Re: [EM] Apportionment (biased?) let me add some more confusion to the mix :)
From: [EMAIL PROTECTED] One more tool that can be useful in some situations is the hierarchical structure of the states/parties. To guarantee that certain set of states/parties will not be underrepresented they could form a team/alliance. When seats are allocated to that team they could lose (in typical allocation methods) only one seat to rounding errors instead on many of them losing a seat. Geographic alliances would maybe be more natural than e.g. an alliance of small states. What about sorting the States based on population and then splitting them into 2 groups such that the total population in each group is as equal as possible. The fractional seat is then split between the 2 groups based on (Webster?) ... or maybe Webster should be used directly? This is then applied to each group recursively. If any State ends up with zero seats, it is removed from the process and given a seat directly. The process is then re-run, until it completes with all remaining States getting at least 1 seat. This pretty much is forced to be unbiased between small and large States size. However, perhaps it would be biased in other ways. An additional rule could then be that States are allowed to form groups 'manually', and manual groups cannot be split in two by the algorithm (until the group being processed is the manual group itself). I already mentioned the different voting power. A simple method in that direction would be to elect one representative from every state and give her voting power in relation to the number of people she represents. Or maybe large states would be given n seats with 1/n of the voting power of the state etc. Maybe the building where these representatives will work has a fixed number of physical seats = fill those seats and allocate voting power according to that. The logistics of this would make the legislature less efficient. One possible rule would be that all Representatives must have voting strengths between 0.9 and 1.1 and a detailed count only happens if the vote is close (or if there is a motion demanding it). Check Out the new free AIM(R) Mail -- 2 GB of storage and industry-leading spam and email virus protection. election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Apportionment (biased?) let me add some more confusion to the mix :)
On Dec 11, 2006, at 12:38 , [EMAIL PROTECTED] wrote: From: [EMAIL PROTECTED] One more tool that can be useful in some situations is the hierarchical structure of the states/parties. To guarantee that certain set of states/parties will not be underrepresented they could form a team/alliance. When seats are allocated to that team they could lose (in typical allocation methods) only one seat to rounding errors instead on many of them losing a seat. Geographic alliances would maybe be more natural than e.g. an alliance of small states. What about sorting the States based on population and then splitting them into 2 groups such that the total population in each group is as equal as possible. The fractional seat is then split between the 2 groups based on (Webster?) ... or maybe Webster should be used directly? This is then applied to each group recursively. Ok. A binary tree like structure makes the division quite balanced (maybe even more than necessary for most practical needs). If any State ends up with zero seats, it is removed from the process and given a seat directly. The process is then re-run, until it completes with all remaining States getting at least 1 seat. Careful with this. There is a risk that the calculation rules steal seats from the states that have slightly more than one seat worth of inhabitants. This pretty much is forced to be unbiased between small and large States size. However, perhaps it would be biased in other ways. An additional rule could then be that States are allowed to form groups 'manually', and manual groups cannot be split in two by the algorithm (until the group being processed is the manual group itself). It is possible to support multiple proportionalities. It is possible to make more than one of them exact (=all divisions followed to the accuracy of rounding errors that are smaller than one seat) at the same time or approximate (= one division based on one rule, then another rule applied in each group (of the first division), e.g. first the manual groups and then the automatic size based groups within the manual groups). A more typical situation would be to use some more orthogonal measures like party/ideology proportionality and regional proportionality. The ideological and regional proportionality requirements are the most common ones. What others could there be? The state size based one was already discussed. Countries that have clear ethnical or religious division lines could use such additional proportionality rules. Maybe also different age or sex groups could be guaranteed a proportional share of the seats. It is quite straight forward to develop methods that respect such criteria either exactly or approximately in hierarchy. The number of seats should be large and the criteria should be as orthogonal as possible if we want to use several of them (to avoid situations where there for example are no female catholic candidates left in Hawaii when we would need one). Strong requirements on exact divisions also lead to pushing the rounding errors to some less critical areas but in a way that makes them very visible (e.g. (exact) ideological/party proportionality in 50 states with (exactly) one seat in each state would probably lead to electing a green candidate in some state that has only a 5% minority of green votes). I already mentioned the different voting power. A simple method in that direction would be to elect one representative from every state and give her voting power in relation to the number of people she represents. Or maybe large states would be given n seats with 1/n of the voting power of the state etc. Maybe the building where these representatives will work has a fixed number of physical seats = fill those seats and allocate voting power according to that. The logistics of this would make the legislature less efficient. One possible rule would be that all Representatives must have voting strengths between 0.9 and 1.1 and a detailed count only happens if the vote is close (or if there is a motion demanding it). I agree that some reasonable restrictions should be applied. Also my scenarios where the seats were divided in time may lead to too short times in office. If parties are allowed to fill the seats as they wish, one could also consider terms that last longer than one election period and terms that need not end and start at election time. Everything is ok as long as the party has exactly the agreed number of representatives active at any given time. I however think that also a method that gives two votes to a candidate that got two quotas of votes and so on would be quite ok (i.e. the maximum number of votes could be infinite or some fixed limit instead of 1.1). Giving very long terms to candidates that get lots of votes is not as natural (since voters and candidates and the world change).
Re: [EM] Apportionment (biased?) let me add some more confusion to the mix :)
Yes, random allocations are yet another way to balance the situation. Since the population of a state changes quite slowly some fixes (random, time division, voting power) may be wanted to reduce the risk of continuously getting less seats than the population would give right to. Changes in the support of political parties are maybe faster and therefore do not need similar fixes as badly. One more tool that can be useful in some situations is the hierarchical structure of the states/parties. To guarantee that certain set of states/parties will not be underrepresented they could form a team/alliance. When seats are allocated to that team they could lose (in typical allocation methods) only one seat to rounding errors instead on many of them losing a seat. Geographic alliances would maybe be more natural than e.g. an alliance of small states. I already mentioned the different voting power. A simple method in that direction would be to elect one representative from every state and give her voting power in relation to the number of people she represents. Or maybe large states would be given n seats with 1/n of the voting power of the state etc. Maybe the building where these representatives will work has a fixed number of physical seats = fill those seats and allocate voting power according to that. Juho Laatu On Dec 11, 2006, at 0:43 , Warren Smith wrote: Actually, I claim EVERY apportionment method so far discussed is biased, in the sense it will, under the right circumstances, systematically always-down-round one class of states and always-up-round the other. (Just make the small states all have exactly the right sizes and the large states all have the right sizes, and voila, this'll happen. You can make pretty much all the methods prefer larger or prefer smaller states, at your whim, by setting up the populations right in your contrived scenario.) Is there a way to get around that? Yes: randomized rounding. The idea would be you use a random number generator as part of the input into your decision to round a state up or down, and in such a way the expected net gain, was zero. Example: 5.3 -- 5 with probability 0.7 and -- 6 with probability 0.3. (That is for absolute unbiasedness. Also important is ratio- unbiasedness, which you can also assure by the same kind of method.) OK, so, here is a possible such method: do this kind of rounding. If the total number of congressmen comes out wrong, then try again, and keep trying until it comes out right. The end. This method seems totally unbiased. (Incidentally, the same idea was suggested in the 1980s for rounding floating point numbers inside computers. Biases can build up and result in large errors, and randomized rounding prevents that. This is a good idea but no computer hardware I know of implements it. The round to even approach is often used, which tries to get unbiasedness but isn't perfect.) Only problem with it is, it is randomized!! Warren D Smith http://rangevoting.org 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
