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

[Kevin Venzke]

Chris said:
> "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.)"
>  
> Mike replied  (Sun.Jan.18, 2004):
> 
> ""Should"? Why? Because Woodall says so?
> 
CB:
> "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.)

That being true, I wonder if meeting SC brings any other advantages to the table.

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

It's true that FPP and IRV (and Margins) incidentally meet SC.  But it's easy
to imagine people complaining about those of Woodall's methods which enforce
SC compliance, such as SC-DC (Symmetrically-Completed Descending Coalitions).
(DAC and DSC are identical when all ballots strictly rank all candidates.)

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

No doubt Mike is thinking of Margins here.

The question for Chris' method must be: Will you sometimes have incentive to
defensively order-reverse?  And would WV require it under the same circumstances?


Kevin Venzke
stepjak at yahoo.fr


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