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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