[EM] Truncation error in STV

Olli Salmi olli.salmi at uusikaupunki.fi
Mon Aug 4 05:01:03 PDT 2003


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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