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Fruits & Votes is the Web-log of Matthew S. Shugart ("MSS"), Professor of Political Science, University of California, Davis.

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  • 29 August 2005

    Planted by MSS
    Planted in: AMERICAN POLITICAL REFORM; Cube Root Rule; US House

    After each census, the number of seats in the US House that each state is entitled to must be recalculated. Rick Hasen’s Election Law Blog contains a pointer to an opinion piece in the Grand Rapids (Michigan) Press that suggests a change in the way this process is done.

    U.S. Rep. Candice Miller, R-Macomb County, has proposed a fairer and more sensible system for deciding the number of Congress members from each state. [...] Ms. Miller’s proposed amendment would change the word “persons” in the 14th Amendment to “citizens.”

    The article goes on to say that this would grant Michigan one more seat than it currently has and California six (!) fewer.

    Counting only citizens for the sake of determining how many people to have in Congress seems like common sense. Only citizens can vote and enjoy the full rights and privileges the country has to offer.

    Well, yes, only citizens vote; however non-citizens pay taxes and receive government services–two reasons that would seem to make them relevant to calculating how much weight a state ought to have in the House of Representatives.

    However, there is an alternative solution, and it does not force us to get into a divisive debate about citizenship and representation. It is so simple that it is rather amazing to me that it is rarely discussed:

    INCREASE THE SIZE OF THE HOUSE.

    It really makes little sense that a state should gain population (citizen or non-citizen) yet lose House seats, as Michigan and other states did after the 2000 census.

    We are one of the few democracies in the world that does not periodically adjust the size of its lower (or sole) house. There is nothing set in stone about 435. It is just in federal law. In fact, we used to increase the size of the House periodically as population increased. We could do so again. Look at this graph:

    Assembly size

    (This is for a forthcoming book on American democracy in comparative perspective; all rights reserved, of course.)

    You can see two things here:

    1. The US used to keep its House size just below the cube-root of its population (as Rein Taagepera’s model predicts), but has not done so since its population was under 100 million (in 1912!).

    2. The US House is one the smallest in the world among established democracies with over around 60 million residents (citizen or otherwise).

    So, why not make the House even a little bit bigger? We don’t have to go all the way up to 600 or so (which would still leave us below the cube root) all at once. We could just make long-term adjustments with each subsequent census (say 480 next time, then 500, and so on), thereby not depriving Michigan and other states of existing congressional districts.

    Further discussion in subsequent posts:

    Increase the size of the House via the “Wyoming Rule” (December 1, 2005; also has several interesting comments from readers)

    US House size, continued (December 4, 2005)

    See also Steven Taylor’s analysis: An Intriguing Proposal (December 2, 2005)

    Propagation: Seeds & scions (21)


    Fruits and Votes grafted Electoral reform and assembly-size reduction in Hungary?
    Fruits and Votes grafted Book review by Dahl on US constitution
    Fruits and Votes grafted Partial citizenship breakthrough for DC?
    Fruits and Votes grafted Reduce the size of the House?
    Fruits and Votes grafted Increase the size of the House rather than bash immigrants

    21 ideas sprouting »

    1. First post – and thanks for dropping by at my site. One idea I’ve seen suggested for the US House is the ‘Wyoming Rule’ – that the standard size for a Congressional district should be the population of the smallest entitled unit, i.e. Wyoming. This would remove some of the bias towards very small states and increase the size of the House – in 2000/2 this would have given a House with 569 members. The California delegation would have 69 members.

      Seed planted by Lewis Baston — 30 November 2005 @ 05:07

    2. Increase the size of the House rather than bash immigrants

      Scion grafted by Fruits and Votes — 24 January 2006 @ 17:58

    3. Cube root might be the theory, but I’m not sure it is sound. To share power between the representatives and the represented, the square root is appropriate.

      If you have a cube root system, I have this sneaking suspicion that you should have two level elections (the first root elects the second root[delegates] who elect the main body).

      Anyway, the reason is simple. Have you ever tried to run a chamber with more than 435 members?

      There is only one larger assembly in the English speaking world (UK Commons). I live in New Hampshire and we are constantly bragging that our House (which has 400) is third largest.

      Your graph would be a lot more effective, in my humble opinion, if you went back as far as the 1790 apportionment.

      Seed planted by JS Narins — 02 February 2006 @ 15:33

    4. JS, thanks for the comments. I am not sure I understand the case for square root rather than cube root. The theory of the cube-root law is deductively derived and, as the graph shows, is also a good empirical fit to the data (and other graphs with slightly different data sets also confirm its applicability). So, an alternative theory (such as a square-root law) would have to be superior both deductively and empirically, which apparently would not be the case.

      The deductive reasoning behind the theory is a bit extensive to explain in a blog post, and is best understood with references to diagrams. See Taagepera and Shugart, Seats and Votes (Yale University Press, 1989), pp. 173-83.

      English-speaking or otherwise, the US House is small for the population, while that of the UK is large. As the graph shows, there are several other countries with larger houses (in absolute numbers), including India, France, and Germany. So, while I personally have never tried to run a chamber with more than 435 members, others apparently have managed OK!

      400 for New Hampshire is, of course, really large for the population. I had no idea it was so large. On the other hand, out here in California we have only 80, which is ridiculously small.

      Thanks again for the comments!

      Seed planted by Professor Matthew Søberg Shugart — 02 February 2006 @ 17:34

    5. I followed the election-methods list for a while. It’s a bit crazy sometimes (some are _very_ attached to their method) but one can learn a lot, and most anyone is willing to answer questions.

      The proof for the square root hypothesis is, I admit, a form of proof that I hate from economics.

      The Laffer Curve is an imaginary Supply Side Economics curve. It says that if taxes are 0%, government “revenue” will be $0. And if taxes are 100%, then government “revenue” will be $0 (for why would anyone lift a shovel for an income if all the income went somewhere else). Ergo, somewhere between 0% and 100% there is a tax rate which maximizes government revenue.

      It’s an amoral argument (for a variety of reasons) and it is also sickening to even _begin_ to think of government as a revenue maximizer, but there it is.

      Now, back to voting.

      In a chamber, if there were only 1 representative for all the people, then the people would have the least possible power over the process. If every citizen was in the legislature, citizen power would be maximized. I believe these statements are as true as the 0% and 100% statements above.

      The leap I made to the point where “the ideal point is the square root” comes from the logic of the decision making itself. Taking the concrete numbers of 100 citizens, if the assembly has 10 members, then each district is 10 citizens. Both the citizen and the representative have the exact same “pull” in their respective arenas.

      And, hence, the power is balanced between them.

      I’m not surprised _at_all_ that cube root matches the record better. I don’t think many people understand politics at all, and that few people like to participate in activities like that (where they are, more often than not, the fool).

      New Hampshire’s system is pretty amazing. My city of 12K has four representatives. I see three or four of them each month at the city Democrat’s meeting. One of them gave me a ticket to the biggest annual Democrat event of the year.

      I just came up from Manhattan (did I mention that?) where we had 8,000,000+ people for about sixty City Council seats.

      Down side of the NH House? It pays $100.

      By the way, and of this I am quite proud, I calculated that the square root of Earth’s population is about 77,000. I wrote software to manage an arbitrarily large assembly.

      It needs a lot more tire kicking, but it basically works.

      I’ve not got enough interest in it, yet, to bring it to the “clinical trial” level yet. Maybe someday I’ll head a committee (I’m on the city Planning Board now) and I’ll just force it on everyone :)

      Seed planted by JS Narins — 04 February 2006 @ 07:17

    6. And my solution to the above problem is to create a third house, without power, of about 10,000 citizens (less than the 17,000 square root, but within the constitutional limit of 1 rep/30,000). If you are a Solonic Republican (did you realize Solon had a reputation for giving pretty names to awful things?) you might like the named United States Assembly.

      Even though they don’t have power, since the division of power between the States and the Feds is (ostensibly) distinct, it will give citizens a grounding in Federal legal matters. It always seems ironic to me that a person who was a Governor is all of a sudden, with no practical experience at all, going to run a foreign policy establishment. The same could be said of the move from State House to Federal Congress.

      Seed planted by JS Narins — 04 February 2006 @ 07:35

    7. Reduce the size of the House?

      Scion grafted by Fruits and Votes — 30 May 2006 @ 14:14

    8. Partial citizenship breakthrough for DC?

      Scion grafted by Fruits and Votes — 04 January 2007 @ 13:35

    9. A transitional rule could be to add one seat for the most underrepresented state, repeating so long as doing so does not exceed some preset limit nor increase the disparity between the most underrepresented and the most overrepresented.

      Or, if Congress were to confine its activities to Article I Section 8, maybe the job would be small enough for 435 or even fewer to handle.

      Seed planted by Anton Sherwood — 27 April 2007 @ 16:06

    10. The logic for the cube root might be as follows:

      Assume a society of 27,000,000 citizens and 300 national legislators.

      Each legislator is answerable to about 300 party activists and political insiders.

      And about one in every 300 citizens is a party activist or political insider (involved in actively selecting new candidates, that is, and “compiling” the ballot: the other 299 turn out and vote on election day, whether primary or general, but only choose among the half-dozen or so leading candidates or tickets already on the ballot).

      300 x 300 x 300 = 27,000,000.

      300 is probably the maximum number of names you can keep in your Rolodex and maintain meaningful personal contacts with, ie, enough to strike deals and bargains that will be adhered to (you’re in a “village”, not dealing with strangers).

      Federalism allows an extra layer and division of work, but even then you cann have States/ Provinces (California, Uttar Pradesh) and nations (India) that just get too damn big.

      This puts another spin on the view, expressed by such democracy sympathisers as Daniel Bell, that PR of China at 1,300,000,000 people is just too big for democracy. It seems that a polity as populous as China or India would need a higher-than-the-Western-norm degree of repression to avoid anarchy – so China has repression without (as much) anarchy, India has anarchy without (as much) repression. You can’t rely solely on civic feelings and good neighborliness to ensure compliance when the fellow citizens who are outvoting you, or siphoning away your water, are more distant and different than many foreign countries.

      But then that’s a good argument for breaking up huge mega-nations into smaller nations, rather than enlarging the legislature until it reaches George Lucasian proportions.

      Seed planted by Tom Round — 01 August 2007 @ 00:04

    11. Remember too that the size of the US House indirectly affects the Electoral College. Gore would have won in 2000, Florida aside, if there had been 500 or 600 CongressReps instead of only 435.

      As an Australian, I find it ironic that Australia’s Constitution strictly caps the size of the two Houses (the “nexus ratio”) at two to one, when this does not affect the balance of political power except at a joint sitting on a disputed bill following a double dissolution. There has been exactly one such joint sitting held, and exactly four Acts passed thereat, over the objections of a majority of Senators, in 106 years since the Constitution began operating.

      Yet, in the USA – where the ratio between houses can directly affect who controls the presidency and the executive branch every four years, via the College – the Constitution imposes no meaningful cap. (The “max 1 per 30,000 people” limit, is not meaningful, since no one really wants 1,000 Reps!).

      At least Switzerland and South AAfrica – the only other democracies I know where the combined numbers in both houses (ie, as distinct from the lower house alone, or a direct election) determine the executive and/or Cabinet – fixes the size of the Lower house as well as the Upper in the Constitution.

      If I were Madison, I would have de-linked the number of “population-based” Electors from the number of Reps and made it something more like “eight times the number of States, plus 35″ so the ratio of president-electing power is beyond legislative fiddling (and the total is always odd).

      Having said that, of course allocation among electorates per capita and/or per Statum is only one part of the equation. The system used within each district makes a big difference. Thus, a lot of the time the advantage (on paper) of less-populous States having more seats than strict population proportionality warrants, in the US Electoral College or the Australian joint sitting, because they have equal numbers of Senators, is nullified by the fact that the Electors (USA) or House of Reps members (Aust) are chosen by a winner-take-all system, so that (barring freak elections like 1993 or 2000) whoever wins the most popular votes, almost always wins a majority in the EC/ JS also.

      Seed planted by Tom Round — 01 August 2007 @ 02:14

    12. By the way, if y’all can bear one more Australian comparison… here, House of Reps seats are reapportioned [*]among States based on population (because the Constitution, drafted in the late 1890s when voting was voluntary, requires it) – but seats are then redistricted[*] within each State based on numbers of enrolled voters. Because enrollment and voting are compulsory here, “all enrolled voters” diverges less from “the entire population” (and a fortiori from “all citizens”) than the two figures would in the USA or most other democracies.

      The Whitlam Labor Govt tried to make intra-State redistricting [*] population-based as well, but the Senate blocked it and the successor Fraser Liberal Govt did not introduce that particular change (unlike other changes, such as tightening the allowable variation among Reps districts from 20% to 10%, where the urban-based Liberals were happy to pick up Labor’s reforms, even if their rural-based Country/ National coalition partners didn’t).

      Seed planted by Tom Round — 03 August 2007 @ 03:11

    13. [*] Footnote: I note with great amusement that The Simpsons – that great cultural barometer of our age – presented a TV debate on the difference between “reapportionment” and “redistricting” as the topic that would send Bart and Lisa screaming to change channels, and “[Galactic] Senate redistricting” as the eponymous “Gathering Shadow” that made “Cosmic Wars: Episode 1″ suuch a snoorze-a-rama.

      (Just to bring the topic back to George Lucas again…)

      Seed planted by Tom Round — 03 August 2007 @ 03:17

    14. Tom,

      In South Africa the President of the Republic is elected by the National Assembly alone. The National Council of Provinces, the other house, has no role.

      Seed planted by Alan — 06 August 2007 @ 22:41

    15. Thanks, Alan, I stand corrected. Maybe I am thinking of the 1994 provisional constitution, not the 1996 one (as indicated by the fact I am thinking “Senate” rather than “Council of the Provinces”).

      Seed planted by Tom Round — 07 August 2007 @ 02:14

    16. Am I correct in concluding that the post-1997 Council of the Provinces replaces the “Australian rule” (Senators vote individually) with the “German Bundesrat rule” (each federal region’s delegation of Councillors must vote as a bloc)?

      Seed planted by Tom Round — 08 August 2007 @ 01:59

    17. I actually believe the Australian’s and the Irish have the best electoral system in the world. I’m glad to see ranked-choice voting catching on in America. San Francisco has started using it. May it catch on like wildfire in the U.S.

      I would use the a model that brings ranked-choice voting (a.k.a. “preferential voting”) directly to America and eliminate the insipid and antiquated electoral college entirely.

      I do think the ratio of citizen to legislator is ridiculously large, but the answer to me lies in decentralizing power to the states and local government where those ratios are smaller. Even with that, I’d establish a House of Representatives with 555 members, with each state electing a minimul of 3 instead of 1. Congressional Districts would be between 3 and 5 members each with as equal ratios as possible throughout the country, similar to the Irish model.

      The Senate would remain the same with 2 per state, elected with ranked-choice similar to the Australian lower house.

      The President would be directly by national popular vote using the same ranked-choice vote that Ireland uses to directly elect its President.

      The Civil War is over. The Electoral College should go. It’s not about “state power” anymore or protecting the interests of “slave” states. It’s about empowering citizens. Increasing the size of the House to 555 and raising the minimum per state to 3 is adequate compensation for eliminating the Electoral College. 555 members is still a workable size legislature.

      Now enacting any change, of course, is the hard part. :)

      I am more frustrated and worried about California’s dangerously high ratio of population to legislator in its lower house. I would like to see this situation rectified first.

      Seed planted by Dan Wentzel — 05 September 2007 @ 19:31

    18. Book review by Dahl on US constitution

      Sabato wants a 135-seat Senate and a 1,000-seat House… One thousand would make the US House by far the world’s largest representative body… If one had 1,000 members and nonpartisan redistricting, it would certainly increase the percentage of potential swing districts and maybe even make the odd third-party plurality achievable. But this goes too far on House size and not nearly far enough on electoral reform.

      Scion grafted by Fruits and Votes — 30 November 2007 @ 21:11

    19. Tom Round asked in 2007:

      “Am I correct in concluding that the post-1997 Council of the Provinces replaces the “Australian rule” (Senators vote individually) with the “German Bundesrat rule” (each federal region’s delegation of Councillors must vote as a bloc)?”

      I don’t know if Tom already knows the answer, but in the current South African constitution, there are some questions on which delegates to the Council of Provinces vote individually, and others on which delegates vote as provincial blocs. In the latter, each province has one vote on the Council. In the former, limited mainly to exclusively national questions, each delegate has one vote.

      Seed planted by Ren Aguila — 03 September 2008 @ 09:03

    20. Thanks, Ren.

      Re size of US House… it occurred to me this week that perhaps the unusually small size of the US HR is partly compensated by the fact that, every four years, the major parties hold conventions of 2-4,000 delegates. More elective offices as prizes to share around.

      It’s hard to compare across nations – not only is the number of seats only indirectly related to population (so Malta, with 300,000 people, has 65 MPs, while Germany, with 80 million, has 650+), but what do you compare? National lower house only? All elective national legislators (which makes the US/UK ratio 535/660 rather than 435/660)? All members of consitutionally sovereign/ entrenched legislatures? (so you would include members of US State legislatures but not the Scots or Welsh Assemblies?) Like I said, it’s apples and oranges (to introduce a possibly inappropriate “fruit” metaphor into the study of comparative political institutions).

      Seed planted by Tom Round — 04 September 2008 @ 23:15

    21. Electoral reform and assembly-size reduction in Hungary?

      Hungary may be in the process of simplifying its overly complex system and reducing its overly large assembly to match the estimates of the cube-root law.

      Scion grafted by Fruits and Votes — 16 February 2009 @ 17:45

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