# Gerrymandering. An Example

Suppose we want 7 voting districts in a state of 100,000 square miles (e.g., Colorado). In the first round, we randomize all registered voters into one of the 7 voting tranches (A, B, C, D, E, F, G). Voting tranches are completely artificial (i.e., not determined by geography, affiliations or any other physical contrivance). Voter #1 can be randomly assigned to any of the 7 tranches. Each tranche gets assigned the same number of voters. This is a very easy spreadsheet calculation. Each voter is assigned a random number and the random numbers are sorted and divided numerically into 7 equal-size tranches.

For each resulting voting tranche we draw a geographical boundary so as to encompass the maximum number of assigned voters who live within 200 miles of each other (π*r2 = 31,415 sq. miles). This is a straightforward mathematical calculation, but requires a bit of algebra. These become the voting districts. In heavily populated states this results in many geographically overlapping districts. For sparsely populated states, this may result in a single district. For small populous states, this results in multiple wholly overlapping districts.

Voters who fall outside the boundary of their voting district after the first round of randomization are re-randomized into one of the districts within which they live, or in the case of sparsely populated regions into one of several close districts. This calculation is a bit more complicated, since we simultaneously want voting districts to have approximately the same number of voters, and we want this re-randomization to indeed be random by having a choice for placing these distant voters into one of several voting districts. The math is more complicated, but it is still mechanical.

Back. Gerrymandering. The Mechanics