[EM] Combined elections

[Juho]

On Dec 4, 2009, at 12:12 PM, Raph Frank wrote:

> On Fri, Dec 4, 2009 at 12:12 AM, Juho <juho4880 at 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