The raw demographic map of a state, showing 9/15 (two thirds) of populace who support Red Star, and 6/15 (one third) who support Green Dot.
The state needs to be divided into 3 areas with equal number of people each. Each area gets one vote, and what party the area votes for is determined by the will of the voting populace.
This is what a fair division would look like – two areas have more Red Star supporters while one area has more Green Dot supporters. Thus ultimately Red Dot would have 2/3 representation and Green Dot would have 1/3 representation… Just like the actual demographics.
The state ends up leaning Red Star.
If a Red Star supporter were in charge of setting the 3 areas and did it to give his party the maximum benefit, he would divide the state in such as way as to have each area have more Red Star supporters than Green Dot supporters. Each of the three areas would choose to vote Red Star, none would choose to vote for Green Dot. Red Star has 3/3 and Green Dot 0/3.
The state ends up leaning Red Star as it would in a fair division, but now with zero concern for Green Dot supporters.
If a Green Dot supporter were in charge of setting the 3 areas and did it to give his party the maximum benefit, he would divide the state in such as way as to lump as many of the Red Star supporters together in one area. That area would of course vote for Red Star. The remaining two areas have more Green Dot supporters, and thus those areas vote Green Dot.
The state ends up leaning Green Dot, even though overall there are more Red Star supporters!
Head on over to Zombie for a more detailed explanation, an example of real-world gerrymandering where you can see how crazily distorted the area divisions end up, and an explanation of why Democrat-initiated gerrymandering backfired and led to the nationwide Republican landslide in 2010.
And here’s an example of a blatant gerymandering from Zombie’s worst-offenders list:
Here it is: The most ridiculous congressional district in the entire country. No, you’re not looking at two districts; IL-4 has two absurdly gerrymandered halves held together by a thin strip of land at its western edge that is nothing more than the median strip along Interstate Highway 294. The end result is a gerrymandered gerrymander, a complete mockery of what congressional representation is even supposed to be. As with AZ-2, the intention behind IL-4 was to create an ethnic enclave, in this case an Hispanic-majority district within an otherwise overwhelmingly non-Hispanic Chicago. Problem is, Chicago has two completely distinct and geographically separate Hispanic neighborhoods — one Puerto Rican, the other Mexican — but neither is large enough to constitute a district majority on its own. Solution? Lump all Hispanics together into a supposedly coherent cultural grouping, and then carefully draw a line surrounding every single Hispanic household in Chicago, linking the two distant neighborhoods by means of an uninhabited highway margin. Voila! One Hispanic congressperson, by design. And as a side-effect, the most preposterous congressional district in the United States.
A commenter notes that the two halves could have been joint marginally more sensibly by a bar down the middle, but this was rejected as it would separate the black-majority neighborhood. Hence the highway margin solution.