Press "Enter" to skip to content

Redistricting by Pure Math: French Hexagons Everywhere!

My Democratic friends often complain that the Republicans have gerrymandered us out of several seats in the South Dakota Legislature. Such complaints return my attention to a topic of frequent interest here: redistricting.

This is your state's Legislative map:

South Dakota Legislative Districts, in effect for elections from 2012 to 2020.
South Dakota Legislative Districts, in effect for elections from 2012 to 2020. (Image from Brian Olson, Click image to view official interactive map!)

This is your state's Legislative map on math:

Possible equipopulational, optimally compact legislative districts, mapped by Brian Olson,
Possible equipopulational, optimally compact legislative boundaries for 35 Senate districts, mapped by Brian Olson, (Click for original data and bigger image!)

Brian Olson of mapped out legislative districts for every state based strictly on 2010 Census data and distance. His maps ignore local boundaries and political affiliations. His math produces hexagonal districts that make South Dakota look like a state of little Frances (O! that we could make it so!).

Interestingly, this arrangement reduces the average voter distance from district center by just a tenth of a mile, to 20.75 miles. No matter how you slice South Dakota, districts from the James River Valley west are going to cover a lot of ground.

Break our 35 districts into single-member districts for our House, and the map produces some more amusing results:

Possible equipopulational, optimally compact legislative boundaries for 70 single-member House districts, mapped by Brian Olson, (Click for original data and bigger image!)

New districts bubble up along I-90 on the northeast edge of the Black Hills and from Plankinton to Sioux Falls. These districts again reflect the beautiful math that ignores political affiliation, but they also ignore the court-ordered boundaries that support fair American Indian representation under the Voting Rights Act.

Would shifting district boundaries by Olson's politically blind math make a difference in the partisan make-up of the Legislature? I welcome your guesses on that count. But consider these numbers:

  1. 66% of the votes cast in 2014 for State Senate went to Republicans. 34% went to Democrats.
  2. Look only at contested races (that eliminates 13 Republicans and 5 Democrats), and you find GOP Senate candidates drawing 58% of the vote, Dems 42%.
  3. The incoming Senate is 77% Republican, 23% Democrat.

We should be careful what we wish for: if pure mathematical redistricting also happened to perfectly distribute Republicans and Democrats, then this year's election could have resulted in 66%–34% GOP–Dem splits in every district, meaning the whole Senate would have been Republican. Uff da—imagine that!

Related Reading: This May 2014 Vox article shows what Congressional districts would look like if we ignored state boundaries and used the shortest split-line algorithm:

Split-line Congressional districts, produced by Warren Smith and Jan Kok,
Split-line Congressional districts, produced by Warren Smith and Jan Kok, (Click to embiggen!)

Aberdeen, Huron, and Watertown would share a Representative with Fargo, Jamestown, and Devil's Lake. Pierre and West River would be in with Bismarck, Minot, and the Bakken oil fields. Mitchell, Yankton, Vermillion, and Dakota Dunes would go with Sioux City, Norfolk, and Grand Island. Sioux Falls would come out as the population hub of a quadrilateral consisting mostly of southwestern Minnesota and northwestern Iowa. 


  1. grudznick 2014.12.28

    It is amazing how these fellows can do all that surveying and mark out the lines on the map so well. What is the white areas that both the LRC and these French surveyor fellows all seem to leave blank on each map? I notice that all of them surveyed out the exact same areas so I can figure that those are either lakes or places where the locals are registered independent or where certain conspiracy sects are buckled down.

  2. Richard Schriever 2014.12.28

    Algorithmic districting was an issue I supported in my last campaign - and still do. The perfectly proportional distribution of Rs and Ds is a non-issue. In fact, the whole problem with out current scheme is that it IS based on creating an advantage for one party by setting boundaries that create districts that take as many minority party registrants as possible into a majority district to assure as small a margin as possible in majority minority districts.

  3. Lynn 2014.12.29

    District 33 looks like it is so obviously rigged. Brown and Spink counties seem messed up and around Bon Homme also. There has to be a better way of doing this as Richard mentions above. Doesn't Minnesota have redistricting done by a non-partisan entity?

    What about these full-time RVer's that are technically residents of our state to escape their home state's taxes or where they presently spend the most time, vote in South Dakota yet rarely spend any actual time or have a real stake in our state? Is anything going to be done about this?

  4. Nick Nemec 2014.12.29

    The full time RVer issue is worth talking about but don't expect anything to be done about it because full time RVers are a nearly lilly white, retired, upper income population, they vote overwhelmingly Republican and the Republicans in Pierre like it that way.

  5. Troy 2014.12.29


    You mean we could have done better in re districting and gotten 100% of the Senate by being purely mathamatical and ignored the politics? You Dems should be thanking the GOP for our altruism. :)

    Seriously, I think it is bad policy to ignore existing political boundaries as they mean something (county seats are the center of activity and thus the "public square." Because of this, I think the current map is as good as we can get because this is way counties got split the least possible way, including where it was inevitable because of large population counties (Brown, Pennington, Lincoln and Minnehaha).

    The only thing that could be better is to use a wagon wheel concept from some of the trade centers.

  6. Steve Sibson 2014.12.29

    If we want true representation, then each county should be a district. Imagine all the districts within Sioux Falls becoming one district for Minnehaha county? The crony capitalists would have less power.

  7. jerry 2014.12.29

    The RV folks should still be able to vote, but as Nick Nemec points out, they vote republican and should be considered in the equation as such. They should not be districted in the manner they are right now as a voting bloc for Jensen.

  8. jerry 2014.12.29

    Actually Sibson, that is not a bad idea. Why not? The boundaries have already been established. What is the difference between that and what we are doing on a national level? If you own land in more than one county, you take the county in which you have the homestead.

  9. Bill Fleming 2014.12.29

    Sibby's idea makes some sense from an 'organizational' perspective. Aside from facilitating statewide elections, there really isn't any other 'governing' function for voting districts is there? I realize there is a population distribution issue, but considering that only about half of the people actually vote, is it really the most compelling issue representationally speaking. It would indeed be interesting to see how things would work in Pierre if, for example, Shannon and Todd counties had exactly the same voting power as Pennington and Minnehaha counties do. Are there any other states who have organized their state legislatures by county? And setting Sibby's suggestion aside for a minute, what representation DO counties (as counties) have in our state legislature anyway?

  10. caheidelberger Post author | 2014.12.29

    Jerry, Steve, the difference is that at the national level, the by-state representation of the Senate is balanced by the proportional representation of the House. Steve, would you support a House consisting of one Representative from each county and a Senate consisting of one representative from each of the above mathematically drawn, populationally proportional districts (either 35 or 70)?

  11. Steve Sibson 2014.12.29

    Bill, the counties are represented by the Association of County Commissioners, which is another collectivist tool to eliminate individual counties from having any kind of political power.

  12. Steve Sibson 2014.12.29

    Cory, that would be an interesting scenario to consider.

  13. caheidelberger Post author | 2014.12.29

    Cube-root rule—interesting! By that formula, the South Dakota House should have 94 representatives.

    Nationally speaking, 435 Reps means one Rep per 729,000 citizens. South Dakota is thus 14% underrepresented. Go for the cube-root rule, increase the U.S. House to 682, and you'd have one Rep per 465,000 people. Give South Dakota two, and we'd be overrepresented by 12%.

    Maybe the problem is not the House, but the Senate. Maybe 100 Senators is too few, concentrating too much power in such a tiny group of individuals. Maybe each state should have six Senators, two elected each election year, same way we elect our state reps. Dilute their power, make it harder for lobbyists to buttonhole [oh! you should have seen the Freudian typo there!] a few key Senators to sway a vote.

  14. Steve Sibson 2014.12.29

    " Dilute their power, make it harder for lobbyists to buttonhole"

    That would be best done by reducing the size and scope of government. Simply sending more politicians elected with crony money will not fix anything.

  15. Bill Fleming 2014.12.29

    Cory, a nitpick perhaps, but wouldn't the theoretical equivalent be the other way around? i.e. The 'people's House' would be derived from the mathematically proportional districts, and the 'Senate' by county? Very interesting idea. How long woul it take for the 'urban' and 'rural' coalitions to form... Or the 'East River' and 'West River' caucuses? So much more interesting and uniquely South Dakota than the usual 'D vs R vs I' divides.

  16. Steve Sibson 2014.12.29

    Bill, you are right theoretically. The problem would be the size of the legislative chambers. The House chamber is big enough for 60 plus legislators, The Senate chamber is not.

  17. Bill Fleming 2014.12.29

    Sibby, I don't see how your idea addresses the 'crony money' issue per se, except perhaps to reconfigure the composition of the various 'crony' networks. The only way to do that would be campaign finance reform, wouldn't it?

  18. Bill Fleming 2014.12.29

    Sibby, the 'chamber size' issue is simple enough. Just rename them. ;-)

  19. Nick Nemec 2014.12.29

    Bill F. I don't have a link, but many years ago the US Supreme Court ruled against legislative schemes that proportion members based on factors other than population. Such methods of drawing districts violate the principle of "one man, one vote." The US Senate is exempt from the ruling since the two Senators per state rule is written into the Constitution.

  20. Bill Fleming 2014.12.29

    Thanks, Nick. As per Cory's refinement of Sibby's idea, above, the resultant two chambers would still be Constitutional, wouldn't they? If not, why not?

  21. Bill Fleming 2014.12.29

    ...or, Nick, are you saying that it would be unconstitutional to treat counties like 'mini-states'?

  22. Richard Schriever 2014.12.29

    Sibby- Okay -we could go to county-based representation - IF those representatives votes were WEIGHTED to assure one-man-one-vote values. So the Senator or representative from Minnehaha County would have 4.5 votes to Brown County's ONE vote - for example. Or 45 votes to Hanson County's ONE.

  23. Nick Nemec 2014.12.29

    It is unconstitutional to treat counties like mini-states for the purposes of drawing legislative districts as per Reynolds v. Sims. This ruling has also been applied to other districts, such as county commissions, school boards or town councils, where voters elect representatives from specific districts.

    Districts must be of roughly equal population, within reason, to be considered constitutional. There have been several cases in SD, notably in counties with reservation and non reservation areas, where the courts have ruled against a map because it violated the one man one vote rule.

    Especially egregious was a county commission map in Buffalo County, from 15-20 years ago, where 2 districts each had around 100 people (mostly white) and one district had around 1500 people (nearly all Native). The ACLU threatened to challenge in Federal District Court and the county, realizing they had a loosing case, conceded.

  24. Richard Schriever 2014.12.29

    As to national representation, I have long championed the idea of expanding the US House to representation at the SAME level it was at the founding - which the founders felt was a good "sample" of the population. That would be one Representative for every 40,000 people. That would give us 7,700 Representatives. Lobby THAT body, or buy THAT vote, big PAC $$$. Go ahead, give it a try.

  25. Steve Sibson 2014.12.29

    Now this thread has turned into a discussion of implementation of a democracy (one-man-one-vote) that has been used to destroy the Constitution, which set up a "republic". So now we have Sioux Falls and the other urban populations implementing cronyism. Sadly, that is one reason why rural areas are depopulating...go to the city and work for a corporation.

  26. Steve Sibson 2014.12.29

    "I don't see how your idea addresses the 'crony money' issue per se"

    Bill, thanks for brining the point up as it does need explanation. Industrialization caused urbanization. Without out those two, it would be difficult if not impossible to have cronyism, because you need to have that concentration of wealth. The Soviet's learned that the rural individualistic farmer posed a problem for their collectivist brand of government. And they could not be bought off with "jobs".

  27. jerry 2014.12.29

    The squeal of loosing power is actually fun to hear. The rural counties have not been heard since territory days when we were all rural. The fact that the populated areas have the most voice is not fair in a one man one vote democracy, as Sibson points out. There should be a representative and a senator for each county to follow existing term limits for those offices. It is long past time for equal representation at the state level.

    The Cube Rule for the house nationally for sure. I kind of like the idea you put forth Cory regarding the Senate. The house is where the money is directed to run the place. Maybe if we had better representation we could cut the defense department drastically. Why do we need them? How long are we going to be training the Iraq army? Don't you think 14 years is a long time to be in basic training? Our military leaders have failed us.

  28. larry kurtz 2014.12.29

    President Jefferson believed the State of Virginia should have given fifty acres to every white head of household and bought Indian Country from France.

    Happy Wounded Knee Massacre Day.

  29. Bill Fleming 2014.12.29

    LOL, Nick. It figures doesn't it? One of the rare times Sibby and Jerry and I seem to agree on something and it turns out to be illegal! ;-)

  30. jerry 2014.12.29

    True Bill Fleming, like the Supreme Court really knows anything after their last failures.

  31. Steve Sibson 2014.12.29

    The Supreme Court is about destroying the Constitutions.

  32. Nick Nemec 2014.12.29

    The one man one vote ruling is one I support. It makes gerrymandering a little more difficult and less obvious.

  33. Steve Sibson 2014.12.29

    Nick, the problem is that the men, including farmers, are being bought off with big government programs.

  34. larry kurtz 2014.12.29

    Sibby is right: paving over the whole state will facilitate cleaning up oil spills from Bakken pipelines and vacuuming up heavy metal oxides from upwind coal-fired power plants. Doze Mitchell into a pile and give everybody fifty acres for subsistence farming using water from the James River.

  35. Patrick Duffy 2014.12.29

    I handled the Crow Creek case to which Nick Nemec makes reference as local and trial counsel to the ACLU's Voting Rights Project in Atlanta. As "obvious" as the result in the case may have seemed on its face, it didn't resolve itself quickly. The County hired a USD law school professor to assist the States' Attorney who handled the case. This kind of litigation is expensive and almost inordinately complex, more so in my experience than either of the two types of cases seemingly most complex, securities or antitrust cases. Victories are hard won.

    Suffice it to say that no redistricting plan can run afoul of the Voting Rights laws. The precision with which this can be done is gasp-inducing, as Tom DeLay and Texas showed recently in an off-year attempt to redistrict the State of Texas. Computer programs that employ everything from IRS data to zip codes can deftly slice districts right down the middle of streets to insure a redistricting plan is in compliance.

    There are really no such protections for the rest of us. The process of redistricting has always been seen as one of the fruits of political victory. And so districts will always mirror the will of the political party in power at every decennial redistricting. Thus, in a State like South Dakota where single-party rule has been the order of the day for nearly forty years, districts are carved out in a way that preserves majority rule.

  36. jerry 2014.12.29

    So, in other words Mr. Duffy, we really do not have the democracy we think we have.

  37. Patrick Duffy 2014.12.29


  38. JeniW 2014.12.29

    We have known all along since Janklow was governor, that dictatorship is what rules in SD, at least on the state level.

  39. 96Tears 2014.12.29

    More important to the future of South Dakota than stopping payday loan sharking is the issue of misrepresentation in Pierre, or one-party hyper-representation. Computer models based on voter history, age and income projections and race, as well as more and more refined voter suppression techniques, have allowed a one-party machine to shut out stake holders from access to controlling their state government. South Dakota is about as pure an example of hyper-representation as any other state.

    I congratulate the Republicans in South Dakota for expertly controlling statehouse and now congressional politics without peer. Brilliantly done, my friends. But continuing down this path guarantees something that is anti-American and abusive.

    The constitution needs to be changed to prevent decades more of one-party rule that denies adequate representation. The remedy must be fair and appropriate. It also must sell with everyday folks. As Lynn mentioned the Minnesota example, South Dakota can be better served if a nonpartisan committee, spelled out in the constitution, were to meet every 10 years to construct the new state legislative district voting map. That power must be removed from the legislature.

    People don't want their city limits or school districts or county lines determined as spoils for partisan victories. Why would they want their legislative district to be treated that way?

    If Democrats want an issue that can get agreement as a ballot measure, taking partisan selfishness out of determining their home legislative districts would be a solid reform measure.

  40. Bill Fleming 2014.12.29

    And so, one more time, given all that we have learned here, why is it not the case that the single best solution for us to retrieve our democracy is to abandon our party, at least for the primary, and vote as Republicans?

    It's a lot of paperwork, I know, switching back and forth, but at least you'll have a say in who gets elected.

    And, come to think of it, why even bother to switch back?

    Nothing says you have to vote for the same person in the general.

    So go ahead... be that rare type of Republican who votes for anyone they want to... the kind we used to have way back when. Here's your chance, SD Dems.

    Want the SDGOP to change?

    Be the change. :-)

  41. jerry 2014.12.29

    I have thought the same thing Bill Fleming. That is not being defeatist either, it is a matter of practicality. You can even get to go to their meetings and yell bullshit! What is there not to love about that.

  42. 96Tears 2014.12.29

    I've heard that one before from elders in the party who saw 20 years ago this was no longer a viable enterprise, Bill. I understand it and can sympathize with it. I just can't imagine that I could despise my nation and fellow Americans enough to call myself a Republican, knowing what that party has stood for since 2001. Good luck. If it works for you, more power to you brother!

  43. leslie 2014.12.30

    bill f.-maybe you are right if we all permanently register republican but vote democratic. :) "robber barons"-freedom now means capitalism.

    and no, troy, the current map is not as good as can be had.
    "this is a class war. the war just hasn't started yet." moyers

    Dave Lust, Esq. (R.)-mumbles something to the effect that "the legislature rightly ignored EB5 ... its a phantom ... we don't have investigative expertise." rcj

    NOTE TO SDDP & SDP: Why was Larry Lucas absent from GOAC meeting when Wismer needed a second to consider a subpeona of the joopster?

    just some thoughts.

  44. caheidelberger Post author | 2014.12.30

    Reynolds v Sims—very useful, Nick! That should save us time in further redistricting debates. One citizen, one vote has to guide any redistricting scheme.

    I am intrigued by Justice Harlan's dissent: why can't states set up their own legislatures the way the Constitution sets up the U.S. Senate? Why are states not allowed to forge their own "Great Compromise" to preserve their own unions of large urban counties and small rural counties? I guess the distinction lies in the nature of federalism: states exercise a sovereignty within their federal union that counties do not within their state union. Counties did not come together to form South Dakota; counties exist as formal subdivisions of the state. They thus cannot claim any special right to representation that trumps "one citizen one vote"... or so I feel one would have to argue to knock down Justice Harlan's dissent.

    So if West River and rural counties are really bent out of shape at the dominance of South Dakota's "urban" centers, is their only option to preserve their power to secede and form their own state à la California (oops—that effort didn't go too well)?

  45. Steve Sibson 2014.12.30

    "Reynolds v Sims—very useful, Nick!"

    Very useful for destroying republics and then establishing democracies, which are the foundation to communism.

  46. Steve Sibson 2014.12.30

    "So, in other words Mr. Duffy, we really do not have the democracy we think we have."

    You mean the SDGOP Establishment were not voted into office? Of course they were. We indeed have a democracy and not a republic.

  47. larry kurtz 2014.12.30

    Sibby, you won: the legislature is doing your bidding.

  48. Donald Pay 2014.12.30

    There is a growing movement away from partisan political dominance of the redistricting process. Twelve states use independent commissions to redistrict, and totally eliminate that Legislature from process. Iowa has a mixed system, where an independent commission draws the boundaries and the Legislature votes to accept them.

    Redistricting must meet the one person-one vote standard, and it also must not be obviously racially discriminatory. In Iowa they also try to get compact districts (no gerrymandering to favor any party) that follow political boundaries.

    In Wisconsin, as in South Dakota, they use the spoils system, which results in safe districts and uncontested elections. At least SD has term limits to clear out the dead wood.

Comments are closed.