On Dec 4, 2009, at 12:12 PM, Raph Frank wrote:
On Fri, Dec 4, 2009 at 12:12 AM, Juho <juho4...@yahoo.co.uk> wrote:
27: A=1 B=0 C=0 D=2
26: A=0 B=2 C=1 D=0
25: A=2 B=0 C=1 D=0
22: A=0 B=1 C=0 D=2
A would win the first Condorcet election (or Plurality or whatever
common
single-winner method). C would win the second Condorcet election.
Let's then combine these elections into one election in which the
outcome
alternatives (sets of winners of the two component elections) will
be AC,
AD, BC and BD. We can sum up the preferences so that each voter is
considered to prefer outcome x to outcome y if the sum of his/her
ratings of
the candidates is higher in outcome x than in y. The first 27
voters are
thus considered to prefer outcome AD (1+2 points) to BD (0+2) and
AC (1+0)
and BD (0+0).
27: AC=1 AD=3 BC=0 BD=2
26: AC=1 AD=0 BC=3 BD=2
25: AC=3 AD=2 BC=1 BD=0
22: AC=0 AD=2 BC=1 BD=3
Based on the resulting preference orders we will then use some
Condorcet
method (=some good single winner method) to determine the winning
outcome.
So, for each voter, you use the ratings to create a ranked list of all
combinations of the options, and then pick the condorcet winner?
Yes.
The effect is to allow voters to trade-off one candidate against the
other.
Yes, and to be able to elect the best combination in general, and to
allow also rating information to be used when determining which
combination is the best.
This is similar to the effect of coalition negotiations.
To some extent yes. But I kept this part very limited. The method has
some compromise oriented properties like changing a Condorcet winner
to something else, but the intent (and reason behind this property)
was to just elect the best alternative among the combined result
alternatives. One could go further and try to explicitly find such
"best strategies" but so far I consider this method to just to aim an
electing the best winner (from the point of view of the society / all
voters).
A&B could be one policy question and C&D could be another.
Yes.
A party could very easily accept an undesired decision in the AvB
direction in order to get what it wants in the CvD axis.
Yes, that's what the ratings are used for.
With lots of options, you could just do a random search method. Pick
a random result and compare it to the winner so far. If the majority
prefer it, then that becomes the provisional winner. You could also
allow people to submit their own options.
Yes. I used term generic optimization algorithms with the intention to
cover this approach. Also gradient based search of local optimums (and
then pick the best one of these) would be one typical method that
could be used to optimize the result. I'm referring to some very basic
methods that have been around already for decades. It is also possible
that each party or whoever could try to beat the official calculation
process and find better results than they will. The used criteria and
preference functions should be such that optimization is feasible and
one can always find close to best possible results. The comparison
function between two proposed outcomes should be simple to calculate,
so there would be no problems when deciding which one of the proposed
outcomes is the best. (Possible new findings after the results of the
election have been declared final should maybe be ignored. Better luck
next time :-).)
There might be some issues with having control of the questions being
put. Adding a "poison pill" as an option could cause problems. Maybe
options which have the support of 75% of the population (or opposition
of 75% of the population) are excluded.
Yes, I think there are many questions where a supermajority could be
required. One simple implementation is to include an approval cutoff
entity among the set of candidates (=> my vote could be e.g.
A>B>ApprovalCutoff>C>D) and then require that the winner must beat
this entity by 75%. I didn't understand why you wanted to exclude also
candidates that are too popular(?). (One could also agree that some
numerical value (e.g. 0) is considered to represent the level of
acceptance. One could also try setting a supermajority requirement to
the combined outcome of the election.)
I think it might have some strategy problems.
Maybe inherited from the ratings side?? What would that be? I tried to
use the ratings in such a way that the ratings of one voter would be
compared against the ratings of this voter herself and not against the
rankings of other voters to keep the most common ratings related
problems away.
Juho
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