[EM] Re: "Complete" truncated rankings? Does Woodall give a reason?

Chris Benham chrisbenham at bigpond.com
Mon Jan 19 06:56:01 PST 2004

In response to my:

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.)"
You replied  (Sun.Jan.18, 2004):

""Should"? Why? Because Woodall says so?

Woodall, or anyone else, of course has the right to make whatever rules they 
want for a method that they propose. But any claim that truncated rankings 
should be "completed" needs justification. Just asserting a claim like that 
won't do."

"Symetric Completion" is the title of a criterion/standard that he has worded more like a standard.
The "should" is a value that is epressed 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.)
Having said that, I like the criterion. Why should a truncated ballot be treated differently from its
symetric completion? To claim that (if there are 3 candidates)that "1A truncate" isn't equivalent to
"1A 2B 2C" is absurd.What other reasonable interpretation is there? One voter likes filling in boxes
more than the other.

You continued:
"If truncated rankings were falsified in that way, changed into somethiing 
that the voter didn't vote, many would rightly object that 
ballot-modification isn't democratic."

"Falsified" is absurd. "Ballot-modification" is not exactly the right phrase. FPP (aka Plurality method)
and IRV both meet Symetric Completion.

"And, with the best methods, rankings falsified in that way would hamper 
those methods' ability to deter offensive order-reversal by defensive 

THIS is the statement that "needs justification". Condorcet completed by symetrically completed 
reversed-rankings IRV Elimination, meets Symetric Completion while WV does not. So how about a few
examples of WV doing a better job of "deterring offensive order-reversal"?

Chris Benham

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