[EM] Classifying 3-cand scenarios. LNHarm methods again.

[Juho]

The same logic applies also to the Condorcet criterion. We all  
probably agree on what terms "Condorcet criterion", "Condorcet  
method", "Condorcet-complying method" are intended to refer to. Term  
"Condorcet" might refer to any of these or maybe to Marquis de  
Condorcet (in the EM framework). If one wants to be exact it is good  
to use the longer versions like "Condorcet criterion". On the other  
hand I'm perfectly happy with common use of the shorter version  
"Condorcet" whenever it is obvious from the context what the intended  
meaning is.

I'm also ok with referring to "Condorcet method" as one particular  
election method. The definition is not complete since this does not  
define what the result is when there is a "circular tie" / top cycle.  
Condorcet methods are a rich family of methods but on the other hand  
for some purposes they are all similar enough to be referred to just  
as one single method.

Also more accurate descriptions of Condorcet methods may be  
incomplete. Copeland's method is known to lead to ties more often than  
many other Condorcet methods. Or Condorcet methods may not be exact in  
the sense that they are themselves families of methods. For example  
the Schulze method is described in Wilipedia so that it covers also a  
margins based version in addition to the winning votes based version.  
We however typically consider term "Schulze method" to be exact enough  
(may refer to the beatpath style of determining the winner or maybe by  
default to the winning votes based version). Most defintions don't  
specify what one should do in case of an exact tie (maybe lottery,  
maybe elect two, maybe arrange a new election, maybe use some  
additional criterion).

I think Dave Ketchum's comment on clones and Condorcet methods was  
also quite ok. In a typical election there is no top cycle and in that  
situation all Condorcet methods are equal and they all handle clones  
very well. In this kind of use term "Condorcet method" might refer to  
the behaviour when there is no top cycle or alternatively e.g. to the  
behaviour of the typical (fully specified) Condorcet methods.

Juho



On Apr 21, 2010, at 10:05 PM, Chris Benham wrote:

> Dave Ketchum wrote 17 April 2010:
>
> "First, quoting Wikipedia:
>> A Condorcet method is any single-winner election method that meets
>> the Condorcet criterion, that is, which always selects the Condorcet
>> winner, the candidate who would beat each of the other candidates in
>> a run-off election, if such a candidate exists. In modern examples,
>> voters rank candidates in order of preference. There are then
>> multiple, slightly differing methods for calculating the winner, due
>> to the need to resolve circular ambiguities—including the Kemeny-
>> Young method,Ranked Pairs, and the Schulze method. Almost all of
>> these methods give the same result if there are fewer than 4
>> candidates in the circularly-ambiguous Smith set and voters
>> separately rank all of them.
>
>
> I have heard this complaint before, so am listening for help.
>
> WHAT should I say when I want EXACTLY what is described as "Condorcet"
> above?"
>
> Dave,
> The Wikiipedia piece you quote doesn't say *the* Condorcet method. It
> says "A Condorcet method..".
>
> So you couuld say that, or "a Condorcet-complying method".
> You asked "Will not Condorcet attend to clones with minimum pain?"
> Plain "Condorcet" won't do anything except elect a voted CW if
> there is one.
> Some Condorcet-complying methods are clone-proof and some aren't.
> Chris Benham
>
>
>
> On Apr 17, 2010, at 9:25 PM, Markus Schulze wrote:
>> Hallo,
>>
>> Dave Ketchum wrote (18 April 2010):
>>
>>> Why IRV? Have we not buried that deep enough?
>>> Why not Condorcet which does better with about
>>> the same voting?
>>>
>>> Why TTR?  Shouldn't that be avoided if trying
>>> for a good method? TTR requires smart deciding
>>> as to which candidates to vote on.
>>>
>>> Will not Condorcet attend to clones with minimum
>>> pain? Voters can rank them together (with equal
>>> or adjacent ranks).
>>>
>>> Does not Condorcet properly attend to "symmetric"
>>> with a voted cycle?
>>
>> In my opinion, "Condorcet" refers to a criterion
>> rather than to an election method.
>>
>> Markus Schulze
>
>
>
>
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