[EM] Ranked Ranks

Forest Simmons fsimmons at pcc.edu
Thu Jun 6 14:19:32 PDT 2019

Great Suggestion!

I was just thinking what the possibilities would be in the four slot case:

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

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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