tag:blogger.com,1999:blog-264226589944705290.post4187853019879635100..comments2023-11-05T03:45:25.001-08:00Comments on God Plays Dice: A quirk of electoral apportionmentMichael Lugohttp://www.blogger.com/profile/15671307315028242949noreply@blogger.comBlogger9125tag:blogger.com,1999:blog-264226589944705290.post-66450420378744433782008-11-10T20:33:00.000-08:002008-11-10T20:33:00.000-08:00Sorry if this is familiar to you (or if you wrote ...Sorry if this is familiar to you (or if you wrote it about it, though a search of your blog suggested not), but you might enjoy this while on this topic of apportionment: http://en.wikipedia.org/wiki/Apportionment_paradox#Alabama_ParadoxAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-60449066823711370382008-11-10T20:16:00.000-08:002008-11-10T20:16:00.000-08:00Boris,I agree that there's a very small probabilit...Boris,<BR/><BR/>I agree that there's a very small probability of ties -- but in any case the numbers involved are so large that one really shouldn't worry about the probability of ties. <BR/><BR/>The link seems to work; I'm not on campus right now, and I don't feel like dealing with my library's web site, but I'll probably take a look at the paper tomorrow.Michael Lugohttps://www.blogger.com/profile/15671307315028242949noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-76366478662965212432008-11-10T20:13:00.000-08:002008-11-10T20:13:00.000-08:00Re ties: Huntington, one of the originators of the...Re ties: Huntington, one of the originators of the "method of equal proportions" (Congress seems to often call it the "Hill method"; I've always heard "Huntington-Hill method") actually commented on the issues of ties in his 1928 paper "The Apportionment of Representatives in Congress" in the Transactions of the AMS. See <A HREF="http://www.jstor.org/stable/1989268?seq=15" REL="nofollow">page 15 of 26 of his article</A> (page 99 in the journal) -- hopefully my deep link works if you have access to JSTOR.<BR/><BR/>He says that there are very few possibilities for ties under his method, and actually considers this a "theoretical argument in favor of [his] method".<BR/><BR/>Incidentally, it appears that your intuition as to which tie-breaking is written into the law might be incorrect. The actual law for the matter simply says to <A HREF="http://www.law.cornell.edu/uscode/html/uscode02/usc_sec_02_00000002---a000-.html" REL="nofollow">use the method of equal proportions</A>, which isn't helpful at all with regards to specifics. As far as I can tell, there is no actual description of the method anywhere in the U.S. Code; thus, in some sense, <I>neither</I> tie-breaking scenario is considered.<BR/><BR/>However, Huntington mentions that in the case of a tie like the one you're talking about (different n and m in your notation), "convention .. provides that in case of a tie preference shall be given to the state having the larger population".Unknownhttps://www.blogger.com/profile/06229416831400925212noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-33134643917633871412008-11-10T20:03:00.000-08:002008-11-10T20:03:00.000-08:00The real tragedy is that the House stopped growing...The real tragedy is that the House stopped growing nearly a century ago, and the population hasn't. A simple calculation (300M/435) shows that each Rep represents, on average, 690K people, which is way too many for a single person to represent. It also means that, despite population growth, representation in the House can, and will, fall for many states.<BR/><BR/>I'd like to see the laws changed to allow a dynamic number of House members. One method would be to allocate using the existing "Equal Proportions" method until all states had at least two representatives. Another would be to continue allocating until the average constituency size was a fixed number significantly smaller than the current size -- say a measly quarter million people.Buddha Buckhttps://www.blogger.com/profile/17167036913705912859noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-83531309245561220472008-11-10T19:47:00.000-08:002008-11-10T19:47:00.000-08:00Re what will change: Wikipedia has projections for...Re what will change: Wikipedia has <A HREF="http://en.wikipedia.org/wiki/United_States_congressional_apportionment#Projected_changes_following_the_2010_census" REL="nofollow">projections for 2010</A>.Unknownhttps://www.blogger.com/profile/06229416831400925212noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-63743390743739640832008-11-10T19:42:00.000-08:002008-11-10T19:42:00.000-08:00Ben,I heard something similar, although I recall t...Ben,<BR/><BR/>I heard something similar, although I recall that they were considering expanding the House to 437 -- for partisan balance, basically, because DC would almost certainly elect a Democrat -- and that the plan was to give the extra seat to Utah because Utah was close to getting another seat and had argued that their population was being undercounted because of the large number of Mormon missionaries who are Utah residents but who were elsewere at the time of the census.Michael Lugohttps://www.blogger.com/profile/15671307315028242949noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-7363882394549612242008-11-10T19:38:00.000-08:002008-11-10T19:38:00.000-08:00Actually, the most likely outcome would just be ex...Actually, the most likely outcome would just be expanding the house to 436, which would just require a change of law (the states in question would lobby hard for it, and I can't see anyone fighting them). There was talk of doing this in 2000, since Utah and NC were so close (the difference was probably a miscount in a dorm at UNC).Unknownhttps://www.blogger.com/profile/08510939704154066339noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-43367670016022704222008-11-10T19:27:00.000-08:002008-11-10T19:27:00.000-08:00Jonah,I don't know. I know that they do not get a...Jonah,<BR/><BR/>I don't know. I know that they do <I>not</I> get a fourth electoral vote; the 23rd Amendment (which gives electoral votes to DC) says that DC gets the number of electoral votes it would get if it were a state with that population, except it doesn't get more than the least populous state. I think the non-voting representatives are not mentioned in the Constitution, so I suppose it would be up to whoever decides the internal workings of Congress.Michael Lugohttps://www.blogger.com/profile/15671307315028242949noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-58323681426079081992008-11-10T19:23:00.000-08:002008-11-10T19:23:00.000-08:00Question: if Washington, DC gets big enough, do th...Question: if Washington, DC gets big enough, do they get a <I>second</I> non-voting representative?Jonahhttps://www.blogger.com/profile/15159561721777836053noreply@blogger.com