[EM] Multiwinner Condorcet generalization on 1D politics

[Kristofer Munsterhjelm]

I have to consider the STV-CLE part further, perhaps run some 
simulations. But the minimization objective has another problem, which 
I'll show here.

Dan Bishop wrote:

> This is true.  But it doesn't mean that MMPD minimization is a bad 
> criterion, just that we need to consider other criteria as well.  Just 
> like the Condorcet Criterion: It's possible for a method to comply while 
> being non-monotonic.  That doesn't mean the Condorcet Criterion is 
> defective, just that we should prefer that a method should meet both 
> Condorcet AND Monotonicity.

It doesn't seem obvious to me that MMPD minimization is good. Consider 
this scenario:

  0|.A...BC..DE.|1

Three to elect. A is supported by 49% just left of him, E by 50% just 
right, and D by 1% slightly closer to D than to E. Minimizing the 
distance would call for electing {A, D, E}, but this gives the {D, E} 
coalition disproportional power. Instead, it would be better to elect 
{A, C, E}: C is slightly to the right of B (which is dead center), so 
the 1% D supporters pull the last candidate somewhat away from the 
center, but not enormously so.