James--
I'll adopt your convention of putting the speaker's name before a colon, to indicate who said what.
One reason why that's convenient is because many of the "James:"s and "Mike:"s are already there before I copy and reply.
Mike (said):
And
one way of defining the strength of that majoritly pairwise preference has to
do with how big a majority that is. Completely arbitrary, of course :-)
James (said):
Not arbitrary, but also not the only valid way to define it.
Mike:
But, as I already said in the message to which you're replying, it wasn't possible to define it in every way, and use all those deinitions when I use the term, and so it was necessary to choose just one way to define it.
James:
Another way to define the strength of a majority preference is the size of the majority times the strength of the preference on each ballot comprising the majority. This is the definition given by cardinal weighted pairwise, and it has an equally valid claim to be a definition of majority preference strength.
Mike:
If you're talking about majority preference, then you aren't talking about majority rule, because my majority rule definition involves majority pairwise votes, rather than majority pairwise preferences.
Majority pairwise preferences are used in my definition of defensive strategy. For that purpose, I'm interested in how many prefer X to Y, because if a majority prefer X to Y, then it's possible to make some guarantees about what they won't have to do in order to keep Y from winning. Siimple as that. For that purpose, there's no need for me to get into the matter of how intensely they prefer X to Y, because the mere fact that they all prefer X to Y is sufficient to give them the power to keep Y from winning without, with the guarantee that they won't need certain degrees of drastic strategy to do so, with complying methods.
That's why I define majority pairwise preferences (MPPs) as I do.
But itsn't it true that majority rule is what you're really more interested in here? In that case, you're questioning my definition of majority pairwise votes (MPVs) rather than my definition of MPPs.
But it's for a similar reason that I define MPVs in terms of a majority voting X over Y, instead of the intensity with which a majority vote X over Y. Becasue the mere fact that they vote X over Y makes it possible to say things about what should or shouldn't happen. I'm talking about majority rule as the term is usually understood and used. If a majority votes X over Y, then electing Y violates majority rule, unless that MPV is nullified. And what could nullify an MPV other than it being in a cycle whose other MPVs are at least as large as it is? Hence my definition of majorilty rule.
Look, you know I have no quarrel with Cardinal Pairwise, and when it saves the CW by violating majorilty rule, violating an un-nullified MPV, that's an MPV based on dishonest voting. I completely agree that it's a good thing to violate majorilty rule in that instance, via the preference-intensity voting that CP collects and uses.
There's no need to quibble about what majority rule means. I'm just telling you what it means to most people when they use the term. My defintion merely copies the term's accepted meaning.
That's all my defintion attempts to do. I had no intent to write a new definition, but rather only intended to put into words the usual accepted meaning of majority rule.
James:
Lately, I have been defining majority rule violation as the selection of
an option outside the Smith set.
Mike:
The Smith set has nothing to do with majority.
James:
It has everything to do with majority. The Smith set is the smallest set of candidates who are preferred by a majority to every candidate outside the set.
Mike:
No, I'm sorry, but that isn't the definition of the Smith set. There are two things wrong with that definition: 1) It speaks of majority; 2) It speaks of preference instead of votes.
Here's the definition of the Smith set:
The Smith set is the smallest set of candidates such that every candidate in that set pairwise-beats every candidate outside that set.
[end of Smith set definition]
How can any discussion get anywhere when terms are used in a way so different from their accepted definition?
Maybe you want "majority" to mean a majority of those voting a preference between X and Y. But then "majority defeat" justs becomes another word for "pairwise defeat". In other words, majority loses its meaning, the "more than half of the voters" meaning that it has in its accepted use. Additionally, a set of voters consisting of more than half of the voters is a set of voters for whom certain strategies can be guaranteed. That's my interest in majority.
James:
If you pick a non-Smith candidate, you are needlessly ignoring a majority preference.
I reply:
Not at all. Maybe, due to truncation, someone is out of the Smith set because of a sub-majority defeat.
James:
Hence it is necessary to chose from the Smith set in order to guarantee that no majority preference will be unnecessarily ignored.
Mike:
Not at all, if someone is out of the Smith set due to a sub-majority defeat.
James:
I think that the Smith set is the narrowest majority rule definition we can make that stands some chance of gaining general consensus.
Mike:
...except that the Smith set isn't a majority rule definition.
James:
Of course it is, in the following sense: If a voting method chooses a non-member of the Smith set, I say that it has violated majority rule. If a method chooses a member of the Smith set, I say that it has upheld majority rule.
Mike:
Oh, ok, if you define majority rule as the Smith set, then, by your defintiion, it is. But, by the usual definition of the Smith set, and by the accepted meaning of majority, it is not.
James:
If a voting method always elects a member of the Smith set, I call it a strong majority rule method. I argue that this definition is meaningful and useful.
Mike:
That definition is completely at odds with the accepted definition of the Smith set and the accepted definition of majority.
It's possible to write definitions that don't contradict already-widely-accepted definitions.
James, I don't criticize you because you're new to this subject. CP is a perfectly good idea, a good Condorcet enhancement, and probably meets the criteria that I judge methods by. But, for some reason, in voting system discussion, some people new to the subject arrive with some degree of arrogance--the notion that they have it right, and that someone else has been wrong all this time.
Well, ok, I claim that lots of others have been wrong about some things, but I thoroughly defend those claims. All I'm saying, James, is that when you're new to a subject, be a little more tentative with your statements. Don't express them in the form of assertions that you're sure that someone else is wrong. Not till the discussion has gone on long enough for you to be able to make such claims with assurance.
Do you see that your definition of the Smith set suggests that you're a little premature with your statements about who is wrong?
James:
Mike:
I have to object to the defeat strength part of your definition, in part on the behalf of cardinal pairwise. Winning votes is surely one way to define defeat strength, and it is not a bad one, but I do not accept it as the one and only definition
I have never said that wv is the only way to define defeat strength.
Perhaps you would like me to define defeat strength in all of the possible ways. Forgive me, but it seemed best to only define it in one way, and, if it's
ok with you, I chose wv.
James:
My contention is that there is no basis on which to define it in only one way. You can do so if you want, but you shouldn't expect other people to accept your definition.
Mike:
...then I should define it in every possible way, and, then, when I speak of pairwise defeat strength, use every possible definition of it? Does that sound to you like a good idea?
What I (would like to) expect others to accept is that wv makes certain guarantees about strategy that aren't possible without wv. And that wv avoids overruling unnecessarily many individual paiirwise votes, when overruling a publicly-voted pairwise defeat. And that the magnitude of a majority defeat is most meaningfully measured by the number of people who favor that defeat.
But no, I don't expect anyone to accept that wv is the only possible way to define defeat-strength, because it obviously is not. The best isn't necessarily the only.
Mike:
You don't say how you'd rather define the magnitude of a majority pairwise vote. Margins?
James:
No. When it comes to choosing an actual method, I prefer the defeat strength definition that CWP gives. When it comes to defining majority rule for general purposes, I prefer to leave defeat strength out of the definition, i.e. to define majority rule compliance as choosing from the Smith set.
I reply:
I've answered your statement about the Smith set being a majority rule definition.
About CP as a way to judge pairwise defeat-strength, fine. Whatever is useful. Remember that usefulness is part of the reason I like wv. If CP is useful, then it's useful to measure defeat-strength as CP does. I've never denied that, and I don't now deny it. Are we aguing about something that don't disagree on?
Mike:
But why is that important to you, how many people accept my definition of majority rule.
James:
If you don't care if anyone accepts it, why bother posting it on a discussion list?
Mike:
This is unbelievable. I've just finished telling you, in the message to which you're "replying", why I post definitions of terms that I use. But I'm going to repeat it again for you, just one more time:
I post definitions of terms that I use because telling what you mean by the terms that you use is part of saying what you want to say.
Someoe's acceptance or non-acceptance of those definitions is something that, I must admit, had never occurred to me. Tell me if you don't know what I mean, but I don't know what it means for you to tell me that you don't accept those MPV, MPP, majority rule, or defensive strategy definitions.
Yes, I really should put all these answers into a FAQ, so that I can just post the FAQ when these questions and objections are repeated.
James:
By doing so, you are implicitly asking for others' feedback.
Mike:
I always welcome feedback. But please, out of respect for yourself, consider your feedback more carefully.
James:
If you don't care if anyone adopts your criteria, you might as well not mention them to other people.
Mike:
Wait--were we talking about criteria definitions? Please note that my defensive strategy and offensive strategy defintiions aren't used in my criteria definitions. And that my MPV, MPP, and majority rule definitions aren't used in my criteria definitins.
Yes, the broad name that I give to my criteria is "defensive strategy criteria", and that makes it good to have a definition of defensive strategy.
As for caring about if anyone accepts what I say, as a way to decide whether to say it, I can't say that I agree with you. I say what I want to say because, for some reason, I want to. But, as I've repeated here again and again, I'm not interested in the outcome. I couldn't care less what anyone else does or doesn't do with anything that I've proposed to them. That isn't my department.
Having said that, of course I answer objections to my criteria, because that's part of proposing the criteria.
But you aren't, in the message to which I'm now replying, objecting to criteria, are you?
But, since you mentioned that subject, here are several grounds on which you can object to my criteria:
1. You don't consider important the goal of getting rid of the lesser-of-2-evils problem, or the goal of minimizing the need for favorite-burial, and other defensive strategies that conceal or reverse people's preferences. I'm not being sarcastic here: I've been told by a few people on EM that that isn't important to them. Fine.
2. You don't believe that my criteria measure for accomplishment of the abovementioned goal, and can tell us why.
3. You claim that my criteria aren't well-defined, and can show us an example where, with some method, preferably a proposable method, one of my criteria doesn't unambiguously say whether not that method fails the criterion in that example.
Go for it.
Mike Ossipoff
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