[EM] uses of truncation
davek at clarityconnect.com
Thu Mar 15 21:41:16 PDT 2007
i.m.voter says: Why bother?
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.
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
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.
> 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.
davek at clarityconnect.com people.clarityconnect.com/webpages3/davek
Dave Ketchum 108 Halstead Ave, Owego, NY 13827-1708 607-687-5026
Do to no one what you would not want done to you.
If you want peace, work for justice.
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