C 346.67
The winners are A and C.
------------------------------------------------------------------
Note: Find the 2 IFPP winners of this 2 winner election:
A 670
AC 10
B 320
If the system was IFPP, then the election would proceed this way:
C -0
B -320
A -670
AC -10
B can win since its -320 exceeds the 1/3 quota which is -333.33..., so
the Alternative Vote is applied inm this case, and the winner is C,
so the two winners of the original 2 winner problem are A and B.
------------------------------------------------------------------
Condorcet can be imagined to have transfer values, and those values
would be 0 or 1. The value 0.14 is a better transfer value than 0.11,
say.
At 00:48 26.09.99 , Donald E Davison wrote:
>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
Mr G. A. Craig Carey, research at ijs.co.nz
Auckland, New Zealand.
Snooz Metasearch: <http://www.ijs.co.nz/info/snooz.htm>
More information about the Election-Methods
mailing list