A common assumption is that a neutral process is inherently fair. However, due to natural population clustering (e.g., Democrats in cities), a randomly drawn map can still heavily favor one party. Achieving fairness may require intentional design to counteract geographic disadvantages, not just the absence of malicious intent.

Politicians are fundamentally incapable of drawing fair electoral boundaries due to an inherent conflict of interest: they want to ensure their party wins. Using a randomly sampled citizens' commission, as Michigan did, removes this conflict. This allows ordinary people, guided by a sense of fairness, to create equitable maps where politicians and courts have failed.

The perception of a deeply divided society is largely an artifact of a political system built on competition and elections, which forces people into two opposing camps. A system based on deliberation would reveal that most people's views are not so rigidly coherent, and it would encourage finding common ground rather than winning at all costs.

The Catholic Church's method of selecting a Pope—a secret, deliberative process where cardinals vote repeatedly until a supermajority is reached—is a powerful example of an "election without candidates." This bottom-up meritocracy prioritizes finding a formidable, consensus candidate over rewarding the person who campaigned the hardest, a model that could be adapted for political and organizational leadership.

A common focus in redistricting reform is preventing 'crazy-looking' districts. However, this is a red herring. A legislature can easily create visually compact, 'nice-looking' districts that are just as politically skewed, making district shape an unreliable metric for fairness.

To analyze a proposed map's fairness, mathematicians compare it to a representative sample of alternatives. They use a Markov chain—a 'random walk' making sequential changes to a map—to explore the astronomically large space of possibilities without enumerating it, creating a baseline for what 'typical' maps look like.

The combinatorial complexity of drawing district maps is vastly underestimated, even by Supreme Court justices. The number of possibilities isn't in the thousands but is astronomically large (like a googol), making it impossible to check every option and thus requiring sophisticated mathematical sampling techniques.

Instead of single-winner districts, a powerful reform is creating larger, multi-member districts that elect several representatives (e.g., 4 districts electing 3 members each). This allows for more proportional outcomes that reflect an area's political diversity, as a minority group can win one of the multiple seats.

The US was structured as a republic, not a pure democracy, to protect minority rights from being overridden by the majority. Mechanisms like the Electoral College, appointed senators, and constitutional limits on federal power were intentionally undemocratic to prevent what the founders called "mobocracy."