All posts by brian

Replicating the Kansas Vote Fraud Study

A Wichita State University statistician, Beth Clarkson, has been in the news lately regarding a study she conducted on voting results in several states, and specifically her challenge in her home county to release election records to sort out whether voter fraud took place in the 2014 election. In a nutshell, she replicated an earlier paper by Choquette and Johnson that looked at the 2008 and 2012 elections; the authors sorted precincts in a county or state by the number of votes cast in each precinct, then plotted a “cumulative precinct vote tally”, displaying the change in the vote share for a particular candidate starting with the least populous precincts, and adding in the more populous ones to the running average moving rightward in the charts.

The strange effect that Choquette, Johnson, and Clarkson find is that there is an upward trend in these charts after a certain point in precincts that used certain types of electronic voting equipment, which they take as an indication of vote fraud. While Dr. Clarkson doesn’t specify the exact method of fraud she suspects, Choquette and Johnson theorize that “vote-flipping” is occurring – in more populated precincts, where it is easier to hide and more efficient, votes are changed from one candidate to the preferred candidate of the fraudster, leaving the total number of votes cast the same.

In this post, I’m going to replicate the 2014 Kansas Senate race results Dr. Clarkson presents, as this has become the newsworthy case given Clarkson’s challenge in her home county, and provide a couple comparisons to explain why this trend occurs.

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Cropping the Mercator Projection


The Mercator projection is the map people love to hate. The West Wing humorously laid out the case in one of their “big block of cheese” episodes, and the complaints generally fall on the issue of distortion: things far from the equator are stretched more than things near the equator. Greenland appears to be the same size as Africa, but is actually about 14 times smaller.

One thing that people generally don’t comment on is the fact that a Mercator world map never actually shows the entire world. It’s not uncommon, like the image above, to cut off the northern latitudes at 80 or 82 degrees, leaving off the northernmost parts of Canada, Russia, and Greenland, and to slice Antarctica at a point that just barely leaves in all the coastline. Even Google Maps – yes, Google Maps, like most online mapping services, uses a form of Mercator – cuts off at right around 85 degrees (although the precise choice is for a secondary cool reason I’ll mention below).

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Checking District Contiguity

Though not a federal standard, contiguity is the most common state-applied standard for district maps, and therefore is an important feature to be able to guarantee in any automated redistricting program. Put simply, one should be able to walk from any point in the district to any other point in the district without having to cross a district boundary.

Contiguity checks can be useful in other contexts, too. For example, when examining the changes made between a proposed district plan and its amended version in the redistricting process, it is relatively simple to generate statistics on, say, the people who were moved out of a particular district. But it’s possible that two different chunks of people were moved out, from opposite ends of the district and with different demographic profiles, or perhaps more than a dozen different chunks (see: changes to congressional district 5 in the Florida redistricting process). Sorting out the different groups can be done visually with a program like ArcGIS, but if you’re doing this process on a number of different districts in a number of different maps, it’d be nice to have an algorithm to separate out the pieces for you.

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Measuring District Map Similarity

While working on the various Florida redistricting challenges over the past couple years, one of the major tasks was to sort out the source of district shapes in enacted maps from earlier introduced maps and publicly submitted maps. This was not something that could be done, at least easily, through visual inspection – the Florida Senate redistricting site has over 100 maps for download for the congressional plan alone. Additionally, appearances can be deceiving. An extreme example – fictional, but based on something that actually came up – is presented below.


These districts differ massively in shape, but contain the same individuals, save for 20 people – as you can imagine, the population density of the Everglades is pretty low. One can imagine the reverse, as well, where minor geographic changes in dense city areas can have large impacts on the makeup of a district.

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Preventing Partisan Gerrymandering with Partisan Gerrymandering


Disclaimer: this is not a serious proposal. At best, it’s a thought experiment, but only if you don’t think too much about it.

Florida is interesting in that they are just one of three states (according to Justin Levitt) that explicitly allow for “floterial” districts. A floterial district is one that overlaps one or more other districts in a map. A formerly common example of this type of district arose when a state gained a member of the House, but failed to pass a new congressional map; the new member would be elected by the entire state, at large. These fell out of use with the 1960s reapportionment revolution (though are still the federal statutory remedy should a state fail to pass a map while gaining a seat), when redistricting became mandatory after every census. The only current usage of floterials I’m aware of is in the New Hampshire State House – they place a high value in not splitting towns, and in complying with equal population requirements, they make up population deviations by drawing floterial districts over adjacent underpopulated districts.

But floterial districts could be an interesting way of combating gerrymandering, by allowing both parties to gerrymander. What would happen if you allowed Republicans and Democrats to each draw their own statewide map with half the districts required, and overlaid them into a single, full district plan? Would the net result end up being relatively fair? In the spirit of the re-redistricting of the Florida congressional map that’s going on now, I gave it a shot with Florida’s 27 districts, with a 13-district Democratic gerrymander, a 13-district Republican gerrymander, and a statewide at-large district.

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The Impact of Zeroing Out


The picture above shows part of the line dividing Nevada’s 1st (north) and 3rd (south) congressional districts. The line follows East Russell Road for this stretch almost perfectly, but juts upward for a block and comes back down. What is so special about the 13 residents that live there that warrants a change in an otherwise smooth line? Why not the block next to it? Why a jut at all?

It’s worth noting that that deviation from the line represents a single Census block, which is the smallest unit of geography that the Census reports population counts for. What this means for mapmakers is that the lines of a state’s Census blocks represent the possible lines for their districts: they can’t split a block, since they won’t know how many people are in either division.

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Hillsborough County Commission and the Voting Rights Act

The Hillsborough County Commission currently has seven members, four of which are elected from districts, three elected at-large by the entire county. This is not a new arrangement, and the hybrid system of districts/at-large is not unique – in fact, my home city of Gainesville has the same four district/three at-large setup for their commission. A map of the districts is below (click for a larger view).


The county has seen racial change over the past few decades, especially when it comes to the Hispanic population. In the 1990 Census, 13% of the county was Hispanic, in 2000, 18%, and in the most recent Census, Hispanics made up 25% of the county. However, there is no majority-Hispanic district in the county. Instead, District 3 is a joint Hispanic/African-American majority district, with a voting-age population of 35.5% African-American and 23.4% Hispanic; this district currently has an African-American representative, and there is no Hispanic representative currently on the commission.

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Automated Redistricting and the Florida State Senate

The latest challenge of Florida’s congressional districts wrapped up last week, which brought to light a lot of questionable behind-the-scenes behavior on the part of the Florida legislative leadership during the redistricting process. Should the ruling go in favor of the Democrats and the League of Women Voters/Common Cause coalition, the findings produced during the case make it likely that the state senate maps will be challenged (again) afterward.

It’s easy to get cynical about the process, no matter what supposed safeguards are in place, such as Florida’s 2010 “Fair Districts” constitutional amendments. Many come to the same conclusion as Christopher Ingraham at the Washington Post – why not consider letting computers do it?

Like Ingraham says, algorithms for redistricting already exist, and have for over fifty years now. The operations research literature has had quite a bit of discussion on potential methodologies, as have election law journals and random programmers, ranging in levels of sophistication and computational complexity. There are a couple algorithms in particular I seem to see posted regularly around online. They’re both great in what they set out to achieve, and have made some headway in popularizing the idea of automated redistricting, so I’m a fan of the creators of both. Unfortunately, both algorithms fall on the simplistic side of suggested methods (by design), which has some major drawbacks.

Continue reading Automated Redistricting and the Florida State Senate