Editing Gerrymandering (section)

====Efficiency gap calculation====
{{Main|Efficiency gap}}
The efficiency gap is a simply-calculable measure that can show the effects of gerrymandering.<ref name="TheNewRepublic">{{cite magazine|url=https://newrepublic.com/article/118534/gerrymandering-efficiency-gap-better-way-measure-gerrymandering|title=Here's How We Can End Gerrymandering Once and for All|magazine=The New Republic|author=Nicholas Stephanopoulas|date=3 July 2014|access-date=8 May 2018}}</ref> It measures wasted votes for each party: the sum of votes cast in losing districts (losses due to cracking) and excess votes cast in winning districts (losses due to packing).  The difference in these wasted votes are divided by total votes cast, and the resulting percentage is the efficiency gap.

In 2017, Boris Alexeev and Dustin Mixon proved that "sometimes, a small efficiency gap is only possible with bizarrely shaped districts". This means that it is mathematically impossible to always devise boundaries which would simultaneously meet certain Polsby–Popper and efficiency gap targets,<ref>{{cite journal|title=An Impossibility Theorem for Gerrymandering|journal=[[American Mathematical Monthly]]|volume=125|issue=10|year=2018|last1=Alexeev|first1=Boris|last2=Mixon|first2=Dustin G.|pages=878–884|doi=10.1080/00029890.2018.1517571|arxiv=1710.04193|s2cid=54570818}}</ref><ref>{{cite web|url=https://news.osu.edu/you-cant-tell-a-gerrymandered-district-by-its-shape/|title=You can't tell a gerrymandered district by its shape|date=25 October 2017|work=news.osu.edu|publisher=[[Ohio State University]]|access-date=16 September 2020}}</ref><ref>{{cite web|url=https://www.quantamagazine.org/when-math-gets-impossibly-hard-20200914/|title=When Math Gets Impossibly Hard|last=Richeson|first=David S.|date=14 September 2020|work=[[Quanta Magazine]]|access-date=16 September 2020}}</ref>

Given such theoretical difficulties, a robust, however sub-optimal, anti-gerrymandering rule may be as simple as identifying all maps satisfying a rough efficiency measure, like expected outcome matching voter affiliation proportions, then choosing the one most compact.