Re: [EM] Hamilton vs Webster (Sainte-Lague)
Yes, this one works. But there are still some interesting peculiarities. Example: We have three sates with population A:5, B:3 and C:3 (millions I guess). Seats will be allocated in the following order: A, B*, C, A, B*, A, C,... - Three first seats go to the three states either based on the at least one seat per state rule or by starting the algorithm from zero seats - I used * to indicate where B wins the seat by lottery (instead of C) The strange thing is that the fifth seat goes to B by lottery but C will not get the next seat although it was already entitled (tie) to the previous seat (and B and C are identical states in the sense that they have exactly the same population). Divisor methods like SL/Webster provide ordering of the candidates/ seats by default and they may be nicer to use in places where such ordering is needed. I however tend to think that the Alabama paradox is not a sufficient reason to abandon use of LR/Hamilton in seat allocation to the states. LR/Hamilton does the allocation in a perfectly rational way that can be considered to be ideal (at least from one point of view). LR/Hamilton (Alabama paradox) may look bad to the audience if presented so, but it is another question if it is bad or if it looks bad to mathematicians. Juho Laatu On Dec 14, 2006, at 6:16 , Dan Bishop wrote: MIKE OSSIPOFF wrote: ... Are there other reasons why LR/Hamilton is not favoured? I reply: That's reason enough. Two kinds of nonmonotonicity: Population nonmonotonicity and House-size nonmonotonicitly. Your state can lose a seat because of a population change favoring your state with respect to the others, or because of an increase in the House's total number of seats. There's a pretty simple modification to LR/Hamilton that would eliminate the Alabama Paradox. Give seats one at a time (except at the beginning, when each state is assigned one seat), such that the nth seat goes to the state for which the quantity (state's proportion of population) * n - (state's seats so far) is the greatest. election-methods mailing list - see http://electorama.com/em for list info Send instant messages to your online friends http://uk.messenger.yahoo.com election-methods mailing list - see http://electorama.com/em for list info
[EM] Hamilton vs Webster (Sainte-Lague)
You wrote: I understand that LR/Hamilton may lead to the Alabama paradox and people may dislike LR/Hamilton because of this. But I think LR/ Hamilton is quite proportional and unbiased. I reply: Hamilton is unbiased, as is Webster. But though Hamilton doesn't systematically deviate from proportionality so as to favor large or small states, it sporadically and randomly deviates from proportionality, in an unbiased way. You continued: Are there other reasons why LR/Hamilton is not favoured? I reply: That's reason enough. Two kinds of nonmonotonicity: Population nonmonotonicity and House-size nonmonotonicitly. Your state can lose a seat because of a population change favoring your state with respect to the others, or because of an increase in the House's total number of seats. You continued: SL/Webster is close to LR/Hamilton I reply: Close in the sense of being unbiased. 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. Milke Ossipoff _ Talk now to your Hotmail contacts with Windows Live Messenger. http://clk.atdmt.com/MSN/go/msnnkwme002001msn/direct/01/?href=http://get.live.com/messenger/overview election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Hamilton vs Webster (Sainte-Lague)
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 ___ The all-new Yahoo! Mail goes wherever you go - free your email address from your Internet provider. http://uk.docs.yahoo.com/nowyoucan.html election-methods mailing list - see http://electorama.com/em for list info
