[EM] Hamilton vs Webster (Sainte-Lague)

[Juho]

On Dec 7, 2006, at 3:50 , MIKE OSSIPOFF wrote:
> You continued:
>
> and avoids the Alabama paradox, but LR/Hamilton might still be
> considered more exact in providing proportionality.
>
> I reply:
>
> Why? Hamilton's nonmonotonicity paradoxes are instances of
> unproportionality. And, as I said, Webster, and only Webster has the
> transfer property that I described. For example, given a Hamilton seat
> allocation, it could well be, due to Hamilton's random caprice,  
> that if we
> take a seat from one state, and give it to another state, that seat  
> transfer
> could reduce the factor by which those two states' votes per seat  
> differ.
> Showing that the Hamilton allocation was suboptimal and need of  
> improvement.

Joseph Malkevitch pointed out the Balinski-Young Theorem in another  
mail. That's what I was actually looking for. I don't think this is  
too dramatic since we are only talking about rounding errors. But if  
voters can influence the outcome, then this is more serious. In the  
Alabama case I think LR/Hamilton is quite harmless since people sure  
do not move or give birth to children in the assumption that it might  
change the political balance (especially since you don't know if  
other people are moving too). But if someone is able to influence the  
outcome of the census (after knowing the results of the other  
states), then there is space for doing tricks. My assumption is that  
in most cases LR/Hamilton works ok and people should in a way be  
happy with the paradox since that gives them the "fairest possible  
result". In practice SL/Webster is close enough (and monotonic), so I  
find it ok as well (the difference is anyway only at rounding error  
level here). And SL/Webster would be a good choice if there is a risk  
of foul play.

Btw, in the case that one intentionally wants to favour large parties  
I find methods like d'Hondt/Jefferson better than setting a hard  
limit (e.g. 5%) that parties must reach to get their first candidate  
through.

Juho Laatu


		
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