Lecture on Gerrymandering Detection & Efficiency Gap

Introduction to Gerrymandering

• Discussed how district lines can be drawn to favor one political party over another.
• Focus on detecting unfair map drawing, specifically measuring if a map is unfair.

Example: Wisconsin Map (2018)

• Blue = Democrats, Red = Republicans.
• Dark shades = strong majority, light shades = slight majority.
• Example of packing & cracking against Democrats.
  • Most Democratic districts are dark blue (packed).
  • Republican districts are lighter red (more spread out).
• Result: Republicans won 63 out of 99 districts despite only 45% of voter support.

Measuring Fairness: The Efficiency Gap

• Efficiency Gap measures packing of districts.
• Key concept: Wasted Votes
  • Votes for losers or excess votes for winners.
• Example Calculation:
  • District with 100 votes: D = 47, R = 53.
  • Wasted votes: D = 47, R = 2 (only needed 51 to win).
• Fair District: Loser wastes more votes than the winner.
• Packed District: Winner wastes more votes than the loser.

Calculating the Efficiency Gap

• Efficiency Gap = Difference in wasted votes / Total votes.
• Fairness measure: Zero indicates a fair map; high gap indicates unfairness.

Practice Examples

• Example 1:

  • 5 districts, votes counted from illustration.
  • Calculate wasted votes for each district.
  • Total D wasted: 14, L wasted: 6; Total votes: 50.
  • Efficiency Gap: 8/50 = 16% in favor of L.

• Example 2 (Class Exercise):

  • Another map with 4 districts.
  • Calculate wasted votes, threshold is 9 to win.
  • Total D wasted: 23, L wasted: 5; Total votes: 64.
  • Efficiency Gap: 18/64 = 28% in favor of L.

Conclusion

• Efficiency Gap provides a statistical measure of fairness.
• Zero gap indicates no advantage; high gap suggests bias.
• More practice and examples to follow in the next session.