In many democracies, no single party wins an outright majority. So parties have to team up — forming what's called a coalition government. This happens constantly in Germany, Israel, Italy, the Netherlands, and dozens of other countries. The largest party leads, but it needs partners to hit 50% of parliamentary seats. That dependency is where the math gets strange.

Think about what 'needing a partner' actually means. If Party A has 38 seats and needs 51 to govern, it must find parties willing to join. Maybe Party B has 9 seats and Party C has 6. Together: 53. Majority. Done. Except Party B now knows something important — Party A cannot govern without them. That 9-seat party has veto power over a 38-seat party. Not because they're popular. Because the arithmetic says so.

This is the kingmaker problem. A small party positioned between a large party and its majority becomes disproportionately powerful — not despite its size, but because of it. In Israel's Knesset, ultra-Orthodox parties with 5–10% of seats have repeatedly extracted enormous policy concessions — military draft exemptions, religious funding — from governments that needed their votes to survive. The large parties had more voters. The small parties had the math. The same dynamic collapsed four Italian governments between 2008 and 2022. A coalition partner withdraws support, the government loses its majority, a confidence vote fails, and parliament dissolves. Elections again. New coalition negotiations. Repeat.

There's a compounding problem: the longer a coalition runs, the more each partner needs to show its own voters something. A junior coalition partner that looks like it's just rubber-stamping the senior partner's agenda loses support. So they pick fights — demand concessions, stage public disagreements, occasionally threaten to walk. This is rational behavior for each party individually. For the government as a whole, it's a slow structural stress fracture. Germany's 'traffic light' coalition — Social Democrats, Greens, and Free Democrats — collapsed in November 2024 after the Free Democrats withdrew over budget disputes. The FDP held 92 of 736 seats. Thirteen percent of the coalition. Enough to end it. New elections followed within months. That's not a malfunction. That's the system working exactly as the math predicts.