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).

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@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 >

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@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@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 >> >

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@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@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@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 >>> >>

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@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@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@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@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 >>>> >>>

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@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@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@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@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@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 >>>>> >>>>

Right On! Misunderstandings can be a great source of ideas. On Thu, Jun 6, 2019 at 5:03 PM Ted Stern <dodecatheon@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@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@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@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@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@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 >>>>>> >>>>>