[EM] Ranked Ranks

[Forest Simmons]

Right On!

Misunderstandings can be a great source of ideas.

On Thu, Jun 6, 2019 at 5:03 PM Ted Stern <dodecatheon at gmail.com> wrote:

> Hi Forest,
>
> I realize that I mis-read your original suggestion, but in the process I
> may have come up with a different idea:
>
> Say a set of ballots looks like
>
> x: A > B > C > D
> y: B > D > C > A
> z: C > A > D > B
>
> with x > y > z
>
> Then start with the order of A, B, C, based on the first place ordering.
>
> Add in the second level ratings (as in ER-Bucklin-ratings), and compute
> pairwise, then do Sorted Margins based on the first round scores (first
> rating only).
>
> Continue adding in more rating levels, using the margins from the previous
> round for Sorted Margins.
>
> Stop when all ratings have been handled.
>
> This would be the same as your suggestion if a 5 slot method were
> implemented as A > B >> C >>> D (>>>> E disapproved), with all explicit
> ratings considered approved.
>
>
> On Thu, Jun 6, 2019 at 2:19 PM Forest Simmons <fsimmons at pcc.edu> wrote:
>
>> Great Suggestion!
>>
>> I was just thinking what the possibilities would be in the four slot case:
>>
>> A>B>>C>>>D
>> A>B>>>C>>D
>> A>>B>C>>>D, etc.
>>
>> Six possibilities if all of the symbols are of different strength.
>>
>> If they are allowed to be the same strength, then it looks like 27
>> possibilities.
>>
>> A lot to think about.
>>
>> On Thu, Jun 6, 2019 at 1:13 PM Ted Stern <dodecatheon at gmail.com> wrote:
>>
>>> Forest, using the (n-1) stage approvals is an excellent suggestion.
>>>
>>> The motivation would be that the higher preferences should be more
>>> meaningful when adjusting the overall ranking.
>>>
>>> When a CW exists, it will always sift up to the top, so the method is
>>> Condorcet.  Similarly, a clone set even if cyclic, should also sift to its
>>> appropriate rank, so the method is clone independent.
>>>
>>> But if there is a pairwise cycle, priority is given first to higher
>>> ballot preference.  In terms of burial resistance, it is interesting that
>>> this method is actually more resistant when there is no CW than when there
>>> is.
>>>
>>> I wonder what would happen if the pairwise sorting step used the
>>> Tied-at-Top FBC-compliant pairwise test instead of straight pairwise ...
>>>
>>> On Thu, Jun 6, 2019 at 12:55 PM Forest Simmons <fsimmons at pcc.edu> wrote:
>>>
>>>> Ted,
>>>>
>>>> Your question is a good one, and I am open to suggestions.
>>>>
>>>> If we started out with the approval order (i.e. respecting the
>>>> strongest rank symbols), and then introduce the next strongest symbols for
>>>> detecting out of order pairs, ASM suggests we use approval margins, i.e.
>>>> the margins based on the rankings of stage one to decide which pair we
>>>> should reverse.
>>>>
>>>> What if we continue in that vein, in stage three we use the margins
>>>> from stage two to decide on which out-of-order adjacent pair to attend to
>>>> first?
>>>>
>>>> In stage n we use the margins from stage (n-1) to decide which
>>>> out-of-pairwise order (detected (by the stage n rank symbols) to fix first.
>>>>
>>>> To me that seems like the most natural generalization of ASM in the
>>>> Ranked Ranks context.  But it may not be the optimal solution.
>>>>
>>>> Forest
>>>>
>>>> On Thu, Jun 6, 2019 at 11:02 AM Ted Stern <dodecatheon at gmail.com>
>>>> wrote:
>>>>
>>>>> Hi Forest!
>>>>>
>>>>> This is an interesting method.  It adds a Bucklin-like flavor to
>>>>> Approval Sorted Margins (
>>>>> https://electowiki.org/wiki/Approval_Sorted_Margins), which I like
>>>>> very much.
>>>>>
>>>>> By sorting pairwise, what sort do you want to use?  Are you using the
>>>>> ASM method of looking for the smallest margin and then continuing the next
>>>>> smallest margin until finished?  If so, what is the margin between?  There
>>>>> are several options.
>>>>>
>>>>> I suspect that if you just use total votes at and above the round's
>>>>> rating level, you will run into irrelevant ballot problems unless you use
>>>>> some variant of IBIFA. Perhaps you could use the highest total approval for
>>>>> a candidate on ballots not ranking X as their relevant opposition score.
>>>>>
>>>>>
>>>>> On Wed, Jun 5, 2019 at 7:54 PM Forest Simmons <fsimmons at pcc.edu>
>>>>> wrote:
>>>>>
>>>>>> I don't want to detract from the glory of Improved Copeland with
>>>>>> another post, but here goes:
>>>>>>
>>>>>> A recent suggestion of Kevin was to start with all of the ranks in
>>>>>> place, and then to flatten more and more ranks (in a certain order) until a
>>>>>> ballot CW emerges.
>>>>>>
>>>>>> Here's a way to do it in the opposite order:
>>>>>>
>>>>>> "Annealing"
>>>>>>
>>>>>> Start with only the strongest rank symbols in place.
>>>>>>
>>>>>> This gives an approval order.
>>>>>>
>>>>>> Add in the next strongest rankings, to sort the approval list
>>>>>> pairwise.
>>>>>>
>>>>>> Then add in more rankings, and sort again.
>>>>>>
>>>>>> etc.
>>>>>> Until all of the rankings are used in the final sort.
>>>>>>
>>>>>> I call it "annealing" because it is like the process of compactifying
>>>>>> the molecules in a piece of metal by repeated partial heatings and coolings.
>>>>>>
>>>>>> It could also be called the resistant starch method, because
>>>>>> re-heating and cooling cooked rice or baked potatoes adds additional
>>>>>> resistant starch (up to a point).
>>>>>> ----
>>>>>> Election-Methods mailing list - see https://electorama.com/em for
>>>>>> list info
>>>>>>
>>>>>
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