[EM] Rarity, FBC, Condorcet, comparison of criteria

[Dave Ketchum]

Mike O had written:
> We often hear about how Condorcet, but not Approval, lets you help  
> Favorite against
> Compromise.
I agree, but not with Mike O's many words.  He offers one special case  
- I will try to be general as to the ideas, but base my thoughts on  
Plurality, Approval, and a sample Condorcet method.

Starting with the example Mike O provides below, C is Worse, A or B is  
Favorite, and remaining candidate, B or A, is Compromise.

Any of the three, as well as many other methods, can be used to vote  
for a single candidate:
.     A
.     B

Approval or Condorcet can vote for more than one with equal approval  
or ranking:
.      AB

Condorcet can vote for 1-to-many at each of multiple ranks, with each  
preferred over all but those given the same or a higher rank by the  
same voter:
.     A>B
.     B>A

Condorcet allows voting for both A and B, while showing preference for  
the preferred candidate.

On May 8, 2012, at 1:33 AM, Richard Fobes wrote:
> On 5/7/2012 11:10 AM, Michael Ossipoff wrote:
>> Yeah? How about this, then?:
>>
>> 27: A>B (they prefer A to B, and B to C)
>> 24: B>A
>> 49: C  (indifferent between everyone other than C)
>
> Cases that require carefully chosen numbers, as this example does,  
> become less important than patterns that occur over many elections.

His discussion involved multiple voters considering cooperating -  
possible, but such discussion is not practical when electing such as a  
governor.  A Condorcet voter - notice the ranking implied for the  
voting - can use any ballot variation I describe above.

A Condorcet voter can choose among AB, A>B, and B>A in response to  
what ever his studying and/or debating leads to.
>
> You pointing out a weakness that can only occur in rare cases is  
> quite different than, say, what happened in Burlington and Aspen  
> where IRV declared a non-Condorcet winner after only one (or perhaps  
> just a few?) elections.

IRV requires decisions based only on whatever is weakest top choice on  
each ballot - usually proper loser, but true unwanted requires  
considering all that each voter votes.
>
> Mike, if you really want to elevate FBC above the Condorcet  
> criterion, I suggest that you start by noticing that it is the only  
> voting criterion in the Wikipedia comparison table that does not  
> link to a Wikipedia article about the criterion (and such a link is  
> also missing from the text section just above the table).  I'll let  
> other election-method experts debate with you on Wikipedia if you  
> choose to add a Wikipedia article about FBC.
>
> As for comparing FBC to Condorcet, have you not noticed that other  
> debates about which criteria is more important than another criteria  
> typically end up being inconclusive because mathematics supports the  
> recognition that no single voting method is objectively "best"?

And FBC cannot happen with Approval, for those ballots do not have the  
information for FBC to consider.
>
>
> As I've said on this forum before, some studies should be done to  
> compare _how_ _often_ each method fails each criterion.  Those  
> numbers would be quite useful for comparing criteria in terms of  
> importance.  In the meantime, just a checkbox with a "yes" or "no"  
> leaves us partially blind.
>
> (I changed the subject line because the subject line is not intended  
> to be used to specify who you are writing to.  The subject line  
> should indicate the topic.)

Good point!  Also important to say when they posted it, for readers to  
look back to the previous post.
>
> Richard Fobes
Dave Ketchum