[EM] Truncation error in STV

[Dgamble997 at aol.com]

Olli Salmi wrote

"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?"


What Brian Wickham was trying to do here ( and I admit to not finding this 
the most interesting article ever in Voting Matters ) was suggest how ERS97 (the 
current version of Newland-Britton) could be rewritten in terms of the 
drafting rules of the ISO (International Standardisation Organisation). I believe he 
worked for ISO at one point.

The point he was trying to make is that ERS97 gives the impression that vote 
totals are accurate to 0.01 votes and that in fact they are not.

Take the following example: 

A surplus of 20 votes is to be transferred. This surplus arises from a 
candidate achieving a quota after having 45 votes transferred to him/her. Each vote 
is transferred at a value of 0.44 to 2 decimal places to the next candidate. 
19.8 votes are transferred not 20, 0.2 votes are lost due to rounding to 2 dp. 
In order to obtain accurate totals to 2 dp individual votes must be taken to 
3,4 or more dp.( 0.4444 X 45 =  19.998).

Are you glad you asked this question ?

David Gamble
    
    

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