Unequal Representation

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English: Map of the 112th United States House ...

Map of the 112th United States House of Rep­re­sen­ta­tives by district

When I run a quan­ti­ta­tive analy­sis, I typ­i­cally have some sort of expec­ta­tion as to what I will find. Some­times I’m sur­prised by the results. For exam­ple, in “Take 2: Could Employ­ing Tax Cuts Tax Employ­ment?” I dis­cov­ered that, while higher taxes on the top 20 per­cent of earn­ers cor­re­sponds to increased employ­ment, higher taxes on the next-​​highest quin­tile cor­re­sponds to lower employ­ment. It’s not an out­come I would have predicted.

Today is another such time. In this case, I was look­ing at the rel­a­tive rep­re­sen­ta­tion of each Amer­i­can. To explain what I mean by this requires a bit of background.

As you’re surely aware, each state receives the rep­re­sen­ta­tion of two Sen­a­tors in Con­gress, regard­less of pop­u­la­tion. Addi­tion­ally, each state receives the rep­re­sen­ta­tion of at least one Rep­re­sen­ta­tive in Con­gress, while addi­tional Rep­re­sen­ta­tives are pro­vided at a rate pro­por­tional to the state’s pop­u­la­tion. This, of course, means that the demo­c­ra­tic con­cept of “one man, one vote” doesn’t apply to our rep­re­sen­ta­tive democ­racy, even though our national col­lo­quial rhetoric reg­u­larly implies otherwise.

Our con­gres­sional struc­ture should mean in the­ory is that there is a wide dis­par­ity in the num­ber of peo­ple rep­re­sented by each Sen­a­tor, but a small dis­par­ity in the num­ber of peo­ple rep­re­sented by each Rep­re­sen­ta­tive. More­over, since the red states tend to be sparsely pop­u­lated com­pared to the blue states, one would expect to find that Repub­li­can Sen­a­tors rep­re­sent fewer peo­ple than Demo­c­ra­tic Sen­a­tors. We shouldn’t expect to see any such dis­par­ity in the House.

I put these hypothe­ses to the test.

This is a slightly awk­ward time to run such an analy­sis, because we’re in the midst of reap­por­tion­ment. That is, some states are gain­ing Rep­re­sen­ta­tives this year, while oth­ers are los­ing them. My cal­cu­la­tions are based on the 112th Con­gress, i.e., the cur­rent one. They will shift some­what in the 113th.

I col­lected the pop­u­la­tion of each state, using the same num­bers used for appor­tion­ment. Nat­u­rally, the actual pop­u­la­tion may be dif­fer­ent for a host of rea­sons. First, let’s look at the pop­u­la­tions of the states, along with the num­ber of Rep­re­sen­ta­tives they cur­rently have, and the num­ber of peo­ple cov­ered by each Rep­re­sen­ta­tive and Sen­a­tor. In this table, I’m treat­ing it as if each Sen­a­tor rep­re­sents half of the state, although they actu­ally both rep­re­sent the whole state. It doesn’t actu­ally mat­ter in terms of the final rel­a­tive rep­re­sen­ta­tion cal­cu­la­tions, though.

State  Population House
Seats		 Peo­ple
per Rep		  Peo­ple
per Sen 
Alabama 4,802,982 7 686,140 2,401,491
Alaska 721,523 1 721,523 360,762
Ari­zona 6,412,700 8 801,588 3,206,350
Arkansas 2,926,229 4 731,557 1,463,115
Cal­i­for­nia 37,341,989 53 704,566 18,670,995
Col­orado 5,044,930 7 720,704 2,522,465
Con­necti­cut 3,581,628 5 716,326 1,790,814
Delaware 900,877 1 900,877 450,439
Florida 18,900,773 25 756,031 9,450,387
Geor­gia 9,727,566 13 748,274 4,863,783
Hawaii 1,366,862 2 683,431 683,431
Idaho 1,573,499 2 786,750 786,750
Illi­nois 12,864,380 19 677,073 6,432,190
Indi­ana 6,501,582 9 722,398 3,250,791
Iowa 3,053,787 5 610,757 1,526,894
Kansas 2,863,813 4 715,953 1,431,907
Ken­tucky 4,350,606 6 725,101 2,175,303
Louisiana 4,553,962 7 650,566 2,276,981
Maine 1,333,074 2 666,537 666,537
Mary­land 5,789,929 8 723,741 2,894,965
Mass­a­chu­setts 6,559,644 10 655,964 3,279,822
Michi­gan 9,911,626 15 660,775 4,955,813
Min­nesota 5,314,879 8 664,360 2,657,440
Mis­sis­sippi 2,978,240 4 744,560 1,489,120
Mis­souri 6,011,478 9 667,942 3,005,739
Mon­tana 994,416 1 994,416 497,208
Nebraska 1,831,825 3 610,608 915,913
Nevada 2,709,432 3 903,144 1,354,716
New Hamp­shire 1,321,445 2 660,723 660,723
New Jer­sey 8,807,501 13 677,500 4,403,751
New Mex­ico 2,067,273 3 689,091 1,033,637
New York 19,421,055 29 669,692 9,710,528
North Car­olina 9,565,781 13 735,829 4,782,891
North Dakota 675,905 1 675,905 337,953
Ohio 11,568,495 18 642,694 5,784,248
Okla­homa 3,764,882 5 752,976 1,882,441
Ore­gon 3,848,606 5 769,721 1,924,303
Penn­syl­va­nia 12,734,905 19 670,258 6,367,453
Rhode Island 1,055,247 2 527,624 527,624
South Car­olina 4,645,975 6 774,329 2,322,988
South Dakota 819,761 1 819,761 409,881
Ten­nessee 6,375,431 9 708,381 3,187,716
Texas 25,268,418 32 789,638 12,634,209
Utah 2,770,765 3 923,588 1,385,383
Ver­mont 630,337 1 630,337 315,169
Vir­ginia 8,037,736 11 730,703 4,018,868
Wash­ing­ton 6,753,369 9 750,374 3,376,685
West Vir­ginia 1,859,815 3 619,938 929,908
Wis­con­sin 5,698,230 8 712,279 2,849,115
Wyoming 568,300 1 568,300 284,150
National 309,183,463 435 710,767 3,091,835

A few things may jump out at you right away. For exam­ple, unsur­pris­ingly, California’s Sen­a­tors cover about 60 times as many peo­ple as do Wyoming’s. But there are some other less expected results; Montana’s at-​​large Rep­re­sen­ta­tive cov­ers nearly twice as many peo­ple as does Wyoming’s.

From these,  I cal­cu­lated what I’m call­ing the Rep­re­sen­ta­tive Fac­tor and the Sen­a­tor Fac­tor. If the fac­tor is one, it means that the Rep­re­sen­ta­tive or Sen­a­tor cov­ers exactly the national aver­age. If the fac­tor is greater than one, it means that the Rep­re­sen­ta­tive or Sen­a­tor cov­ers fewer peo­ple than the national aver­age, mean­ing that each con­stituent has more power. For exam­ple, a fac­tor of two means that each con­stituent has twice the power of the national aver­age, while a fac­tor of 0.5 means that each con­stituent has half the power of the national aver­age. I also cre­ated a Com­bined Fac­tor, which cov­ers the con­stituents’ rel­a­tive power in both houses together.

State Rep­re­sen­ta­tive
Factor 		 Sen­a­tor
Factor		 Com­bined
Factor
Alabama    1.04      1.29           1.20
Alaska    0.99      8.57           6.04
Ari­zona    0.89      0.96           0.94
Arkansas    0.97      2.11           1.73
Cal­i­for­nia    1.01      0.17           0.45
Col­orado    0.99      1.23           1.15
Con­necti­cut    0.99      1.73           1.48
Delaware    0.79      6.86           4.84
Florida    0.94      0.33           0.53
Geor­gia    0.95      0.64           0.74
Hawaii    1.04      4.52           3.36
Idaho    0.90      3.93           2.92
Illi­nois    1.05      0.48           0.67
Indi­ana    0.98      0.95           0.96
Iowa    1.16      2.02           1.74
Kansas    0.99      2.16           1.77
Ken­tucky    0.98      1.42           1.27
Louisiana    1.09      1.36           1.27
Maine    1.07      4.64           3.45
Mary­land    0.98      1.07           1.04
Mass­a­chu­setts    1.08      0.94           0.99
Michi­gan    1.08      0.62           0.77
Min­nesota    1.07      1.16           1.13
Mis­sis­sippi    0.95      2.08           1.70
Mis­souri    1.06      1.03           1.04
Mon­tana    0.71      6.22           4.38
Nebraska    1.16      3.38           2.64
Nevada    0.79      2.28           1.78
New Hamp­shire    1.08      4.68           3.48
New Jer­sey    1.05      0.70           0.82
New Mex­ico    1.03      2.99           2.34
New York    1.06      0.32           0.57
North Car­olina    0.97      0.65           0.75
North Dakota    1.05      9.15           6.45
Ohio    1.11      0.53           0.72
Okla­homa    0.94      1.64           1.41
Ore­gon    0.92      1.61           1.38
Penn­syl­va­nia    1.06      0.49           0.68
Rhode Island    1.35      5.86           4.36
South Car­olina    0.92      1.33           1.19
South Dakota    0.87      7.54           5.32
Ten­nessee    1.00      0.97           0.98
Texas    0.90      0.24           0.46
Utah    0.77      2.23           1.74
Ver­mont    1.13      9.81           6.92
Vir­ginia    0.97      0.77           0.84
Wash­ing­ton    0.95      0.92           0.93
West Vir­ginia    1.15      3.32           2.60
Wis­con­sin    1.00      1.09           1.06
Wyoming    1.25    10.88           7.67

This is merely another way of look­ing at the first table. Even in the House, the rel­a­tive power of each con­stituent varies by quite a bit.

What does this mean in terms of the rel­a­tive power of each party’s con­stituents? To answer this, I took a slight short­cut, assum­ing that, within a given state, the num­ber of con­stituents is the same across con­gres­sional dis­tricts. For each state, I broke down the num­ber of Rep­re­sen­ta­tives and Sen­a­tors of each party, and cal­cu­lated the rel­a­tive fac­tor weight based on how many mem­bers of each party are rep­re­sent­ing the con­stituents of that state. I did this by tak­ing the num­ber of peo­ple rep­re­sented by each party, and then com­pared that to the national aver­age of all Rep­re­sen­ta­tives and Senators.

The aver­age Demo­c­ra­tic Rep­re­sen­ta­tive has 703,682 con­stituents (Rep­re­sen­ta­tive Fac­tor of 1.01), while the aver­age Repub­li­can Rep­re­sen­ta­tive has 716,312 con­stituents (Rep­re­sen­ta­tive Fac­tor of 0.99). This means that the con­stituents in Demo­c­ra­tic con­gres­sional dis­tricts have about 1.8 per­cent more power than con­stituents in Repub­li­can con­gres­sional dis­tricts. It’s not a lot, but it’s there.

In the Sen­ate, the aver­age Demo­c­ra­tic Sen­a­tor has 3,282,771 con­stituents (Sen­a­tor Fac­tor of 0.94), while the aver­age Repub­li­can Sen­a­tor has 2,876,524 con­stituents (Sen­a­tor Fac­tor of 1.07). This, you may recall, assumes that each Sen­a­tor rep­re­sents only half of the state. You can dou­ble those num­bers if you wish to assume that each Sen­a­tor rep­re­sents the entire state. In either case, the Sen­a­tor Fac­tors are the same, and the result is that the aver­age con­stituent of a Repub­li­can Sen­a­tor has 14 per­cent more power than the aver­age con­stituent of a Demo­c­ra­tic Sen­a­tor. The impact in the Sen­ate, then, is an order of mag­ni­tude greater than in the House, ignor­ing the clo­ture rules. If one includes clo­ture, the rel­a­tive power of each Repub­li­can con­stituent is that much greater in the Sen­ate, at least to the extent that one wishes to pre­vent the pas­sage of legislation.

As I said at the begin­ning, the results weren’t exactly what I expected. Yes, I expected Repub­li­can con­stituents to have sig­nif­i­cantly more influ­ence on the Sen­ate than would their Demo­c­ra­tic coun­ter­parts. But I thought it would be more than 14 per­cent. And I cer­tainly did not expect to find that Demo­c­ra­tic con­stituents have more influ­ence on the House than their Repub­li­can coun­ter­parts, slight though it is.

What do you think of all of this?

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  1. One of the prob­lems with reap­por­tion­ment has been the Supreme Court’s insis­tence (e.g. in Wes­berry v Sanders) that Con­gres­sional Dis­tricts rep­re­sent the same num­ber of peo­ple, although they refuse to define how close is “the same”.

    This analy­sis shows how point­less that is. While we’re try­ing to cre­ate dis­tricts that rep­re­sent exactly the same num­ber of peo­ple, were rely­ing on cen­sus data that are inher­ently noisy. What’s worse, is that next door, across a state bor­der, they may be cre­at­ing a dis­trict that has hun­dreds of thou­sands more citizens.

  2. Not too sur­prised. Peo­ple often over­state low pop­u­la­tion red states. Of the 12 states with either 3 or 4 elec­toral votes, 6 are red and 6 are blue–although more red states have only 3. Plenty of tiny North­east states.

    As for the House, I assume big­ger GOP dis­tricts are from pop­u­la­tion changes since the last cen­sus and that will fix itself this year.

  3. Nor­mal geo­graphic maps don’t ade­quately depict how the pop­u­la­tion is actu­ally rep­re­sented in Con­gress. It would be inter­est­ing to see a map of rep­re­sen­ta­tion where the sizes of var­i­ous areas depict their pop­u­la­tion instead of geo­graphic extent. Some­thing like this 2008 elec­toral map

    or this 2008 pres­i­den­tial vot­ing map by county:

  4. rgbact,

    As for the House, I assume big­ger GOP dis­tricts are from pop­u­la­tion changes since the last cen­sus and that will fix itself this year.

    Your assump­tion is incor­rect. Run­ning the same basic analy­sis with the new appor­tion­ment still has a huge gap between Wyoming and Mon­tana, for example.

  5. This analy­sis does not pro­vide solace for me.  Repub­li­can con­stituents only have 14% more influ­ence on the Sen­ate than their Demo­c­ra­tic coun­ter­parts?  Sigh…

    Take a look at Alabama with its Sen­ate Fac­tor of 1.29, which makes the con­stituents there have 36% more influ­ence than their Demo­c­ra­tic coun­ter­parts, if I’m doing the math right.   The same fel­low Amer­i­cans who in the year 2000 brought this embar­rass­ment to the nation.

  6. All votes are equal, it’s just that some are more equal than oth­ers.  It sure puts the whole “voter ID” and “sanc­tity of voter iden­ti­fi­ca­tion” into the proper perspective.

    Let’s hear it for a par­lia­men­tary sys­tem!  It may have its own prob­lems, but I think it would work bet­ter than what we have.

  7. It would be inter­est­ing to see a map of rep­re­sen­ta­tion where the sizes of var­i­ous areas depict their pop­u­la­tion instead of geo­graphic extent

    Yes it would. Do any of our read­ers know what sort of soft­ware will pro­duce that kind of map? I’d be happy to go to the trou­ble to col­lect the data needed to gen­er­ate it.

  8. Your assump­tion is incor­rect. Run­ning the same basic analy­sis with
    the new appor­tion­ment still has a huge gap between Wyoming and
    Mon­tana, for example.

    So I guess its because of the smaller states and cuz EV’s are hard to chop at small lev­els? Basi­cally Mon­tana gets screwed cuz it has a few less peo­ple than Rhode Island and Hawaii.…but 1 less House seat?

  9. rgbact,

    So I guess its because of the smaller states and cuz EV’s are hard to chop at small lev­els? Basi­cally Mon­tana gets screwed cuz it has a few less peo­ple than Rhode Island and Hawaii.…but 1 less House seat?

    Pretty much. At lower res­o­lu­tions, things get really blocky, while at higher res­o­lu­tions they get much smoother. This is why the states with at least 14 Rep­re­sen­ta­tives are all within the 0.98 to 1.02 range, while those with 1 to 3 are con­cen­trated at the fringes.

  10. Michael,
    I’d sug­gest a search using “open source sci­en­tific visu­al­iza­tion soft­ware”.  Specif­i­cally, there’s a pack­age named “par­aview” which looks like it would pro­duce pretty pic­tures.  I expect there’s a learn­ing curve to get over.

    It’s some­thing I’ve brushed up against in my pro­fes­sional life, but only peripherally.

  12. Pretty much. At lower res­o­lu­tions, things get really blocky, while at higher res­o­lu­tions they get much smoother.

    So you can prob­a­bly call Wyoming and Rhode Island the two most over­rep­re­sented states in Congress.

    Not sure how smaller coun­tries are rep­re­sented in the Euro­pean Union. Malta and Lux­em­borg are pretty tiny com­pared to Germany.

  13. DC,

    I am shocked you didn’t already have soft­ware like that

    I wish I did. I’m look­ing at Par­aView at shortchain’s sug­ges­tion. I’ll see how read­ily it will do what we need.

  14. rgbact,

    So you can prob­a­bly call Wyoming and Rhode Island the two most over­rep­re­sented states in Congress.

    Yes.

    Not sure how smaller coun­tries are rep­re­sented in the Euro­pean Union.

    I’d expect such state­ments to lead to a degree of intel­lec­tual curios­ity. And, if so, that it would lead you here to sat­isfy such a curiosity.

  15. In keep­ing with the sub­ject, yet touch­ing on the issue of Voter ID, here is a new study that shows just what the actual effect of the Penn­syl­va­nia law will be.

    It seems also to be an exam­ple of good sci­en­tific visu­al­iza­tion methods.

  16. short­chain,

    It’s non­sense. Repub­li­cans assure us that the new voter ID laws won’t dis­en­fran­chise any­one, except lazy and shift­less peo­ple who don’t deserve the vote anyway.