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

[Juho]

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
>
> -- 
>  davek at clarityconnect.com    people.clarityconnect.com/webpages3/davek
>  Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
>            Do to no one what you would not want done to you.
>                  If you want peace, work for justice.
>
>


		
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