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Tweaking The Math Behind Political Representation

Posted by timothy on Thu Jan 10, 2008 05:10 PM
from the as-nature-intended dept.
mlimber writes "Nature magazine's news section has an interesting story about how the seats in the US House of Representatives should be divided up. The problem is that the population isn't evenly divided by the number of seats in the House (435). So how should one allocate the fractional parts? The current method tends to favor big states, while a recent proposal by a mathematician is for what he calls a 'minimally unfair' allotment. He is predicting 'one person, one vote' challenges on this topic in the near future."
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  • eh... (Score:3, Informative)

    by Richard.g.k (1215362) on Thursday January 10 2008, @05:12PM (#21991438)
    Is there anything new in this article? people have been complaining about congress seat inequality forever...
    • by Geoffrey.landis (926948) on Thursday January 10 2008, @05:29PM (#21991688) Homepage
      Of all the problems in the US electoral system, this is undoubtably the least important.

      A vastly more critical glitch is that it is possible to draw congressional boundaries in such a way as to increase the influence of demographics tending toward electing one party and decrease the influence of the demographics tending toward the other, and the people who have the power to redraw districts barely even bother to hide the fact that they're doing so anymore. Solving that glitch with a means to draw boundaries that is guaranteed to be impartial, so that the elected representatives actually did reflect the preferences of the people electing them-- now that would be a serious improvement to democracy.

      • Re: (Score:3, Insightful)

        To prevent gerrymandering, have independent boundary commissions to redistrict after every census. Make one of their priorities be to keep historic and geographic communities-of-interest together when drawing districts. As a part of this, allow for greater differences between districts' populations (say, up to 15%) in order to allow for nice, neat districts that follow county lines, city limits, or established neighbourhoods in big cities.

        Yes, gerrymandering would be just as technically possible under m

        • by jsprat (442568) on Thursday January 10 2008, @07:49PM (#21993480)

          (...) they would by definition be reflecting the people who voted for them.

          Not necessarily. Gerrymandering [wikipedia.org] is the art of changing the boundaries to gain an advantage. In a simple way, this image [wikipedia.org] shows an even distribution redivided to give one party the advantage.
            • by CrimsonAvenger (580665) on Friday January 11 2008, @12:06AM (#21995450)

              It doesn't matter if Gerrymandering has taken place or not. If there are enough votes to elect someone then they are reflective of their voting populous.

              Not quite. Consider the possibility of a state that is 55% Republican, 45% Democrat, with 20 Representatives. Ideally, any districting should elect about 11 Republicans and 9 Democrats.

              It is a relatively trivial exercise, however, to divide the districts up so that 20 Republicans and 0 Democrats are elected.

              And it's not even especially hard to divide them up so that 3 Republicans and 17 Democrats are elected.

              While it is true that each of those districts is reflective of the voting population, alas, it's not necessarily true that the results at the State level are reflective of their voting populations.

            • by Taevin (850923) * on Friday January 11 2008, @12:09AM (#21995476)
              Do you seriously not get it, or are you deliberately trying to be obtuse? Of course the people who get elected got more votes, gerrymandering doesn't change the basic electoral system. What it does do is allow politicians to run virtually uncontested in a gerrymandered district. Since you completely ignored the rather obvious example of how this works provided by jsprat (in pictorial form, even!), I'll attempt to explain it again. In the original image, the two parties, green and magenta, are equally distributed in terms of voters (the dots). This would let to some very close elections, ranging from 4 green representatives to 4 magenta and everything in between (we'll say it evens out to 2 and 2). Now look at the gerrymandered example. There are now 3 representatives elected from the magenta party with no contest. See the problem?

              If for some reason an elegantly simple example, such as the one in the Wikipedia article, is not sufficient, how about some real world examples [rangevoting.org]? Some of these districts are downright ludicrous. Are you seriously trying to tell me these district lines were drawn in an effort to create fair and unbiased voting districts?
        • bullcrap (Score:4, Informative)

          by enos (627034) on Thursday January 10 2008, @08:40PM (#21993958)
          That's just an excuse to keep the current system in place.

          My high school government teacher had a brilliant exercise for us: he gave us a map of Indiana with info on how each county voted (i.e. Democrat/Republican, to keep it simple). Then he assigned every student a party and everyone could draw districts such that their party would win ALL 10 seats.

          The idea is to divide and conquer. By splitting up the opposing party's strong areas and absorbing pieces of them into your party's areas, you could essentially neutralize them.

          The take home lesson is that whichever party is in power when the census is completed and redistricting happens is at a big advantage and they DO use it.
          So sure, technically the representative is elected by the people in their district, but that district is no longer cohesive and is totally arbitrary (where arbitrary = convenient for the party that drew it).
        • Re: (Score:3, Informative)

          Go and play these 5 missions in the redistricting game [redistrictinggame.org] from basic to advanced, and come back and tell me if you've changed your views or not.

          Seriously, be honest.
            • Re: (Score:3, Insightful)

              When you say "Why should a state attempt to do anything that deviates from the existing conditions?" do you realize that the "State" does not do anything, it is actually an individual with political interests in staying in power that does this. Saying "State" makes it sound like a faceless majority, where it is a powerful MINORITY that can influence the results. This is not Democracy.

              So, did you play the game?
  • by wpegden (931091) on Thursday January 10 2008, @05:13PM (#21991446)
    Once they get this little pesky problem fixed, our government will be awesome!
  • How many delegates went to Vermin Supreme?
  • by Naughty Bob (1004174) on Thursday January 10 2008, @05:22PM (#21991588)
    From TFA-

    The method ... doesn't necessarily come up with unique solutions -- there could be many ways to achieve equal 'unfairness'.
    So basically, any re-jigging using this method will arbitrarily (or otherwise) favor one state over another, with no rationale. Additionally, it would likely mire the US electoral process in endless legal challenges. And we can't have that! (waka waka waka)
    • Re: (Score:3, Insightful)

      As I understand it, it's essentially a rounding problem. So why don't we just give states fractional seats and let their fractional representatives cast fractional votes?
  • Correction (Score:5, Informative)

    by sharp-bang (311928) <sharp.bang.slashdotNO@SPAMgmail.com> on Thursday January 10 2008, @05:23PM (#21991610) Homepage
    The current method doesn't favor big states. FTA, "the current method has an inherent bias towards giving small states a boost up".
    • Re:Correction (Score:4, Informative)

      by taniwha (70410) on Thursday January 10 2008, @05:46PM (#21991940) Homepage Journal
      yup - somewhere like Wyoming with a population of 1/453 already gets more representation per person than someone in California (it has about 2/3 or 1/453 of the US population)
      • this problem is even more evident in the european union, look at the "relative influence" table on the right.
        http://en.wikipedia.org/wiki/Apportionment_in_the_European_Parliament [wikipedia.org]
      • I'm not sure what your getting at here. The constitution says with the exception of the original 13 colonies, that there will be one representative for thirty thousand people and that each state will have at least one representative.

        what am I missing here? 1/453 and 2/3? I'm not sure what that is supposed to mean?
        • Re:Correction (Score:4, Insightful)

          by DragonWriter (970822) on Thursday January 10 2008, @06:39PM (#21992678)

          The constitution says with the exception of the original 13 colonies, that there will be one representative for thirty thousand people and that each state will have at least one representative.


          No, it doesn't. It says that (except for the period prior to the first Census, for which it spells out exact by-state representation) each state will have a number of representatives assigned in proportion to population based on a census count, except that each state will have at least one representative. It further states that the total number of representatives shall not be greater than 1 for every 30,000 people (that's not that the number will be 1/30,000: if that was the rule, the House would have, based on the 2000 census, 9,381 members — which would certainly reduce the voting-power impact of rounding problems from fractional seats.)

        • Re: (Score:3, Informative)

          That single representative could be quite influential, especially if he was very senior in years of service and was on the important committees compared to 53 more junior members from a larger state. This is why smaller states tend to elect the same guy over and over again because it increases their chances of getting more and better goodies in disproportionate amounts to their actual population or influence. Seniority matters in Congress.
  • by jfengel (409917) on Thursday January 10 2008, @05:23PM (#21991612) Homepage Journal
    The article starts by noting that California dominates the House of Representatives, but this doesn't really change that fact. Tweaking a seat up or down does change things a bit, especially where the electoral college is concerned, but the real problem is gerrymandering. Seats end up being permanently allocated to one party or another, with the incumbent enjoying an immense advantage.

    If you want to fix a problem, come up with a better algorithm for drawing district boundaries. Right now the party in charge DOES use an algorithm, one designed to create the pessimal boundaries that ensure its maximum advantage.

    Of course, there are many such algorithms, and no matter how fair they are the legislature would vote to choose whichever one favors them best.
    • Re: (Score:3, Insightful)

      If you want to fix a problem, come up with a better algorithm for drawing district boundaries.

      If you want to fix a problem, design a system where the drawing of district boundaries doesn't matter much instead of one where it does. Its easier to do, for one thing: simply increase the number of seats per district, and adopt a preference voting system that generates proportional results, like STV. This makes it difficult to do much to ensure "safe" seats or enhance partisan advantage by messing with district

  • by nebaz (453974) on Thursday January 10 2008, @05:29PM (#21991702)
    From article I
    The number of Representatives shall not exceed one for every thirty thousand

    A house of representatives with 10,000 people might actually be unwieldy enough to actually have to do business, rather than listen to speeches all the time.

      • I'd be willing to bet that a house of representatives with 10,000 people would never even manage to fund the government, let alone get any other business done.

        Perfect!
        • Why is this modded funny? It is actually insightful.

          What is the largest number a person can adequately represent? I actually believe that 30K might be on the high side of that estimation. Right now, a Representative in the House isn't beholden to anyone other than the special interest groups. The Special Interest Groups only need to focus on 435 people currently. If they had to spread their $ around to more people, the amount they could offer each would be much less and more easily overcome by a small band of normal constituents.

          I actuall see no problem with more representation, currently we're getting less and less. You tell me, do you feel adequately represented by anyone, let alone by your congress critter?
          • 17th amendment (Score:5, Insightful)

            by ChristTrekker (91442) on Thursday January 10 2008, @07:07PM (#21993044)

            What is the largest number a person can adequately represent? I actually believe that 30K might be on the high side of that estimation.

            Very insightful! I've been saying this for a long time now. When the 17th Amendment was ratified, populists thought that direct election of US Senators would be a great move for democracy! Instead, they shot themselves in the foot. Do you really think your Senator cares a fig about your opinion? You're one among millions. Back when s/he was accountable to the state's legislature though, you can be darn sure he paid attention to their few dozen opinions. Losing the support of any one legislator was significant.

            Making Senators into super-Representatives was just silly. The House has a 2-year term because the electorate is fickle. Senators have a 6-year term because (in theory) your legislators are wise enough to make more thoughtful decisions. If we trust them enough to make laws for the state, can't we trust them enough to select Senators? But no, now we are stuck with our fickle decisions for 6 whole years - and 6 years after they make dumb decisions they can be sure we've forgotten about them, so they are even less accountable than ever!

            Increase the House membership to 1000, and repeal the 17th Amendment. Those are the two best things we could do to "fix" the Congress in a relatively easy manner.

  • Of course, what the article fails to mention is that your vote is only worth so much depending on what state you live in. Remember, in the US, we elect through the electoral college which generally means (technically, the electors do not have to vote by what the people vote with an exception of a few states) your vote is counted within the state and not within the nation. So, how much is your vote worth? At the extreme ends, Wyoming, which has the least number of people for a state gets 3 electoral votes for about 500,000 people (0.0006%), whereas California has 55 for 38 million people (0.00001%).

    Therefore, for every 1 vote for a Republican in Wyoming, 60 votes for a Democrat in California are needed to cancel each other out. And this mathematician wants to make it more "fair" by giving more votes to smaller states?
    • by joggle (594025) on Thursday January 10 2008, @06:07PM (#21992238) Homepage Journal

      Ummm, I only see one representative listed for Wyoming on the official US House of Representatives [house.gov] website. The guy wasn't suggesting adding representatives to Wyoming, but to Montana and some other states. Montana had a population of 902,195 in the 2000 census and 1 representative. That works out to a voting power of 0.00011% per person in Montana. California had a population of 33,871,648 and has 53 representatives (0.000156% per person).

      His model wasn't trying to be fair, just less unfair. To be fair Wyoming would either need a fractional vote or the size of the House would have to be increased until each person in the house represented about 500,000 people. Since this isn't possible from his model's point of view he does the next best thing (removing votes from large states that have fewer people per representative to smaller states that currently have more people per representative).

      With that said, I agree that small states don't need more representation in the House. They are more than adequately compensated by having 2 votes in the Senate. To put in perspective how powerful that is, imagine that even if San Francisco had 2 senators the Wyoming senators would still be representing fewer people. San Francisco has a population of about 750,000 (4th largest in California) vs. the population of 500,000 for the entire state of Wyoming.

    • No, he wants to make the House of Representatives more fair. The House is supposed to be apportioned according to population, with each state receiving at least one representative. The Senate, on the other hand, has two representatives per state, regardless of population. Each state gets electoral votes equal to its representatives plus senators -- and that's where the small-state bias in the Presidential election comes from.

      If you want to remove that bias, change the number of electoral votes to be eq

    • by alan_dershowitz (586542) on Thursday January 10 2008, @06:11PM (#21992298)
      Everything you say is true, but is not relevant to his definition of fairness. The Electoral College is not meant to be proportional to the population while the House of Representatives is. He's trying to make a system that was MEANT to be proportional more accurate, while you are arguing for a conceptual change to the system. His definition of "fair" is more procedural ("if it's supposed to be proportional, is it?") than yours, which is essentially political ("One Person One Vote is a better system than the Electoral College.") Not to say you aren't right, but he's a mathematician and not a politician so he's studying the former and not the latter.
  • by Presto Vivace (882157) on Thursday January 10 2008, @05:38PM (#21991814) Homepage Journal
    Did he mention Washington, DC [dcvote.org] in his mathematical formula?
  • Add more seats (Score:3, Interesting)

    by kcurtis (311610) on Thursday January 10 2008, @05:38PM (#21991826)
    I have long thought the House should be larger. It is meant to be representative, but the sheer size of each district now means that entire populations go ignored. Think of a conservative enclave in a Democratic district, or vice versa. For example, the wealthy town of Grosse Point Shores is in a very liberal Detroit district. Do you think their views are taken seriously?

    I understand the cost involved - just the buildings alone will be a fortune. But consider how hard it is now for your representative to stay in touch with his or her constituency. The average size of a Congressional district is just below 650,000! That is three times what it was at the turn of the last century. Considering the minimum was set at 30,000, the current sizes are way out of whack compared to the probable intent.

    With 650,000 constituents,it really is no surprise how important campaign donations have become. Worried about lobbiests and PAC's? Well, here is the root of the problem. Yours is a voice in the crowd.
    • Re: (Score:3, Insightful)

      the wealthy town of Grosse Point Shores is in a very liberal Detroit district. Do you think their views are taken seriously?

      Yes, money always gets taken seriously by elected officials.
    • Re: (Score:3, Informative)

      I have long thought the House should be larger. It is meant to be representative, but the sheer size of each district now means that entire populations go ignored.

      That's why to a large extent the States (and even larger extent The People) were originally suppose to be the major government entity, with the Congress tasked with only 18 authorized jobs to do. One of those is to show up one day a year, since the framers thought that there wouldn't be enough work.

  • The REAL problem (Score:3, Interesting)

    by jameskojiro (705701) on Thursday January 10 2008, @05:39PM (#21991846) Journal
    Is gerry Mandering, we need a good mathematical formula for detirmining the SHAPE of the districts not who gets what.

    1. Divide each state into a grid of 1 mile by 1 mile "chunks"

    2. Find the population of each "chunk" using census data.

    3. Start in the Northern-West corner and start adding blocks to the district moving west to east and dropping down one row and changing direction each time you drop down.

    "Drop down, change direction and increase speed" Lurr from Anthology on Interest 2: Futurama

    4. When your population count hits what 1 representative can represent, start a new district.

    5. Repeat

    6. ????

    7. Profit from special interest kickbacks and pork barrel spending.
  • Third House (Score:4, Interesting)

    by Anonymous Coward on Thursday January 10 2008, @05:47PM (#21991944)
    I think we should add a third house, composed of a random sample of people across the entire country. The term is three months, and the only way to come back to the seat is to be (miraculously) drawn again. The job would be to listen to time-limited debates (without involving themselves in the debate), and brainstorming a set of questions they would like answered for the second round of the debate.

    At the end, every law needs a majority vote in this new house in order to pass. Constitutional amendments require a 2/3rds or 3/4ths vote in order to pass.

    If you can't convince a random sample (including people of all national origins, races, religions, sexual orientations, etc.) that a law is a good idea, it simply doesn't pass. The limited term and not being directly involved in the debate (only listening and then X rounds of questions) means that politics and political shenanigans are reduced to a minimum.

    We also give this house the ability to override Presidental veto and Presdiential pardon/commutation. If 2/3rds of this house (alone) agrees that the President should not have vetoed a law or pardoned someone, then the President's action is null and void (i.e.: law passes, or person still goes to jail for obstruction of justice)

    What do you think?
      • Re: (Score:3, Informative)

        It would actually give you the British House of Lords.

        After centuries of titles entitled to a seat there falling through various hands, it is probably the most diverse legislative body in the world. There are plenty of Lords with no property or income other than their stipend for attending Parliament.

        hawk
  • I noticed this article seemed to work under the constraint that there are exactly 435 members of the House. Why stick to this number? Larry J. Sabato deals with this and many other basic assumptions in the Constitution in his book A More Perfect Constitution [amoreperfe...tution.com]. (See bullet 5 for members of HOR.) He suggests that we conduct a new Constitutional Convention to revamp things. And he's not arguing that his 23 points are the absolute best choices, but rather a starting point in the discussion. I would love to
  • Dr Larry Sabato [virginia.edu] at the University of Virginia wrote a really interesting book that devotes some time to this subject, called A More Perfect Constitution [amazon.com]. He talks about the gerrymandering (fixing districts so the incumbent, or at least the same party, always wins) that goes on, and proposes some interesting solutions, including making the House 1000 members to be more representative of the actual population. This, he says, would have the effect of producing smaller constituencies, require less money for s
  • When districts are redrawn after the next census, if your state has a population calling for 4 and 9/13th seats in House of Reps...

    [scene: 5 representatives from state X being sworn in.]
    Congratulations! Now Mr. Representative #5, your honor, if you would just step this way...

    [off stage: chain saw noises]
  • After all, when do politicians not listen to reasoned scientific argument? Oh, shit, wait...
  • The Alabama Paradox (Score:3, Informative)

    by mblase (200735) on Thursday January 10 2008, @06:24PM (#21992482)
    I'm surprised the article could discuss the mathematics of this without bringing up the Alabama paradox [wikipedia.org] of 1880. It's an interesting example of how, using otherwise correct and normal mathematical distribution, increasing the number of seats in the House can actually decrease the representatives for a specific state.
  • by nguy (1207026) on Thursday January 10 2008, @06:58PM (#21992926)
    The current method tends to favor big states

    Yeah, and the current method of allocating senate seats is favoring little states big time. That's one of the reasons our agricultural policies are so messed up and why the little states are getting money from the big states.

    There's nothing to be "corrected" here, at least not until the allocation of senate seats is changed substantially.
  • Legitimacy (Score:3, Insightful)

    by mosb1000 (710161) <mosb1000@mac.com> on Friday January 11 2008, @12:00AM (#21995406) Homepage
    Any poly-sci major will tell you that the main purpose of elections is to grant the governing body "legitimacy". The idea is that if you say people voted for the government, people are more willing to accept governmental authority (if people didn't accept governmental authority, the government would not have any power). Since most people do not have a complete enough understanding of discrete mathematics to understand this problem, it will not grant the government any additional legitimacy and is therefore completely useless.

    As a side note, I would like to take this opportunity to complain that people too frequently equate democracy with freedom. There is nothing about a democracy that means that it increases your level of freedom. People in this country could vote to take away all my money and forcibly sterilize me, and it would be no less of an infringement on my basic freedoms than if some psychopath broke into my house, stole everything I had and cut my balls off.
  • This is not new (Score:3, Insightful)

    by slashname3 (739398) on Friday January 11 2008, @09:09AM (#21998298)
    The founding fathers knew this. When they setup congress the House and Senate were created to make sure the smaller states did not get short shrift. All states get equal representation in the Senate. The House provided a way to give the states a measure of representation based on population.

    The posts complaining about gerrymandering have more of a point that trying to reallocate how the House is allocated. And if you want a really big problem that needs to be addressed then look no further than the electoral college. Of course that one depends on which side you fell on in the last couple of elections.
    • Re: (Score:3, Insightful)

      The small congressional districts where only one candidate gets chosen should be scrapped. Each state should become one voting district and all the congressional seats of the state should be allocated using the proportional D'Hondt method.

      That's a really bad idea. If all the states were equal sizes, this would be arguably a good idea (I think candidate-centered elections are better than party-list, so I'd oppose it even then, but it would at least make some sense.)

      As it is, states have between 1 and 53 repr