[EM] Symmetric ICT reformulation and exploration

Sat Nov 12 13:32:29 PST 2016

Yes, that 2/3 majority rule would avoid having to say:

"(If each candidate has someone rated over hir by a majority, then the
winner is the most top-rated candidate.)"

Tantalizingly greater simplicity, regrettably not workable, as you said.

ICT would avoid the Mono-Add-Plump criticism, but at the cost of
truncation-vulnerability.
I'd rather have the Mono-Add-Plump criticism and truncation-proofness.

The ICT wording you described comes closer to the brevity of MDDTR, but
MDDTR doesn't need a separate "beat" definition at all. ...just the use of
the already-understood majority.

I suggested the 3-slot version of MDDTR because I felt that it should be
used only as an Approval-version, with the Middle rating reserved for the
special chicken-dilemma situation.   ...because I felt that MDDTR, with its
complete vulnerability to burial (like every pairwise-count method),
wouldn't be good as a rank-method.

But maybe that should be reconsidered. Why would it be worse to rank your
inbetween candidates in order of preference, than to rate them all together
at middle?

The burial-vulnerability, the fact that "wv-like" didn't mean as much as
I'd believed it did,  was such a disappointment that it at first made me
not appreciate the fact that MDDTR still has truncation-resistance. Burial
vulnerability isn't a complete disaster:

For one thing, to bury the CWs, you have to know who is the CWs. And if you
know it, then the defending wing knows it too, because the same predictive
information is available to everyone.

If the CWs is more  with your wing, and it's the opposite wing that
dislikes the CWs, and is likely to bury, you can prevent successful burial
by equal-top-ranking the CWs. That was pointed out a long time ago, as
general pairwise-count defensive strategy.

You could protect the CWs in that way in Bucklin too. (in case people might
rank past the CWs).

Of course the difference is that, in Buclin you & the others in your wing
can also just avoid ranking past the CWse (expected or evident CWs).

MDDTR, and pairwise-count methods in general, don't have that protection,
and you only have the defensive strategy of equal-top-ranking the CWse.

So, as regards protection of the CWs, Bucklin is better than the
pairwise-count methods. MDDTR's tradeoff-advantage is its CD.  ...in return
for being able to protect the CWs only by equal-top-ranking.

Conditional Bucklin's and Conditional Approval's FBC failure is of a
different kind than Condorcet's FBC failure, it seems to me. With
Conditional Bucklin, the effectiveness of my equal-top-ranking isn't
diminished by the FBC failure. The FBC failure merely gives me a trick that
I could use, with sufficient predictive information, to gain advantage. Not
a problem. But the problem is that the serious overcompromiser would still
have incentive to rank Hillary alone at top, over the overompromiser's
favorite. So I guess I reluctantly have to not advocate Conditional Bucklin
or Conditional Approval.

...meaning that evidently Bucklin can't have CD, and MDDTR's CD is an
advantage for MDDTR over Bucklin.  So it's MDDTR's CD vs Bucklin's easier
protection of the CWs.

All that time I was calling wv burial-deterrent, because of the 3-candidate
example, where deterrence is achieved by merely not ranking the would-be
buriers' candidate, I never considered a 4-candidate example.

It's easy to make a 4-candidate example where, in wv (& in MDDTR), that
defense won't work: If B is the CWs, and the A voters are going to bury by
insincerely ranking C over B, then just add D, between B and C.

The halfway point between D & C is of course way C-ward from the median,
and so D will have a majority against C, if voters are
uniformly-distributed. (...and probably could, with suitable
distance-relations, even if the voter-distribution is Gaussian).

So, when the A voters make B majority-beaten, by ranking C over B, C
remains majority-beaten (by D), and so now everyone is majority-beaten, and
A wins if s/he's the most top-rated.

I haven't looked at what it would take for A to win in wv, because I no
longer propose wv for official public political elections (or any where
offensive strategy is likely). That would be something for a wv advocate to
discuss.

Maybe I should list, together, some relative advantages of Bucklin & MDDTR:

Bucklin:

* Easier protection of the CWs (relevant if one of your inbetween might be
the CWs)

* Use-precedence

MDDTR:

* CD

* LNHa

* Precinct-Summability

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As for Bucklin's easier protection of the CWs, I'm not entirely sure,
because there's some reason for the individual to rank all of the best
candidates (instead of only ranking down to the CWse), to improve,
somewhat, the probabiliy of electing one of them (but not as much as
equal-top-ranking them all). So I don't know if Bucklin's easier protection
of the CWs would materialize..

Michael Ossipoff

Michael Ossipoff

Maybe a toss-up. Bucklin has the use-precedence advantage, but MDDTR has
the precinct-summability adantage. And I consider MDDTR's LNHa an advantage
too, when you don't have to hesitate to append less-liked inbetweens to
your ranking for fear that you'll help the beat better candidaes.

In Bucklin, when skipping is permitted, you could make sure that, above
some inbetween, you skip enough levels that the better candidates will have
enough rounds to accumulate the coalescing lower-choices that are coming to
them from other candidates' preferrers.

In MDDTR, & maybe in Bucklin, I'd likely top-rate the CWse, along with the
very best of the strong top-set, even if s/he isn't really among those, and
even if I felt like down-rating some of that top-set a bit because of some
fault, or because of likely defection-inclination of their voters.

On Sat, Nov 12, 2016 at 2:56 PM, Forest Simmons <fsimmons at pcc.edu> wrote:

> Perhaps we could modify (non-symmetric) ICT in order to have a less wordy
> definition of "strongly beat."
>
> Candidate X *strongly beats* candidate Y iff  X is preferred over Y on
> more ballots than Y is* ranked* equal to or above X.
>
> All strongly beaten candidates are disqualified unless that would
> disqualify all of them.
>
> Elect the qualified candidate ranked top on the most ballots.
>
> This definition makes it slightly harder for X to strongly beat Y than in
> standard ICT, because all equal rankings have to be overcome, not only
> those at the top.
>
> But it changes nothing in our standard CD examples, because in those
> examples there are no equal rankings (only equal truncations, which don't
> contribute to the strongly beat definition).
>
> It should preserve the FBC and perhaps even introduce a stronger property:
> if some candidate X is raised to the level of the winner on some ballots,
> then the winner is unchanged unless the new winner is X.
>
> I see the wisdom in saying "disqualified" instead of "eliminated."  If we
> said "eliminated," then some people would wrongly think that "favorite"
> refers to the highest among the remaining candidates (after their original
> favorite was stricken from the ballot).
>
> Also a comment about three slot methods in general:
>
> With three slots it is impossible for every candidate to be eliminated by
> a two-thirds majority.  So the following method would be even simpler to
> define in the context of 3 slot ballots:
>
> Elect the favorite candidate who is not beaten by a two-thirds majority.
>
> Of course, for all practical purposes that would be the same as "elect the
> candidate ranked top on the greatest number of ballots," which doesn't
> satisfy the CD criterion.
>
>
> On Sat, Nov 12, 2016 at 9:07 AM, Michael Ossipoff <email9648742 at gmail.com>
> wrote:
>
>> Yes, but ICT defines "beat" in a wordier way, that people hear as
>> complicated.
>>
>> For people who are into voting-systems, I can say "majority-beaten", &
>> they know what I mean...that I'm talking about pairwise defeats.
>>
>> So, here's how I'd define 3-Slot MDDTR, to the public:
>>
>> You rate each candidate as  "Top", "Middle", or "Bottom". If you don't
>> rate someone, that counts as rating hir at Bottom.
>>
>> The winner is the most    favorite candidate who doesn't have anyone
>> rated over hir by a majority.
>>
>> (If everyone has someone rated over hir by a majority, then the winner is
>> the most favorite candidate.)
>>
>> (end of definition)
>>
>> I'd just call it " Majority Disqualification".
>>
>> Michael Ossipoff
>> On Nov 11, 2016 4:39 PM, "Forest Simmons" <fsimmons at pcc.edu> wrote:
>>
>>> You wrote in part ...
>>>
>>> >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.
>>>
>>> Three slot ICT could be defined in the same way;
>>>
>>> Elect the most favorite candidate who isn't strongly beaten.
>>>
>>> Neither definition tells what to do when every candidate is beaten
>>> (majority beaten or strongly beaten, respectively).  But that is just a
>>> detail of the definition that doesn't have to be mentioned immediately.
>>>
>>> Here's a more complete definition that works in both cases:
>>>
>>> Eliminate all candidates that are {majority, strongly} beaten unless
>>> that would eliminate all candidates.  Elect the most favorite among the
>>> remaining.
>>>
>>> So ordinary ICT and MDDTR are equally easy to define.  It's a matter of
>>> which has the best properties.
>>>
>>
>
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