Definitions
- A district is a collection of voters in a single area. We assume a district must be contiguous (i.e. connected), and that each voter is in exactly one district.
- Redistricting is the process of redrawing the boundaries of the districts. This process does not move the location of individual voters but can change who is together in each district.
- Gerrymandering is the process of redistricting to get a specific result.
Exercise
The following map of voters describes their preferences between Party A and Party B.
| A | A | A | A | A |
| B | A | A | A | B |
| B | A | B | B | B |
- What percent of the voters support Party A? What percent support Party B?
- Suppose each column of 3 voters forms a district. How many districts would each party win? Which party would win the majority of the districts?
- Find a way to gerrymander the map (i.e. redraw the districts) to form districts of size 3 so that the other party now wins the majority of the districts. Draw the boundaries of your districts on the map above. Remember that the districts must be contiguous. How many districts would each party win this time?
Exercise
The following is a map of 60 voters describing their preferences between Party A and Party B.
| A | A | A | A | A | A | A | A | A | A | A | A |
| A | A | B | A | A | A | B | B | B | A | B | A |
| A | A | B | B | A | B | B | B | A | A | B | A |
| A | B | B | B | B | B | B | A | A | A | A | A |
| A | B | B | A | B | B | A | A | A | B | A | A |
- What percent of the voters support Party A? What percent support Party B?
- Show that you can make 12 districts, each with 5 voters, so the majority party wins every district. Draw the boundaries of your districts on the map above.
- Find a way to gerrymander the map into 12 districts of 5 voters so that the minority party wins the majority of the districts. Draw the boundaries of your districts on the map below.
| A | A | A | A | A | A | A | A | A | A | A | A |
| A | A | B | A | A | A | B | B | B | A | B | A |
| A | A | B | B | A | B | B | B | A | A | B | A |
| A | B | B | B | B | B | B | A | A | A | A | A |
| A | B | B | A | B | B | A | A | A | B | A | A |
Exercise
Revisit the map of 60 voters in the last exercise. Now suppose that there is to be 10 districts each with 6 voters. Explain why it is no longer possible to gerrymander the map so that B wins the majority of the districts.