[Election-Methods] Determining representativeness of multiwinner methods

[Kristofer Munsterhjelm]

Steve Eppley wrote:
> Hi,
> 
> I prefer a definition of "representativeness" that differs from 
> Kristofer's.  To me, the more similar the *decisions* of a legislature 
> are to the decisions the people themselves would make collectively in a 
> well-functioning direct democracy, the more representative is the 
> legislature.
> Given my definition, a non-proportional legislature comprised solely of 
> centrist majoritarian compromise candidates may be very representative, 
> since the people themselves would reach centrist compromises on the 
> issues in a well-functioning direct democracy.  It might be more 
> representative than a proportional legislature, since the proportional 
> legislator could match her constituents' favorite position on every 
> issue yet fail to match the way they would compromise.

By considering issue representativeness, I was trying to reduce the 
problem of deliberation within a representative assembly to that of a 
direct democracy. Whatever problems the assembly might have, the people 
would also have if a direct democracy on the scale in question would be 
feasible in the first place: problems like tipping-point coalitions 
having undue power (as the Banzhaf and SS indices try to measure) would 
exist in both cases.

However, that, as you say, depends on that issues are the only thing 
that matter. Now, the dynamics among the candidates could differ from 
those of the people, but I don't see how those dynamics could be 
simulated. In order to measure the proportionality of decisions alone, 
there would have to be some sort of "decision generator" that takes the 
dynamics into account.

Also, the centrist majority candidates you mention would have to be very 
good at being neutral, incorruptible, and not belong to the same 
majority. The feedback is much more direct in a proportional assembly: 
if one of the representatives start to diverge, their support wanes, and 
voters can discriminate between dropping support of one part of the 
assembly and of another. If the assembly consisted of centrists, a 
veering centrist could benefit more than he loses just by moving closer 
to a certain majority, since a majoritarian method would reward him for 
doing so.

> Why should anyone care more about the legislature's proportionality than 
> about their decisions?

If the issues are good predictors of decisions, one would care about 
issues for that reason alone.