[EM] A new way to look at d'Hondt and Sainte-Lague

[Adam Tarr]

>The ideal proportionality would be party A getting 1.35 seats and party B 
>getting .65 seats.
>
>If you give party A 2 seats, 21,000 voters were over-represented by .65 
>and 10,000 voters were under-represented by .65.
>
>If you give each party 1 seat, 21,000 voters were under-represented by .35 
>and 10,000 voters were over-represented by .35.  Obviously, the error is 
>nearly half as small.

Writing out the errors this way made me realize a way to present the 
difference between Webster/Sainte-Lague and Jefferson/d'Hondt that I hadn't 
realized before.  I'd imagine (that if I'm right about this) someone's 
thought of this before, but I haven't seen it.

Both Webster's method and Jefferson's method attempt to minimize the error 
from ideal proportionality in the final allocation.

Webster measures the error in terms of a sum of how over-represented or 
under-represented each voter is.

Jefferson measures the error in terms of a sum of how under-represented 
each voter is.  Over-representation is not considered!

So, you could decide which method of allocation you prefer by deciding 
whether you think over-representation is a problem.

There are also some strategic issues involved, which Kevin noted in his 
post.  I have argued in the past that these issues are not as important in 
list PR, since it's not politically viable for parties to split just in the 
hopes of collecting an extra couple seats.  I discussed this with Forest in 
this thread (mainly about PAV):

http://groups.yahoo.com/group/election-methods-list/message/8811

-Adam