# [EM] Re: "Completion" & falsification

Chris Benham chrisbenham at bigpond.com
Thu Jan 22 07:45:02 PST 2004

```Kevin,
Thank you for your contribution to this thread (Wed. Jan.,2004). It was
very well put and  I agree with it completely.
I especially liked :

"According to the mentality of Symmetric Completion (criterion),
two voters voting A=B>C>D should have exactly the same effect as one of
the two voting A>B>C>D and the other voting B>A>C>D.

If Mike thinks this is flawed thinking, it would be interesting to hear
what he thinks the difference in effect should be."

One of the reasons that I didn't refer to an example like that is that my quote from Woodall

"Symetric Completion.
A truncated ballot should be treated in the same way as its symetric
completion. (The symetric completion of a ballot is obtained by
replacing it by all possible completions of it with equal weight chosen
so that the total weight is 1. For example,if there are five candidates
a,b,c,d,e, then the symetric completion of a ballot marked ab consists
of six ballots, each with weight 1/6, marked abcde, abced, abdce,
abdec,abecd, and abedc.)"

only refers to truncated ballots and I hadn't got around to trying to explain the early
equal-preferences version. You once mentioned
"Incidentally, Woodall calls "Symmetric-Completion" the ability to treat equal
equal rankings (or at least truncation) as equivalent to an equal mixture of every
possible strict ordering.  He speaks of methods passing or failing this standard..."

Chris Benham

```