[EM] Multiple Winners, Multiple Offices, and Proportional Approval Voting

[Kevin Venzke]

 --- josh at narins.net a écrit : > On Thu, May 01, 2003 at 04:16:13AM +0200, Kevin Venzke wrote:
> >  --- Alex Small <asmall at physics.ucsb.edu> a ?crit?: 
> > > Imagine an election which selects 2 winners, but one of the winners will
> > > have more power than the other.  The candidate who performs best according
> > > to our election method becomes chief executive.  The runner-up goes to the
> > > legislature to act as the leader of the "Faithful Opposition".  You might
> > > envision this as a unique type of "check and balance" on the power of the
> > > executive.  Originally, the US Constitution did something like this:  The
> > > VP was whoever came in #2 in the electoral vote, rather than the
> > > running-mate of #1.
> > 
> > > 
> > > I'm not sure about how to modify Condorcet or other methods.  Any thoughts?
> > 
> > For exactly two winners, with one specifically being the "opposition," how
> > about if you elect the "first" winner per a Condorcet method, and elect as the
> > "opposition" winner that candidate against whom the "first" candidate fared
> > the poorest?  That is, that candidate who received the most votes going
> > head-to-head with the CW.
> > 
> 
> Does make a certain amount of sense.
> 
> How about taking that candidate, and the #2, and seeing who did better
> between them? 

That won't work well, because the #2 would always beat the candidate who came
closest to beating #1, unless #2 is that candidate.

Here's a simple example:
60: A>B>C
40: C

A is the #1.  If A hadn't run, B would win, so B is #2.  But the candidate who
pairwise does best against A is C, so he should be the "elected opposition."

My suggestion is that if C>A votes were too much fewer, then B should
be the second candidate elected, despite there being no B>A votes.  That
would protect a sizeable minority if it exists, or else elect two compromises.

You could also use STV or "first two past the post" as well.  I don't see a
big problem with these methods, but they would probably decrease the chance that
a compromise can be elected.  That's probably okay, though, if your expectation
is that the winner will never be much of a centrist, for instance if the voters 
are split by ethnicity, or are so apathetic that extremists decide all the elections.


Kevin Venzke
stepjak at yahoo.fr


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