# [EM] Symetric Completion equals "falsification"?

Chris Benham chrisbenham at bigpond.com
Tue Jan 20 07:24:02 PST 2004

```  Quoting Woodall (in the context of equal preferences not being allowed
except for truncation),

"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.)"

"Symetric Completion" is the title of a criterion/standard that he has worded more like a standard.
The "should" is a value that is expressed by the standard, not Woodall himself.
(Woodall is not big on "justifying" standards/criteria, but rather in showing which combinations
are possible and which are not.)

Mike Ossipoff (Tue.Jan.20,2004):
"A guess: Does a method meet that criterion if it gives an unchanged result
after a truncated ballot is "symetrically completed"?"

That is my interpretation. The Woodall quote above is the only definition I have seen.

Let me try to restate some points more clearly. If there are three candidates ABC and two voters
show up to vote, and both have A as their first preference and are indifferent between B and C,
[1]A
[ ]B
[ ]C
[1]A
[2]B
[2]C
then in my humble opinion, it is common-sense (and reasonable) for those two voters to expect that
their votes would  have the same effect ("be treated in the same way", as Woodall puts it).
If the method allows equal early preferences, then it is unfair (and in my opinion absurd and very
bad) that a faction of voters that all vote a set of candidates above all other candidates should
be advantaged or disadvantaged (at least on average) by voting equal preferences.
I think of this "Decisiveness Fairness Standard" as being linked (at least in principle) to SC.

MO:" If a ranking doesn't give support to a particular candidate, could it be that the voter didn't
want to give support to that candidate?"

What exactly does "give support" mean? That phrase smacks of confusing ranking with rating. Pure
ranking is not about "giving support" to candidates; it is only about voting candidates over other
candidates. Therfore, assuming that you accept  that a ranked candidate has been voted over all the
unranked candidates, "not ranked" and "ranked equal last" is in effect the same thing and therfore a
"symetrically completed" ballot has not in any meaningful sense been "falsified".

Chris Benham

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