[EM] Symmetric ICT reformulation and exploration

Michael Ossipoff email9648742 at gmail.com
Fri Nov 11 10:20:58 PST 2016


My version of Symmetric ICT had a problem. It might have been that it no
longer avoided chicken dilemma. So I withdrew my Symmetric ICT proposal,
and went back to advocating ordinary ICT.

Your version isn't simple, but it will be interesting to study.

This is just a preliminary note.

One thing that I'd like to add about 3-Slot MDDTR:

Another advantage that it has over 3-Slot ICT is that 3-Slot MDDTR has a
much simpler definition:

The winner is the most favorite candidate who isn't majority-beaten.

That's a brief enough definition to be proposable, even as a first reform
from Plurality. But admittedly it lacks use-precedent.

Michael Ossipoff




On Thu, Nov 10, 2016 at 4:47 PM, Forest Simmons <fsimmons at pcc.edu> wrote:

> Here's my reformulation of Symmetric ICT:
>
> Ballots are ranked preference style with equal rankings allowed,
> especially at top and bottom, with bottom as default.
>
> Let the notation [phi(X,Y)] mean the number of ballots on which the
> formula phi(X,Y) is satisfied, so that, for example, [X=Y=Top] is the
> number of ballots on which X and Y are ranked equal Top.
>
> Definition:
> X strongly beats Y
>        if and only if
> [X>Y] - [Y>X] > max(0, [X=Y=Top] - [X=Y=Bottom])
>
> Step 1.  Eliminate all strongly beaten candidates unless that would
> eliminate all candidates.
> Step 2.  Among the candidates remaining after step 1, elect the candidate
> ranked Top on the greatest number of ballots.
>
> Is that an accurate restatement of Symmetric ICT?
>
> If it is I would like to make one suggestion to make it even more
> symmetrical, namely ...
>
> Step 2'.  Among the candidates remaining after step 1, elect the candidate
> X with the greatest value of  [X=Top] - [X=Bottom].
>
> I don't think it will worsen the Later-no-help failure.
>
> Of course, then we would have to change the name to something like
>
> IC(TmB), Improved Condorcet (Top minus Bottom).
>
> Does this comply with CD?
>
> 45 C
> 30 A>B
> 25 B>A
>
> Candidate A is elected as the only unbeaten candidate.
>
> If the B>A faction defects by truncating A ...
>
> 45 C
> 30 A>B
> 25 B
>
> then no candidate is unbeaten.  The respective Top minus Bottom scores for
> the respective candidates A, B, and C, are
>
> 30 - 70 = -40
> 25 - 45 = -20, and
> 45 - 55 = -10,
>
> so C is elected.
>
> However, if we reduce C's faction slightly and increase B's faction, we
> can produce a CD failure:
>
> 41 C
> 30 A>B
> 29 B
>
> The Top - Bottom scores are
> 30 - 70 = -40
> 29 - 41 = -12
> 41 - 59 = -18,
> so the B faction benefits from its defection.
>
> So the ICT version appears to be better even though it is not quite as
> symmetrical in its definition as IC(T-B).
>
>
>
>
> ----
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>
>
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