Challenge 3. Gerrymander Fix

Seven states have only one seat in the House, so this discussion pertains to the 43 states that have more than one House seat. However, the problem of gerrymandering is even more pronounced with respect to drawing election districts for state legislatures. Therefore, the solution recommended here for Congress can be applied to all 50 states.

The recommended solution to gerrymandering has two components: 1) Ranked Choice Voting combined with multi-seat Congressional Districts, and 2) fully-automated redistricting based on zip codes. Let me first explain why Ranked Choice Voting and multi-seat Congressional Districts go hand-in-glove together, and then we will tackle fully-automated redistricting.

Ranked Choice Voting Combined with Multi-Seat Congressional Districts

This solution by itself does not eliminate gerrymandering. Rather, this solution makes gerrymandering less important.

The basic idea here is two-fold:

  1. Ranked Choice Voting (RCV) increases the probability that, in any election with multiple winners, opinions held by a significant portion of the electorate will be represented by at least some of the winners.
  2. With RCV, we can expect that multi-seat Congressional Districts will result in a majority of winners who represent the majority view of a CD, but some winners will also represent a widely-held minority view.

As detailed earlier in section 2.1, I recommend RCV for all elections, both those with a single winner and those with multiple winners. RCV produces fairer representation of the entire electorate than the First-Past-The-Post scheme.

In Part I, Section 1.3.4, we mentioned that from time to time some states have had multi-seat CD’s. States sometimes created multi-seat CD’s as a tool in partisan redistricting. A 1965 civil rights era law ended multi-seat CD’s, but that occurred before Ranked Choice Voting was on the table. Let’s apply RCV and multi-seat CD’s to the question of CD boundaries and the problem of gerrymandering.

We could require states with five or fewer seats in the House to elect all their representatives at-large. At present seven states have only one House seat, so these seven are already elected at-large. 17 states currently have from two to five House seats. Hence, with this new rule, 24 states are removed from the Congressional gerrymandering challenge.

Then let’s posit that, in each of the remaining 26 states, the number of CD’s equals the number of seats in the Chamber, and each CD must elect three, four, or five House seats. 14 of these 26 states would have just two CD’s, so again the gerrymandering challenge should be far easier to overcome than it is with single-seat CD’s.

To see how multi-seat CD’s with Ranked Choice Voting might affect the political makeup of Congress, let’s examine the expected results in three-seat and in two-seat CD’s dominated by one political party, and then extrapolate these observations to five-seat and four-seat CD’s. (We address three-seat and two-seat CD’s first, because the math is easier to understand. Once understood, you can readily understand the extrapolation to five-seat and four-seat CD’s.)

Three-Seat Congressional Districts

Given two major parties, Party A and Party B, if Party A has 60% of the voters and Party B has 40%, in most elections we can expect Party A to end up with two seats, and Party B to win one seat. Here is the logic, using plausible suppositions:

Each party fields three (or more) candidates for the three available seats. Each party has one very strong candidate, along with two less strong candidates. So the candidates are designated as A1, A2, and A3 from Party A, and B1, B2, and B3 from Party B. Let’s also assume that Party A’s voters select A1 as their 1st choice, A2 as their 2nd choice, and A3 as their 3rd choice. Similarly, Party B’s voters select B1, B2, and B3, in that order.

In an election with three winners, the threshold for winning is 25% of the total vote plus one vote (which we will refer to here as 25%+). This is because it is mathematically impossible for three other candidates to also have 25%+ votes.

Applying the RCV procedure for tabulating votes in a multi-winner election, we can expect the winners to be candidates A1, A2, and B1. This is because Party A’s 60% elect A1 (using 25%+ first choice votes) and A2 (using another 25%+ second choice votes). The remaining Party A votes (third choice votes) are insufficient to elect A3. Meanwhile, Party B’s 40% elect B1 (using 25%+ first choice votes), with insufficient excess to elect anyone else.

Three other scenarios are possible, but less likely:

  1. Party A wins all three seats, but this can only happen if Party A gets at least 75%+3 votes for its candidates, or if sufficient Party B voters defect from their top choice (B1) to prevent B1 from meeting the threshold. Or
  2. Party B wins two seats, but this can only happen if sufficient Party A voters defect to Party B when making their 1st or 2nd
  3. An independent or third-party candidate captures one of the seats. This is far more realizable with RCV and multi-seat districts than it would be at present. This is because a strong independent candidate might very well become the preferred second choice for voters from both Party A and Party B.

Two-Seat Congressional Districts

Given the same voter setup as with three contested seats – that is, Party A holds a 60% to 40% advantage – we can expect each party to win one seat. Here is the logic:

The threshold for election is 33 1/3 % + 1 vote. Again, this is because it is mathematically impossible for a candidate who meets that threshold to lose.

We can expect the winners to be A1 and B1. This is because Party A’s 60% puts A1 over the threshold, with insufficient votes left over to elect A2. Similarly, Party B’s 40% put B1 over the threshold.

A less likely scenario is that Party A wins both seats. This can only occur if Party A gets 66 2/3% + 2 votes.

For Party B to win both seats is nigh on impossible.

Five-Seat and Four-Seat CD’s

We can extrapolate these results to larger CD’s:

  • In a five-seat CD, the dominant political party will likely win three seats, though two seats or four seats are also quite possible. The minority party will likely win two seats, though one seat or three seats are also possible.
  • In a four-seat CD, the most likely result is a two-two split between the parties, though a three-one split in favor of the dominant party is also on the table.


We can derive several conclusions from this analysis: 1) We are likely to end up with better representation of voters’ views using RCV and multi-seat CDs, and 2) candidates of both Party A and Party B will increase their chances of winning if they appeal to voters of both parties. This tendency will be even more pronounced if we also adopt single, open primaries for all offices. The result will almost inevitably be a Congress that is less partisan, less extreme at both ends of the political spectrum, and more interested in catering to the needs of all voters in their districts.

The advantages of RCV combined with multi-seat districts also accrue to states that adopt these reforms for their state legislatures. is a non-profit organization that discusses and campaigns for more fair election systems. FairVote has been at the forefront of organizations supporting RCV combined with multi-seat CD’s as a solution to gerrymandering (see

Combining Multi-Seat CD’s with Chamber Districts

The fix for the unrepresentative U.S. Senate in Section 2.4 is to replace the Senate with a Chamber of Deputies, made up of one Deputy for every five Representatives in the House. How convenient this is to the establishment of multi-seat CD’s!

The 24 states with five or fewer House seats elect all their House seats and their one Senate seat at large.

For the other 26 states, the number of CD’s in each state equals the number of Deputies in that state. Each CD could therefore elect one Deputy. This does leave some choice to certain states. For instance, Virginia currently has 11 House seats, which would give it three Deputies. Virginia could decide to have one CD elect five House seats and two CD’s each elect three; or Virginia could choose a 4-4-3 scheme. In either case, Virginia could decide to let each CD elect one Deputy, or it could elect all its Deputies at large.

Part B: Fully Automated and Non-Partisan Redistricting

Most observers would agree that the solution to this problem is to remove redistricting from the control of politicians and to use computer software to make the redistricting process easy and automatic. This proposed solution satisfies both of those criteria.

To adopt this fully-automated solution, we must limit our objectives for redistricting to the following:

  • Make the population per House seat within a state as equal as possible;
  • Afford some consideration to geography, keeping neighbors together in the same CD if possible; and
  • Remove humans from making decisions about district boundaries.

The first of these objectives, equalizing the population per House seat, reflects basic fairness, the time-honored notion of “one man – one vote”.

The second objective is intuitively obvious to Americans, but geography is not necessarily the only criterion that could be used. In Florence in the Middle Ages, representatives to the city council were chosen by occupation: construction trades elected one rep, farmers another, merchants another, and so on. We could use religion: Catholics elect their representatives, Protestants elect theirs, Jews elect theirs. We could use age: everyone 18 to 30 elect their reps, those 30 to 55 elect theirs, and so on. We could divide ourselves by social class, as France did before the French Revolution: churchmen in the First Estate, noblemen and aristocrats in the Second Estate, and the bourgeoise in the Third Estate. We could do it by income or by net worth: Starting at the top, the wealthiest 750,000 residents of a state elect one congressperson, then the next wealthiest 750,000 elect the second congressperson, on down to the poorest 750,000 residents who elect the last congressperson. We could also dispense with these distinctions all together, and just let a computer randomly assign each voter in a given state to a CD. But having said all that, we in this country still have some affinity for geographic proximity as a basis for deciding which folks belong in the same election district. Hence an automated solution to redistricting should at least take geography into consideration.

Many state statutes, some federal statues, and countless court cases have addressed the allowable criteria in drawing election districts. Laws and courts have mandated approximately equal populations in each district, as well as geographic compactness. Some redistricting plans consider race or other demographic factors to ensure that the redistricting scheme does not unfairly disadvantage any protected class. Those responsible for drawing district boundaries have also considered (whether openly or secretly) party registrations, previous voting patterns, city and county boundaries, and wealth, among other criteria. Since the 1960’s, the major debates have centered on race, socio-economic status, and political affiliation. It appears that every redistricting plan from every state has been subject to litigation; and courts have had a devil of a time trying to sort out these competing interests in order to decide what is legal, fair, and reasonable.

I propose to end all the debate and all the litigation. This solution is not perfect, but it’s far better than the current conflicted landscape and also far better on balance than any of the human-engineered solutions offered to date.

The actual physical process of drawing boundaries for Congressional Districts should be straight-forward, uncomplicated, easy to understand, completely non-political, and fully automated.

The solution proposed here uses the population data for Zip Code Tabulation Areas (ZCTA’s) developed by the US Census Bureau from the US Postal Service’s 5-digit zip codes.

Zip Codes, developed by the United States Postal Service, represent mail delivery routes, not populations or geographic boundaries. The Postal Service uses the first 3 digits of the zip code to identify a mail delivery center, responsible for mail delivery to all the component 5-digit zip codes. Hence, all the 5-digit zip codes within that mail delivery center’s service area will turn out to consist of a largely contiguous land mass.

The Census Bureau extended the postal zip codes to represent geographical areas, called zip code tabulation areas, or ZCTA’s, and then counted the number of people in each ZCTA. ZCTA’s, unlike zip codes, are geographic and do cover the entire country. For most people, your ZCTA matches your postal zip code. Hence, we can use the ZCTA’s in numerical order, in conjunction with population data for each ZCTA, as a means of creating election districts.

In simple terms, a computer program creates the CD’s for any state from the list of ZCTA’s for that state in numerical order along with the population of each ZCTA. The computer program assigns ZCTA’s to CD 1 starting with the lowest-numbered ZCTA, while calculating the running total for all ZCTA’s assigned to CD 1 until the target population for that CD is reached. At that point, CD 1 is complete, and the program begins assigning ZCTA’s to CD 2. The program continues in this fashion until all CD’s in the state are complete.

I admit that this proposal is less than perfect. The reason this solution is less than perfect is that in some cases around the country, a 3-digit mail delivery center is not contiguous with the next numbered 3-digit mail delivery center. For example, in Maryland, zip codes beginning with 216 and 218 are on Maryland’s Eastern Shore, at the opposite end of the state from zip codes beginning with 215 and 217 in Western Maryland. However, I would argue that religious adherence to contiguous areas and geographic compactness is less important than religious adherence to fair representation. In addition, if Maryland Congresspersons were to complain about the challenge of trying to represent a geographically disperse constituency, I suggest they consider the plight of their Alaskan compatriot, whose one Representative must represent all peoples in an area more than twice the size of Texas!

One more item is necessary to complete this redistricting scheme: Once adopted, how do we prevent politicians (or anyone else) from playing games with the zip codes? The answer is that we use the ZCTA’s created for the 2010 census in perpetuity, updated by population data from the census every 10 years.

Automated Redistricting Using ZCTA’s

This section describes the logic of a computer program that can create CD’s for any state using ZCTA’s. Following the program description is an example of the application of this solution to the state of Maryland.

Here are the steps a computer program will implement to draw CD’s for any state:

  1. The initial step for any solution is to determine how many seats each state will have in the House of Representatives. The US Constitution provides that the number of seats in the House of Representatives accorded to each state be reapportioned following the mandated decennial census. In accordance with current federal law, the total number of seats is 435. Each state gets the same percentage of the 435 seats in the House as that state’s population is a percentage of the total US population. Hence, the solution described here begins with a state’s total population and the number of seats it will have in the next House of Representatives. With that information, one calculates the target population per House seat. The target-per-seat is defined as the quotient of the state’s total population divided by the number of House seats for that state.
  2. We propose multi-seat CD’s. States with fewer than four House seats elect all House members at large. States with four or more House seats are divided into CD’s with two or three seats in each CD, and with as many three-seat CD’s as mathematically possible. Two-seat CD’s are listed first. With this information, we can determine the number of CD’s for any state and the number of seats in each of those CD’s. The target population for any CD is the state’s target-per-seat multiplied by the number of seats in that CD. (Note that the fully-automated solution for drawing CD’s is not dependent on multi-seat CD’s. This solution works for single-seat CD’s and for state legislative districts as well.)
  1. Obtain from the Census Bureau a list of all the ZCTA’s for the state, along with the population in each ZCTA. Put the list in numerical order by ZCTA.
  2. Computer program input data:
    1. Total state population
    2. Number of House seats
    3. List of ZCTA’s, in numerical order, with the population in each ZCTA
  3. Computer program processing/logic
    1. Preliminary processing
      1. Calculate the target population per House seat, which = the state’s population divided by the number of House seats apportioned to that state.
      2. Calculate the number of two-seat CD’s and the number of three-seat CD’s. Each CD will have either two or three seats, with as many three-seat CD’s as mathematically possible. Hence, a state will have 0, 1, or 2 two-seat CD’s.
  • Create a table with four columns labeled CD#, Seats in This CD, Target Population for this CD, and a Running Total of Target Populations for all CD’s (called here the Aggregate Target Population).
  1. Populate column 1 of this table with the CD#.
  2. Populate column 2 with the number of seats for each CD. Two-seat CD’s are listed first.
  3. Populate column 3 with the target population for each CD: The target population for each CD = the target population per House seat multiplied by the number of seats in that CD.
  • Populate column 4 with the aggregate target population (ATP) for each CD. This number = the sum of the target populations for each CD up to and including the current CD.
  1. Repetitive processing
    1. Assign ZCTA’s in numerical order to CD 1, and keep track of the total population assigned. Stop when the addition of one more ZCTA would result in a population for CD 1 greater than the CD 1 ATP. Label this ZCTA as 1MoreZCTA. 1MoreZCTA will be either the last ZCTA in CD 1 or the first ZCTA in CD 2. Add 1MoreZCTA to CD 1 only if adding it would make CD 1’s population closer to the CD 1 ATP as opposed to not adding 1MoreZCTA to CD 1.
    2. Begin assigning ZCTA’s to CD 2, beginning either with 1MoreZCTA if that ZCTA had not been added to CD 1 or beginning with the next ZCTA after 1MoreZCTA if 1MoreZCTA had already been added to CD 1. Keep track of the running total of both the population of CD 2 and the aggregate populations of CD 1 plus CD 2. Stop adding ZCTA’s to CD 2 when one more ZCTA would result in an aggregate population of CD 1 plus CD 2 greater than the CD 2 ATP. This becomes the new 1MoreZCTA. Again, add or do not add this 1MoreZCTA to CD 2, depending on whether or not this brings the aggregate for CD 1 plus CD 2 closer to the CD 2 ATP. Then begin CD 3.
  • Continue creating CD’s in like manner until all CD’s are populated, save the last CD.
  1. Completion of processing
    1. At that point, all remaining ZCTA’s in the state are assigned to the last CD.[1]

In short, this technical solution is completely amenable to automation. The solution can also be applied to state legislative districts.

A Redistricting Scheme for Maryland

As an example for how completely non-partisan redistricting based solely on population could work, I tried it out on my own state of Maryland. I did not write a computer program for this example – though that could easily be done – but rather did this manually, using freely available online data sources.

I developed a redistricting plan using the Census Bureau’s Zip Code Tabulation Area (ZCTA) population tables for Maryland based on the 2010 census. The ZCTA tables show Maryland with a total population in the 2010 Census of 5,773,561. Maryland was allocated eight House seats. Therefore, the target population per House seat is 721,695. According to the proposed rule for creation of multi-seat Congressional Districts, Maryland should have two CD’s with four House seats per CD. (Alternatively, Maryland could choose to have one CD with three House seats and one CD with five seats.) With four seats in each CD, the target population for each CD is 2,886,780.

Creating these two CD’s strictly by the population of ZCTA’s in numerical order results in the following:



CD # 1st ZCTA Last ZCTA Actual population Actual aggregate Population per seat Percent Difference
1 20601 21075 2,895,395 2,895,395 723,849 0%
2 21076 21930 2,878,166 5,773,561 719,542 -0.60%

To create each CD, we add the populations of each ZCTA in numerical order until the addition of one more ZCTA to that CD would result in an aggregate population greater than the aggregate target for that CD. We then either add or do not add one more ZCTA, depending on whether or not the addition of that one more ZCTA brings the aggregate population closer to the target. In this case, the population of CD 1 per House seat is slightly greater than the target, and the population of CD 2 ends up slightly less than the target. CD 2’s population per House seat is 0.60% less than CD 1’s population per House seat, well within the accepted guideline of 5%.

We can note that the CD’s are not completely contiguous land areas. Nevertheless, most of the people in each CD are grouped into identifiable geographic areas. That is, the result is not haphazard. Examine the map of the 3-digit ZCTA’s for Maryland, and compare this to the proposed CD’s. (I found this map of Maryland’s 3-digit zip code Areas online, at

MD 3-digit zip code map

CD 1, with ZCTA’s from 20601 through 21075, are grouped around the Washington, DC metro area and southern Maryland (ZCTA’s beginning with 206, 207, 208, and 209) plus some ZCTA’s northeast of Baltimore (ZCTA’s beginning with 210). CD 2 contains Baltimore (ZCTA 212), Annapolis (ZCTA 214), the northern tier just south of the Mason-Dixon Line (ZCTA’s 215, 217, 211, 219, and the rest of 210), and the Eastern Shore (east of the Chesapeake Bay) (ZCTA’s 216 and 218).

Initially, you might think that CD 2 covers too wide an area for one Congressional District. But then consider that Maryland is a small state, and think about Alaska, where one Congressman represents the Inuit in the Arctic Circle, the oilmen in Valdez and the Alaskan Oil Pipeline, the Anchorage and Fairbanks urban centers, the fishermen in Kodiak, and everything in between. Compared to the single Alaskan CD, Maryland’s “large” CD 2 is tiny.

Conclusion and next steps

When it comes to re-drawing legislative boundaries, gerrymandering is a significant impediment to our “Forming a More Perfect Union”. Until now, the technical challenge is that the process itself has been tedious and complicated. The political challenge is that those who stand to benefit from the results of the process have overseen the process.

Gerrymandering can be solved if we simply decide to do it, and it’s not all that hard to accomplish. It only becomes hard when we take into consideration factors other than population. If we implement automated redistricting based on naught but population, Ranked Choice Voting, and multi-seat CD’s, the gerrymandering problem can be pretty well licked in one reapportionment cycle.

[1] After completing this exercise, the population per House seat for each CD must be calculated. The smallest population per House seat should not be more than 5% less than the greatest population per House seat. Exceeding this criterion is most unlikely: The greatest population ZCTA in the country (ZCTA 60629, near Chicago’s Midway Airport) has 113,916 residents; if that ZCTA were part of a two-seat CD, and if that CD’s target fell on that ZCTA, the maximum effect on the per-seat calculation for that CD would be that ZCTA’s population divided by 4, or 28,479, which is less than 4% of the probable per-seat target for Illinois. In other words, the likelihood of creating a CD whose per-seat population is too small or too large is tiny. But if such an event were to occur, the computer program could split a ZCTA in half by census tracts, which contain ~4000 people per tract.


Leave a Reply

Your email address will not be published. Required fields are marked *