[EM] uses of truncation

[Dave Ketchum]

i.m.voter says:  Why bother?

I care:
      Whether my Plurality thoughts are easy to express when those are my 
thoughts - often happens when voting for such as dogcatcher.
      Whether I can easily express my more complex thoughts that can 
happen when voting for such as governor.  Condorcet is capable; Range 
seems more complex than I need.

Throwing rocks:
      My first impression was that trunc was a complication to the 
Approval ballot - which I claim would disqualify it as Approval - also, 
would it impose more pain than its gain justifies?
      Looking closer, it seems to be a complication in processing 
Approval ballots - no big deal for paper ballots, but old voting machines 
offer no way to extract such info.

I AM NOT trying to restrict such exploration as follows; only to question 
its value.

DWK

On Thu, 15 Mar 2007 17:29:02 -0700 (PDT) Forest W Simmons wrote:
> Various methods that make use of approval have alternative versions 
> that use truncation as the approval cutoff.
> 
> This suggests the concept of a virtual candidate "trunc" that is ranked 
> below the lowest ranked real candidate on each ballot, but above any 
> (and all) truncated candidates.
> 
> How could trunc  be used?
> 
> As mentioned before trunc could be used as an approval cutoff.
> 
> What else?
> 
> Suppose trunc is included with the other candidates in some method like 
> Beatpath, and trunc  turns out to be the method winner.  Then ... (fill 
> in the blank).
> 
> Speaking of Beatpath, for each real candidate C, let C(1) be the 
> strength of the strongest beatpath from C to trunc.  Let C(2) be the 
> strength of the strongest beatpath from trunc  to C.  The winner is the 
> real candidate C for which the difference  C(2)-C(1) is the largest, 
> i.e. for which C(1)-C(2)  is the smallest.
> 
> UncTrunc:
> 
> If trunc is uncovered, then the real candidate that has the greatest 
> pairwise opposition to trunc is the winner, i.e. the candidate that is 
> ranked on the greatest number of ballots wins in this case.
> 
> Else initialize a list with trunc, and as long as the current top 
> member T of the list is uncovered, add to the top of the list the 
> candidate (from among those that cover T) that scores the most pairwise 
> votes against T.  The candidate that ends up at the top of the list is 
> the winner.
> 
> Note that X covers trunc iff X beats every candidate that is ranked on 
> fewer than half of the ballots.
> 
> If trunc is uncovered, then every real candidate X is beaten by some 
> real candidate Y that is ranked on fewer than half of the ballots.  But 
> this can happen only if X is also ranked on fewer than half of the 
> ballots.  Which means that X is also beaten by trunc.  In other words, 
> if trunc is uncovered, then trunc is the beats all candidate.
> 
> Forest
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  davek at clarityconnect.com    people.clarityconnect.com/webpages3/davek
  Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
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