[EM] Olli - Your Truncation error in STV:

[Donald Davison]

Olli - Your Truncation error in STV:

Dear Olli Salmi, you wrote: "Could somebody please explain this to me?  Why
is "about (number of digits in total votes)+1"  implied? What are the
complexities elsewhere?"

Donald here:  The fractional transfer of votes can draw a fine line between
the candidates that should be elected and the candidates that should not be
elected, but the lost of votes due to the dropping of decimals can move
that line and elect a different candidate somewhere in the calculations.

If we are to have the vote sums of each candidate have an accuracy to 0.001
of a vote, then the transfer value will have to contain more decimal places
because the effect of decimals is going to be increased the more the
tranfer value is multiplied, but I do not agree with this Wichmann that the
number should be based on total votes.  Most votes in a STV election are
never transferred.  My thinking is that it should be based on only the
number of papers of the candidate with the surplus.

An extreme example would be if only one fractional part of a vote was to be
transferred.  In that case we would only need three decimal places in the
transfer value in order to maintain three decimal places in the accuracy of
the candidate's vote sum.

Three decimal places in the candidates' vote sums would reduce any error
down to less than one thousandth of a vote.  In order to maintain this
accuracy, the transfer value will need more places because it is multiplied
times the number of papers, hence any error will also be multiplied.  The
transfer value will need three plus the number of digits of the papers.
Example: If there are 25,000 papers held by the candidate with the surplus
votes then the transfer value needs three plus five decimal places in order
to keep the error in the candidates' sums down to one thousandth of a vote.
Any less decimals will not do the job correctly.

The complexities mentioned by Wichmann may be in the hand counting of an
election, but there are hand calculators that can handle more decimal
places, so that should not be a problem.  Complexities may merely mean that
people just don't like to deal with decimals.  The trouble with decimals
for some people is that these people often get the point in the wrong
place.  They like to take an easy solution and not have anything to do with
decimal places, get rid of them, and that is just what some jurisdictions
do, they drop any fractional part of any transfer so that all candidate
sums are kept in whole numbers - so much for accuracy.

Regards, Donald

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[Full text of Olli's post}  Date: Mon, 4 Aug 2003 14:48:49 +0300

A quote from "A review of the ERS97 rules" by B A Wichmann, Voting
matters, Issue 10, March 1999

"5. The calculation of the quota and the recording of
transfers appears to give the impression of
undertaking computations to one hundredth of the
vote. However, this is not achieved, since that
accuracy requires that the transfer values are
computed to a greater accuracy. Indeed, if p votes are
transferred, then there is a truncation error of at most
p/100, which implies that transfer values should be
computed to about (number of digits in total votes)+1
digits. I do not believe that an arithmetic approximation
which can lose a whole vote is acceptable
since the voter could reasonably equate the loss to his/
her vote. Unfortunately, the rules depend upon
(number of papers)*(transfer value) in hundredths of
a vote, so it is difficult to increase the accuracy
without complexities elsewhere. Hence I conclude
that this problem is inherent in this type of rule and
could be seen as a defect in ERS97."

Could somebody please explain this to me?
Why is "about (number of digits in total votes)+1"  implied? What are
the complexities elsewhere?

Olli Salmi
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