1. To be simple enough so voters  can both use it and understand how
it is counted;
2. To minimize the wasting of citizens’ votes (see below),  and
3. To guarantee that the winner among 3 or more candidates is the
candidate most supported by at least 50% plus one (an absolute majority) of
all the citizens voting, and
4. To offer as few incentives and possibilities for voting tactical.

- Place all the grades, high to low, top to bottom, in side-by-side
columns, the name of each candidate at the top of each of these columns.
- The median-grade for each candidate is the grade located half way
down each column, i.e. in the middle if there is an odd number of voters,
the lower middle if the number is even.

Here's an attempt at a statement of Relevant Rating. I would welcome any improvements in the explanation. 1. Voters rate each candidates a rating of max rating down to 0. Blank ballots will be counted as 0 / Disapproved. Any non-zero rating is counted as approved. A ballot can contain any number of candidates at any rating level, but all equal-bottom rated candidates will be counted as 0. In other words, a ballot must disapprove at least one candidate. 2. A candidate's total approval rating on a set of ballots is the total number of those ballots rating the candidate above zero. 3. For each candidate X, imagine dividing the ballots into MAXRATE+1 piles. In each pile are the ballots rating X at rating R from MAXRATE down to zero. For a particular rating R, we can see the total vote for X at and above that rating by adding up the sizes of the piles from MAXRATE down to R. Then, looking at the ballots in the remaining piles (R-1 down to 0), look for the candidate with highest total approval. 4. If X's votes at and above a rating R exceed the highest total approval for any candidate on ballots that rate X below R, then X's relevant rating is R. 5. Starting at the top rating, see if any candidates have that relevant rating (i.e., they satisfy criterion 4). 6. If there is at least one such candidate, then see if there is among them a candidate Y for whom the total number of ballots rating Y *above* R is also greater than the highest total approval for any candidate on the ballots that rate Y below R. If so, the candidate Y with highest total number of ballots rating Y above R is the winner. Otherwise, the candidate X satisfying criterion 5 with highest total number of ballots rating X at R and above is the winner. 7. If there is no non-zero rating at which a candidate can be found who satisfies criterion 4, then the candidate with highest total approval is the winner. Here's a somewhat contrived example of an election in which Relevant Rating and IBIFA get a different result. 49: A > B 03: B > A > C 10: D > B > C 38: E > F > C 05: G > D > H Ratings of 3, 2, 1, 0. At rating 3, we see that A has 49 vs total approval C:51 on the complementary ballots, so A's relevant rating must be below 3. At rating 2, A has 51 ballots at and above rating 2, as opposed to C's approval of 48 on complementary ballots, so A's relevant rating is 2. But we see that B has 61 ballots at and above rating 2, meeting the same criterion. If we are using IBIFA, B wins with 61 vs A's 48. But using Relevant Rating, we see that A's 3-level total of 49 is greater than the total for C on ballots voting for A below 2, and B's total at rating 3 does not exceed the highest approved candidate on ballots that exclude B at 3, so A wins the RR tie-breaker. MJ and Median rating both choose B. Condorcet winner is A. Since I announced this method (as "EXACT") a year or so go, I've found a fairly natural way to extend this to quota-based multiwinner, also. If interested, I will describe details. On Fri, May 24, 2019 at 11:09 AM Ted Stern <dodecatheon@gmail.com> wrote: > Hi Chris, > > You write (emphasis mine): > > On Wed, May 22, 2019 at 5:12 AM C.Benham <cbenham@adam.com.au> wrote: > >> Steve, >> >> Earlier I responded briefly to your 4-point list: yes, yes, not >> possible,yes. >> >> To expand a bit, MJ is a Median Ratings method with a relatively >> complicated tie-breaker, *justified by I've no idea what.* >> >> Bucklin is likewise a Median Ratings method and will usually give the >> same winner, but the "tie breaker" is simple. >> > > The justification for the Majority Judgment tie breaker is that when two > candidates have the same median rating, the proper way to resolve the tie > is to look at the minimal number of ballots that must be removed to change > their median rating. So it is similar to Minimax Pairwise Margins > justification of minimal change. This tie breaker leans towards those > candidates with stronger support above the median rating. > > My privately proposed method of Relevant Ratings (formerly known as EXACT) > uses a MJ-like tie breaker with your IBIFA method to get a similar effect. > > >> An example I recently came up with to critique another Bucklin-like >> proposal: >> >> 46: A >> 03: A>B >> 25: C>B >> 23: D>B >> >> 97 ballots (majority threshold = 48) >> >> (If you want MJ-style multi-slot ratings ballots, assume that all the >> voters have given their favourite the highest possible >> rating and those that rated B above bottom all gave B the same middle >> rating and that truncating here signifies giving the >> lowest possible rating). >> >> MJ and Bucklin both rightly elect A. IBIFA and IRV also elect A. A >> is the Condorcet winner: A>B 49-48, A>C 49-25, A>D 49-23, >> A>E 49>0. >> >> A is the most Top-rated candidate: A49, C25, D23, B0, E0. >> >> So suppose the votes are counted and it is announced that A has won, but >> just before this is officially and irrevocably confirmed >> someone pipes up, "Hang on a minute, we found a few more ballots!" >> (Maybe they are late-arriving postal votes that had been >> thought lost.) >> >> These 3 new ballots are inspected and found that all they do is give the >> highest possible rating to E, a candidate with no support >> on any of the other 97 ballots. What do we do now? Laugh and carry on >> with confirming A as still the winner? No. >> >> 46: A >> 03: A>B >> 25: C>B >> 23: D>B >> 03: E >> >> 100 ballots (majority threshold = 51) >> >> Now MJ and Bucklin and any other Median Ratings method elects B. All >> methods that I find acceptable elect A both with >> and without those 3E ballots. >> >> >> To expand a bit my earlier response to your point 4, I think it's highly >> desirable for a method to meet FBC (the Favorite Betrayal >> Criterion), especially in the current US situation. >> >> >> Potentially popular candidates the mainstream media and political >> establishment doesn't like can be sunk by fake polls and >> the voters' fear of some perceived Greater Evil. >> >> They can say "Forget candidate X! X is only polling at 1 or 2%. That >> justifies us ignoring X. If you vote for X you'll just be helping >> Greater Evil win!". And their prophesy that X won't be a viable >> candidate tends to be self-fulfilling. >> >> But if the used voting method meets FBC, the voter can in response reply >> (or at least think) "Ok, maybe I have to top-rate some >> 'realistic' Compromise candidate to maximise the chance of beating >> Greater Evil, but I like X and I know that it can't possibly hurt >> me to also top-rate X so I will." >> >> If the method meets FBC no voter who knows and understands that can be >> cowed into not voting their sincere favorite at least >> equal-top. FBC is met by Approval, MJ and the currently proposed version >> of Bucklin, and IBIFA. >> >> Of those I judge IBIFA to be by far the best. IRV and all Condorcet >> methods unfortunately fail FBC. >> >> For a method that doesn't meet FBC, I consider meeting the Condorcet >> criterion to be desirable. Unfortunately all Condorcet >> methods are (to greatly varying degrees) vulnerable to Burial strategy, >> i.e. insincerely down-ranking to make a higher (usually >> top) ranked candidate win. >> >> In my humble opinion the best of the methods that are invulnerable to >> Burial is IRV. >> >> >> Chris Benham >> >> On 21/05/2019 5:16 am, steve bosworth wrote: >> >> Re: Best Single- Winner Method >> >> >> Sennet Williams, Forest Simmons, Robert Bristow-Johnson, Abd dul Raman >> Lomax, and Chris Benham have recently addressed each others’ claims >> about IRV, 3-slot Methods, IBIFA, and Asset. This discussion prompts me >> to request some help later after I have clarified several issues. >> >> Firstly, please correct me if I am mistaken but currently I am assuming >> that we all would ideally want the Best Single-Winner Method: >> >> 1. To be simple enough so voters can both use it and understand how >> it is counted; >> 2. To minimize the wasting of citizens’ votes (see below), and >> 3. To guarantee that the winner among 3 or more candidates is the >> candidate most supported by at least 50% plus one (an absolute majority) of >> all the citizens voting, and >> 4. To offer as few incentives and possibilities for voting tactical. >> >> Given these desires, currently I see Majority Judgment (MJ) as superior >> to all of the above methods on each of these counts. However, since the >> above discussions have not mentioned MJ, I assume that many contributors >> would reject this claim for MJ. This is why I would very much >> appreciate receiving any of your clarifications or explanations of how my >> claim for MJ cannot be sustained. What important flaws to you see in MJ? >> >> To help you to marshal your criticisms of MJ, please let me explain more >> full my own understandings and reasons for favoring MJ. Firstly, I see >> a citizen’s vote as being wasted *quantitatively* to the degree that it >> fails equally to help one of their most trusted candidates to win. A >> citizen’s vote is wasted *qualitatively* to the degree that it instead >> helps to elect a candidate whom they judge less *fit* for office, rather >> than an available candidate judged to be more fit. >> >> Other than in MJ, such waste is present in all the existing methods, >> whether they ask voters to rank, score, or approve as many of the >> candidates as they might wish. Of course, most dramatic is the waste >> provided by plurality or First-Past-The-Post voting. >> >> To counter qualitative waste, Balinski and Laraki (*Majority Judgment, *2010 >> MIT) argue that our capacity for judging qualities of human behavior can be >> most meaningfully expressed in an election by each voter grading each >> candidate’s suitability for office as either Excellent (*ideal*), Very >> Good, Good, Acceptable, Poor, or “Reject” (*entirely unsuitable*). These >> grades are more discerning, meaningful, and informative than merely >> expressing preferences or using numeric scores[MOU1] >> <#m_-2818294270155005541_m_-2981034959420349233__msocom_1> , X’s or >> ticks. Such grading makes it more likely that the highest quality >> candidate will be elected in the eyes of the electorate. >> >> Each candidate who is not explicitly graded is counted as ”Reject” by >> that voter. As a result, all the candidates will receiv the same number of >> evaluations, but a different set of grades from the voters. The >> Majority Judgment (MJ) winner is the one who has received grades from an >> absolute majority of all the voters that are equal to, or higher than, the >> highest *median-grade* given to any candidate. This median-grade is >> found as follows: >> >> - Place all the grades, high to low, top to bottom, in side-by-side >> columns, the name of each candidate at the top of each of these columns. >> - The median-grade for each candidate is the grade located half way >> down each column, i.e. in the middle if there is an odd number of voters, >> the lower middle if the number is even. >> >> >> If more than one candidate has the same highest median-grade, the MJ >> winner is discovered by removing (one-by-one) any grades equal in value to >> the current highest median grade from each tied candidate’s total until >> only one of the previously tied candidates currently has the highest >> remaining median-grade. >> >> Also, in contrast to the alternatives, Balinski explains how MJ reduces >> by almost half, both the incentives and opportunities for effective >> tactical voting. Thus, each voter has every appropriate incentive, not >> only to vote but to reveal their honest evaluations of each candidate. >> >> Thus, to me, using MJ should be simpler and more satisfying because >> grading many candidates is both easier and more meaningful than ranking or >> scoring them. Also, finding and comparing the median-grades of all the >> candidate is quite simple. Unlike MJ, IRV, Condorcet methods, and >> Scoring do not guarantee the election of the candidate most preferred by at >> least 50% plus one of all the citizens voting. Unlike IRV but like >> Condorcet methods and Score, MJ does not eliminate any candidate until the >> winner is discovered. >> >> Finally, I would favor the following Asset option to be added at the >> bottom of each MJ ballot: Any citizen who currently feels that they do not >> yet know enough about any of the candidates to grade them, can instead give >> their proxy vote to the Register Elector who will do this for them. They >> could do this by WRITING-IN the published code of that Registered Elector. >> >> I look forward to your comments. >> >> Steve >> ------------------------------ >> >> [MOU1] <#m_-2818294270155005541_m_-2981034959420349233__msoanchor_1>Numerical >> scores >> >> >> ---- >> Election-Methods mailing list - see https://electorama.com/em for list info >> >> >> >> <http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=emailclient> Virus-free. >> www.avg.com >> <http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=emailclient> >> <#m_-2818294270155005541_m_-2981034959420349233_DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2> >> ---- >> Election-Methods mailing list - see https://electorama.com/em for list >> info >> >

1. Voters rate each candidates a rating of max rating down to 0.
Blank ballots will be counted as 0 / Disapproved.  Any non-zero rating is
counted as approved.  A ballot can contain any number of candidates at any
rating level, but all equal-bottom rated candidates will be counted as 0.
In other words, a ballot must disapprove at least one candidate.
2. A candidate's total approval rating on a set of ballots is the
total number of those ballots rating the candidate above zero.
3. For each candidate X, imagine dividing the ballots into MAXRATE+1
piles.  In each pile are the ballots rating X at rating R from MAXRATE down
to zero.  For a particular rating R, we can see the total vote for X at and
above that rating by adding up the sizes of the piles from MAXRATE down to
R.  Then, looking at the ballots in the remaining piles (R-1 down to 0),
look for the candidate with highest total approval.
4. If X's votes at and above a rating R exceed the highest total
approval for any candidate on ballots that rate X below R, then X's
relevant rating is R.
5. Starting at the top rating, see if any candidates have that
relevant rating (i.e., they satisfy criterion 4).
6. If there is at least one such candidate, then see if there is among
them a candidate Y for whom the total number of ballots rating Y
*above* R is also greater than the highest total approval for any
candidate on the ballots that rate Y below R.  If so, the candidate Y with
highest total number of ballots rating Y above R is the winner.  Otherwise,
the candidate X satisfying criterion 5 with highest total number of ballots
rating X at R and above is the winner.
7. If there is no non-zero rating at which a candidate can be found
who satisfies criterion 4, then the candidate with highest total approval
is the winner.

1. To be simple enough so voters  can both use it and understand how
it is counted;
2. To minimize the wasting of citizens’ votes (see below),  and
3. To guarantee that the winner among 3 or more candidates is the
candidate most supported by at least 50% plus one (an absolute majority) of
all the citizens voting, and
4. To offer as few incentives and possibilities for voting tactical.

- Place all the grades, high to low, top to bottom, in side-by-side
columns, the name of each candidate at the top of each of these columns.
- The median-grade for each candidate is the grade located half way
down each column, i.e. in the middle if there is an odd number of voters,
the lower middle if the number is even.

For reference, here was my previous statement of EXACT: http://lists.electorama.com/pipermail/election-methods-electorama.com/2017-December/001646.html in my example, I misstated B's total at and above rating 2 as 61; it should have been 62. I should also note that without the irrelevant 5 G ballots, MJ chooses A (like Relevant Ratings), but MJ's winner changes to B when irrelevant ballots are added. Ted On Fri, May 24, 2019 at 12:10 PM Ted Stern <dodecatheon@gmail.com> wrote: > Here's an attempt at a statement of Relevant Rating. I would welcome any > improvements in the explanation. > > 1. Voters rate each candidates a rating of max rating down to 0. > Blank ballots will be counted as 0 / Disapproved. Any non-zero rating is > counted as approved. A ballot can contain any number of candidates at any > rating level, but all equal-bottom rated candidates will be counted as 0. > In other words, a ballot must disapprove at least one candidate. > 2. A candidate's total approval rating on a set of ballots is the > total number of those ballots rating the candidate above zero. > 3. For each candidate X, imagine dividing the ballots into MAXRATE+1 > piles. In each pile are the ballots rating X at rating R from MAXRATE down > to zero. For a particular rating R, we can see the total vote for X at and > above that rating by adding up the sizes of the piles from MAXRATE down to > R. Then, looking at the ballots in the remaining piles (R-1 down to 0), > look for the candidate with highest total approval. > 4. If X's votes at and above a rating R exceed the highest total > approval for any candidate on ballots that rate X below R, then X's > relevant rating is R. > 5. Starting at the top rating, see if any candidates have that > relevant rating (i.e., they satisfy criterion 4). > 6. If there is at least one such candidate, then see if there is among > them a candidate Y for whom the total number of ballots rating Y > *above* R is also greater than the highest total approval for any > candidate on the ballots that rate Y below R. If so, the candidate Y with > highest total number of ballots rating Y above R is the winner. Otherwise, > the candidate X satisfying criterion 5 with highest total number of ballots > rating X at R and above is the winner. > 7. If there is no non-zero rating at which a candidate can be found > who satisfies criterion 4, then the candidate with highest total approval > is the winner. > > Here's a somewhat contrived example of an election in which Relevant > Rating and IBIFA get a different result. > > 49: A > B > 03: B > A > C > 10: D > B > C > 38: E > F > C > 05: G > D > H > > Ratings of 3, 2, 1, 0. > > At rating 3, we see that A has 49 vs total approval C:51 on the > complementary ballots, so A's relevant rating must be below 3. > > At rating 2, A has 51 ballots at and above rating 2, as opposed to C's > approval of 48 on complementary ballots, so A's relevant rating is 2. But > we see that B has 61 ballots at and above rating 2, meeting the same > criterion. If we are using IBIFA, B wins with 61 vs A's 48. But using > Relevant Rating, we see that A's 3-level total of 49 is greater than the > total for C on ballots voting for A below 2, and B's total at rating 3 does > not exceed the highest approved candidate on ballots that exclude B at 3, > so A wins the RR tie-breaker. > > MJ and Median rating both choose B. > > Condorcet winner is A. > > Since I announced this method (as "EXACT") a year or so go, I've found a > fairly natural way to extend this to quota-based multiwinner, also. If > interested, I will describe details. > > On Fri, May 24, 2019 at 11:09 AM Ted Stern <dodecatheon@gmail.com> wrote: > >> Hi Chris, >> >> You write (emphasis mine): >> >> On Wed, May 22, 2019 at 5:12 AM C.Benham <cbenham@adam.com.au> wrote: >> >>> Steve, >>> >>> Earlier I responded briefly to your 4-point list: yes, yes, not >>> possible,yes. >>> >>> To expand a bit, MJ is a Median Ratings method with a relatively >>> complicated tie-breaker, *justified by I've no idea what.* >>> >>> Bucklin is likewise a Median Ratings method and will usually give the >>> same winner, but the "tie breaker" is simple. >>> >> >> The justification for the Majority Judgment tie breaker is that when two >> candidates have the same median rating, the proper way to resolve the tie >> is to look at the minimal number of ballots that must be removed to change >> their median rating. So it is similar to Minimax Pairwise Margins >> justification of minimal change. This tie breaker leans towards those >> candidates with stronger support above the median rating. >> >> My privately proposed method of Relevant Ratings (formerly known as >> EXACT) uses a MJ-like tie breaker with your IBIFA method to get a similar >> effect. >> >> >>> An example I recently came up with to critique another Bucklin-like >>> proposal: >>> >>> 46: A >>> 03: A>B >>> 25: C>B >>> 23: D>B >>> >>> 97 ballots (majority threshold = 48) >>> >>> (If you want MJ-style multi-slot ratings ballots, assume that all the >>> voters have given their favourite the highest possible >>> rating and those that rated B above bottom all gave B the same middle >>> rating and that truncating here signifies giving the >>> lowest possible rating). >>> >>> MJ and Bucklin both rightly elect A. IBIFA and IRV also elect A. A >>> is the Condorcet winner: A>B 49-48, A>C 49-25, A>D 49-23, >>> A>E 49>0. >>> >>> A is the most Top-rated candidate: A49, C25, D23, B0, E0. >>> >>> So suppose the votes are counted and it is announced that A has won, but >>> just before this is officially and irrevocably confirmed >>> someone pipes up, "Hang on a minute, we found a few more ballots!" >>> (Maybe they are late-arriving postal votes that had been >>> thought lost.) >>> >>> These 3 new ballots are inspected and found that all they do is give the >>> highest possible rating to E, a candidate with no support >>> on any of the other 97 ballots. What do we do now? Laugh and carry on >>> with confirming A as still the winner? No. >>> >>> 46: A >>> 03: A>B >>> 25: C>B >>> 23: D>B >>> 03: E >>> >>> 100 ballots (majority threshold = 51) >>> >>> Now MJ and Bucklin and any other Median Ratings method elects B. All >>> methods that I find acceptable elect A both with >>> and without those 3E ballots. >>> >>> >>> To expand a bit my earlier response to your point 4, I think it's highly >>> desirable for a method to meet FBC (the Favorite Betrayal >>> Criterion), especially in the current US situation. >>> >>> >>> Potentially popular candidates the mainstream media and political >>> establishment doesn't like can be sunk by fake polls and >>> the voters' fear of some perceived Greater Evil. >>> >>> They can say "Forget candidate X! X is only polling at 1 or 2%. That >>> justifies us ignoring X. If you vote for X you'll just be helping >>> Greater Evil win!". And their prophesy that X won't be a viable >>> candidate tends to be self-fulfilling. >>> >>> But if the used voting method meets FBC, the voter can in response reply >>> (or at least think) "Ok, maybe I have to top-rate some >>> 'realistic' Compromise candidate to maximise the chance of beating >>> Greater Evil, but I like X and I know that it can't possibly hurt >>> me to also top-rate X so I will." >>> >>> If the method meets FBC no voter who knows and understands that can be >>> cowed into not voting their sincere favorite at least >>> equal-top. FBC is met by Approval, MJ and the currently proposed >>> version of Bucklin, and IBIFA. >>> >>> Of those I judge IBIFA to be by far the best. IRV and all Condorcet >>> methods unfortunately fail FBC. >>> >>> For a method that doesn't meet FBC, I consider meeting the Condorcet >>> criterion to be desirable. Unfortunately all Condorcet >>> methods are (to greatly varying degrees) vulnerable to Burial strategy, >>> i.e. insincerely down-ranking to make a higher (usually >>> top) ranked candidate win. >>> >>> In my humble opinion the best of the methods that are invulnerable to >>> Burial is IRV. >>> >>> >>> Chris Benham >>> >>> On 21/05/2019 5:16 am, steve bosworth wrote: >>> >>> Re: Best Single- Winner Method >>> >>> >>> Sennet Williams, Forest Simmons, Robert Bristow-Johnson, Abd dul Raman >>> Lomax, and Chris Benham have recently addressed each others’ claims >>> about IRV, 3-slot Methods, IBIFA, and Asset. This discussion prompts >>> me to request some help later after I have clarified several issues. >>> >>> Firstly, please correct me if I am mistaken but currently I am assuming >>> that we all would ideally want the Best Single-Winner Method: >>> >>> 1. To be simple enough so voters can both use it and understand how >>> it is counted; >>> 2. To minimize the wasting of citizens’ votes (see below), and >>> 3. To guarantee that the winner among 3 or more candidates is the >>> candidate most supported by at least 50% plus one (an absolute majority) of >>> all the citizens voting, and >>> 4. To offer as few incentives and possibilities for voting tactical. >>> >>> Given these desires, currently I see Majority Judgment (MJ) as superior >>> to all of the above methods on each of these counts. However, since >>> the above discussions have not mentioned MJ, I assume that many >>> contributors would reject this claim for MJ. This is why I would very >>> much appreciate receiving any of your clarifications or explanations of how >>> my claim for MJ cannot be sustained. What important flaws to you see >>> in MJ? >>> >>> To help you to marshal your criticisms of MJ, please let me explain more >>> full my own understandings and reasons for favoring MJ. Firstly, I see >>> a citizen’s vote as being wasted *quantitatively* to the degree that it >>> fails equally to help one of their most trusted candidates to win. A >>> citizen’s vote is wasted *qualitatively* to the degree that it instead >>> helps to elect a candidate whom they judge less *fit* for office, >>> rather than an available candidate judged to be more fit. >>> >>> Other than in MJ, such waste is present in all the existing methods, >>> whether they ask voters to rank, score, or approve as many of the >>> candidates as they might wish. Of course, most dramatic is the waste >>> provided by plurality or First-Past-The-Post voting. >>> >>> To counter qualitative waste, Balinski and Laraki (*Majority Judgment, *2010 >>> MIT) argue that our capacity for judging qualities of human behavior can be >>> most meaningfully expressed in an election by each voter grading each >>> candidate’s suitability for office as either Excellent (*ideal*), Very >>> Good, Good, Acceptable, Poor, or “Reject” (*entirely unsuitable*). These >>> grades are more discerning, meaningful, and informative than merely >>> expressing preferences or using numeric scores[MOU1] >>> <#m_1116843553331214489_m_-2818294270155005541_m_-2981034959420349233__msocom_1> >>> , X’s or ticks. Such grading makes it more likely that the highest >>> quality candidate will be elected in the eyes of the electorate. >>> >>> Each candidate who is not explicitly graded is counted as ”Reject” by >>> that voter. As a result, all the candidates will receiv the same number of >>> evaluations, but a different set of grades from the voters. The >>> Majority Judgment (MJ) winner is the one who has received grades from an >>> absolute majority of all the voters that are equal to, or higher than, the >>> highest *median-grade* given to any candidate. This median-grade is >>> found as follows: >>> >>> - Place all the grades, high to low, top to bottom, in side-by-side >>> columns, the name of each candidate at the top of each of these columns. >>> - The median-grade for each candidate is the grade located half way >>> down each column, i.e. in the middle if there is an odd number of voters, >>> the lower middle if the number is even. >>> >>> >>> If more than one candidate has the same highest median-grade, the MJ >>> winner is discovered by removing (one-by-one) any grades equal in value to >>> the current highest median grade from each tied candidate’s total until >>> only one of the previously tied candidates currently has the highest >>> remaining median-grade. >>> >>> Also, in contrast to the alternatives, Balinski explains how MJ >>> reduces by almost half, both the incentives and opportunities for effective >>> tactical voting. Thus, each voter has every appropriate incentive, not >>> only to vote but to reveal their honest evaluations of each candidate. >>> >>> Thus, to me, using MJ should be simpler and more satisfying because >>> grading many candidates is both easier and more meaningful than ranking or >>> scoring them. Also, finding and comparing the median-grades of all the >>> candidate is quite simple. Unlike MJ, IRV, Condorcet methods, and >>> Scoring do not guarantee the election of the candidate most preferred by at >>> least 50% plus one of all the citizens voting. Unlike IRV but like >>> Condorcet methods and Score, MJ does not eliminate any candidate until the >>> winner is discovered. >>> >>> Finally, I would favor the following Asset option to be added at the >>> bottom of each MJ ballot: Any citizen who currently feels that they do not >>> yet know enough about any of the candidates to grade them, can instead give >>> their proxy vote to the Register Elector who will do this for them. They >>> could do this by WRITING-IN the published code of that Registered Elector. >>> >>> I look forward to your comments. >>> >>> Steve >>> ------------------------------ >>> >>> [MOU1] >>> <#m_1116843553331214489_m_-2818294270155005541_m_-2981034959420349233__msoanchor_1>Numerical >>> scores >>> >>> >>> ---- >>> Election-Methods mailing list - see https://electorama.com/em for list info >>> >>> >>> >>> <http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=emailclient> Virus-free. >>> www.avg.com >>> <http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=emailclient> >>> <#m_1116843553331214489_m_-2818294270155005541_m_-2981034959420349233_DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2> >>> ---- >>> Election-Methods mailing list - see https://electorama.com/em for list >>> info >>> >>

  From: steve bosworth <stevebosworth@hotmail.com>

The best single-winner method probably depends on the particular election and also the limitations of how it can be run. If, for example, an election for some position could be run over the internet, then what I would regard to be the best method would not be the same as for an election for public office where people turn up to vote in person on a particular day. For such an internet election, I like the following: Score voting, but where the current total/average is available to see and continuously updated, and where people are able to change their vote as many times as they like. Obviously you could end up with a lot of people withholding their vote until right near the end or completely changing it to prevent people from optimising their tactical vote, so I would suggest a couple of things to limit the effect of this. The deadline to set your initial vote could be earlier than the deadline to change your vote, and the end time for changes could be non-deterministic. For example, voters might have nine days to cast their initial vote. Then there would be one guaranteed extra day where votes can be freely changed (they can also be changed within the initial nine days). After that the election would end randomly with a half life of two hours. So if you were organising such an election there would be three variables to set. This avoids the problem of score voting that people wouldn't know how to rate their second favourite candidate etc. because they can see how the candidates are doing. And it would have the advantages of score voting that the results are clear and easy to understand (as it's just a total or average) and that it isn't subject to weird unexpected paradoxes that most voting methods we talk about have (e.g. Condorcet methods can have cycles and fail participation). Strength of preference would matter but with voters more aware of what to do so that later-no-harm failures wouldn't be at so much risk of happening. In the following example involving honest score ballots (scores out of 10): 49 voters: A=10, B=0, C=149 voters: A=0, B=10, C=12 voters: A=9, B=8, C=10 C would be the Condorcet winner but is really a non-entity. Under normal score voting (where voters cannot change votes), C would have no chance of winning. Under this method, it's very unlikely that there would be anywhere near enough tactical voting to get C anywhere near close enough to winning, so it keeps the advantages of score voting and enhances it in terms of giving the voters knowledge of how to vote tactically, but without throwing the baby out with the bathwater and going full pairwise. Toby From: steve bosworth <stevebosworth@hotmail.com> To: EM list <election-methods@electorama.com> Sent: Monday, 20 May 2019, 20:46 Subject: Re: [EM] Best Single-Winner Method #yiv0883059675 P {margin-top:0;margin-bottom:0;}Re: Best Single- Winner Method Sennet Williams, Forest Simmons, Robert Bristow-Johnson, Abd dul Raman Lomax, and Chris Benham have recently addressed each others’ claims about IRV, 3-slot Methods, IBIFA, and Asset.  This discussion prompts me to request some help later after I have clarified several issues.Firstly, please correct me if I am mistaken but currently I am assuming that we all would ideally want the Best Single-Winner Method: - To be simple enough so voters can both use it and understand how it is counted; - To minimize the wasting of citizens’ votes (see below), and - To guarantee that the winner among 3 or more candidates is the candidate most supported by at least 50% plus one (an absolute majority) of all the citizens voting, and - To offer as few incentives and possibilities for voting tactical.