[EM] Is there a criterion for identical voters casting identical ballots?

[Dave Ketchum]

How did we get here?

You talk of a method in which ONE voter can say BOTH A>B AND B>A.

Assuming such a method could claim useful value to justify the headaches 
of implementing it and making it understood, I have seen nothing to 
suggest Condorcet might have such an ability.
     In Condorcet the sum of all the ballots in an election can be a 
combination of some voters voting each preference in a way to, 
collectively, create a cycle - a problem to solve but not a feature to 
brag about.

You also use the word "loops" in a manner I do not understand.

DWK

On Sun, 17 Dec 2006 21:40:02 +0200 Juho wrote:
> I thought mostly use scenarios where the favourite candidate is not  
> involved in the cycles and the voters know very little about the  
> anticipated results. Another example in this direction would be  
> situation where there are n parties that each have 3 candidates.  Voters 
> would then vote so that they first put their own candidates in  the 
> front (in some order (ffs)) and then the other parties in the  order of 
> preference but arranging the individual candidates within  the parties 
> so that they will form cycles (between each others within  the parties).
> 
> Note btw that this failure of FAVS (as Warren Smith named it) is not  
> really related to the calculation process of the Condorcet methods  but 
> to the ballot style. In the typical ballots voters give the  candidates 
> a linear order, which prevents them giving cyclic  preferences. If they 
> were able to give cyclic preferences then all  voters could vote the 
> same way.
> 
> In principle (to be general) one could allow voters to fill a matrix  
> instead of giving a linear order. This would make it possible to use  
> also cycles and all kind of partial orderings. A related topic is the  
> tied at the top and tied at the bottom rules where the top candidates  
> may all win each others (or at the bottom lose to each others).  Support 
> of the tied at bottom feature would make it unnecessary to  vote loops 
> since this way all unwanted candidates would lose to each  others. This 
> feature could also be added in the "matrix preference  votes" to 
> eliminate some strategic loop considerations.
> 
> Also the linear order based ballots could have explicit ways to mark  
> "both lose" and "both win" etc. (instead of the default rules "tied  at 
> top",...), but of course this makes voting more complex to the  voters 
> (just like allowing full matrix preference votes would do).  Using "+" 
> and "-" a ballot might look e.g. a+b>c=d>e-f>g-h-i.
> 
> Just for your consideration. Different ballot styles may have an  impact 
> on strategies too.
> 
> Juho Laatu
> 
> 
> On Dec 15, 2006, at 15:02 , Dave Ketchum wrote:
> 
>> How did we get here?
>>
>> I assume no ties to simplify the discussion - not to change the rules.
>>
>> If there is a cycle, such as X>A>Y>X, A backers have no control as  to 
>> X>A, but they can influence whether there is also a Y>X to  create a 
>> cycle.
>>
>> Else, assuming more voters back X than A, A loses and it matters  not 
>> what ordering A backers choose for others.
>>
>> If there is no such X, A wins and it matters not how A backers sort  
>> those losing to A.
>>
>> LOOKING CLOSER - If A backers want to be neutral as to B/C/D, they  
>> can simply vote for A as they would in Plurality.
>>
>> On Fri, 15 Dec 2006 00:01:04 +0200 Juho wrote:
>>
>>> Here is one very basic case where a group of voters has identical   
>>> preferences but they benefit of casting three different kind of  ballots.
>>> In a Condorcet method there is an interest to create a loop to  your  
>>> opponents. In its simplest form there are four candidates.  One of 
>>> the  candidates is our favourite and the others we want to  beat. 
>>> The  others may or may not be from one party (this  influences the  
>>> probability of being able to generate a cycle at  least if there are  
>>> more than 4 candidates). Let's anyway assume  that all the 
>>> candidates  will get about the same number of votes.  Also in a zero 
>>> info  situation this may be a good voting strategy.  The A supporters 
>>> vote  according to three patterns as follows.
>>> A>B>C>D
>>> A>C>D>B
>>> A>D>B>C
>>> If all candidates have same number of first place supporters (and   
>>> other preferences are mixed) and B, C and D supporters don't try  to  
>>> create loops, A wins.
>>> Juho Laatu
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