Sometimes you get different outcomes if you divide state in half north-south vs. east-west, depending on how the cluster is divided between districts.
Here's an idealized example. Imagine a state with 1,000,000 people. 400,000 Democrats live in a narrow strip on the Eastern border, uniformly distributed in that strip. The 600,000 Republicans are uniformly distributed in the rest of the state.
Split the population in half by a north-south line. The Eastern district has 400,000 Democrats and 100,000 Republicans, and so has a Democratic representative. The Western district has 500,000 Republicans and so had a Republican representative.
Now try an east-west line. Each district has 200,000 Democrats and 300,000 Republicans. There are two Republican representatives.
Yet on a map, both divisions look fine.
That's one reason the anti-gerrymandering rules specify looking deeper than just population and compactness.
"You can easily get rid of gerrymandering simply by proscribing an algorithmic process for districting."
There were several people who said this, here and on Reddit and on Hacker News. I believe they are defining gerrymandering as a deliberate and intentional act. By contrast, I was using the word "gerrymandering" to refer to the fact that any geographic boundary will establish a gap between the will of the voters and the final result of voting. So even if an algorithmic process is followed, and the damage done is accidental and unintentional, I am still referring to that as "gerrymandering." Indeed, the whole point of my essay is that if one group does its best to be fair when drawing lines on the map, and another group is evil and immoral and corrupt, and does its worst when drawing lines on a map, the damage done by both groups will be about the same, over the long-term.