[EM] Symmetric ICT reformulation and exploration

[Michael Ossipoff]

{Replying farther down) :

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?
>

Yes, with just a re-arrangement of terms...except that I don't remember the
max operator in it.

You mention that your modification of Symmetric ICT fails CD, as the
original Symmetric ICT version does.

Ordinary original ICT is the best ICT version.

But I claim that 3-Slot MDDTR is better than 3-Slot ICT, because of its
truncation-resistance for the demoted candidate.

Michael Ossipoff



>
> 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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