[EM] Symmetric ICT reformulation and exploration

[Forest Simmons]

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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