[EM] Kevin, 8 April, '05, 0533 GMT

[Kevin Venzke]

Mike,

I don't consider it useful to not consider Plurality a ranked method. I've
explained that in the past. I know you have a different view.

 --- MIKE OSSIPOFF <nkklrp at hotmail.com> a écrit : 
> But consider this example:
> 
> AB66, BC51, CA51
> 
> The Beatpath Criterion that you quoted doesn't say that B shouldn't win. It
> nullifies the AB66 defeat because there's a majority beatpath from B to A.
> 
> But why should just any majority beatpath nullify a majority defeat? 

Why shouldn't it? In any case, the electorate hasn't returned a clear decision.

> Shouldn't it have to be a beatpath consisting of defeats at least as large?

Why?

I don't think there's any popular concept of "stronger majority" that needs
to be fitted into the term "majority rule."

> I suggest that a defeat isn't nullified unless it's in a cycle with defeats 
> that are all at least as large as it is.

I'm not so fond of this suggestion for practical reasons: It creates a
Later-no-harm problem that doesn't exist when all majority-strength defeats
are considered equal.

> Kevin continued:
> 
> If this criterion is too strong (although I doubt you think so), then I'd
> suggest Minimal Defense: When a majority rank X>Y and Y over no one, then
> Y mustn't win.
> 
> I comment:
> 
> Is that Steve's Minimal Defense, or is it Kevin's Minimal Defense?

Steve has offered that "nearly equivalent" version, but adds that the method
must allow every possible preference order to be voted.

> Then, in addition to that definition of the verb "rank", there should be an 
> explicit statement that the criterion applies only to rank methods. 
> Otherwise Plurality passes because no failure example can be foiund. Paul's 
> "A pork-chop passes" loophole.

That was Chris who said that.

> I have no idea what that means. What Kevin says above wouldn't be a crime 
> against majority rule, but it could be a violation of majority rule, 
> depending on what Kevin's method is. More details would be needed before one 
> could say whether that method violates majorilty rule.

Ok, the method is "CDTT,FPP." That is, elect the candidate with the most first
preferences for whom the following is true: When some other candidate has a
majority-strength beatpath to him, then he also has a majority-strength beatpath
to the other candidate. Equal ranking and truncation are permitted.

This method fails your definition of "majority rule" if I've understood it.

> Kevin says:
> 
> An advantage of using Minimal Defense rather than Smith is that you don't
> have to use terms like "innermost," "minimal," "pairwise," or even "beats."
> 
> I comment:
> 
> I can't speak for Kevin's definition of the Smith set, but my definition of 
> the Smith set doesn't use the word "innermost" or "minimal". And though it 
> uses "beats", I define "beats".

> The sincere Smith set is the smallest set of candidates such that every 
> candidate in that set is publicly preferred to every candidate outside that 
> set.

Well, if you use Minimal Defense instead of Smith then you don't need to use
terms like "smallest set" or "preferred" (when referring to a pairwise win)
or even "set."

> The word "innermost" is used in my definition of the Schwartz set. In that 
> definition, I clearly state what an innermost unbeaten set is. Keven also 
> forgot to tell us why it's a disadvantage for a Schwartz set definition to 
> use "innermost".

Because it's easier to explain to someone.

> Though Kevin doesn't say it there, Kevin also thinks that it's an advantage 
> for a criterion to not use the word "prefer". That's one reason why Kevin 
> pointed out Steve's criteria that are counterparts to my majority defensive 
> strategy criteria. What Kevin perhaps doesn't know is that, of those 3 
> criteria of Steve's that are counterparts to the majority defensive strategy 
> criteria, 2 of those 3 use the word "prefer" in their defintion, just as do 
> the majorilty defensive strategy criteria.

First of all, I don't know why you singled out the word "prefer."

Secondly, I use the term "Minimal Defense" rather than "SDSC" because Steve
Eppley has offered a votes-only wording of Minimal Defense. I don't have any
particular comment on his official wordings.

> Steve's Minimal Defense may be on of those. Someone might want to look up 
> Steve's definition of Minimal Defense, to find out if Kevin has written his 
> own Minimal Defense.

Does this mean you've lost the URL to Steve Eppley's website?

> Kevin says:
> 
> I begin to think that Minimal Defense slash SDSC would be more popular if
> they had been named without reference to defensive strategy. Those criteria
> are very useful even if no offensive strategy is possible.
> 
> I comment:
> 
> But I don't agree that it would be good to name the majorilty defensive 
> strategy criteria without reference to defensive strategy--because defensive 
> strategy is what they are about.

My concern is that people won't understand the term "defensive strategy."
In the process of explaining what that is, you might have also to explain
"offensive strategy."

But it seems to me that it's better to present votes-only Minimal Defense
as a criterion dealing simply with electing the "best" winner, according
to principles of majority rule.

Kevin Venzke



	

	
		
__________________________________________________________________
Découvrez le nouveau Yahoo! Mail : 250 Mo d'espace de stockage pour vos mails ! 
Créez votre Yahoo! Mail sur http://fr.mail.yahoo.com/