Seats and places

Most apportionment systems operate inside two hard constraints at once. The chamber has a fixed total — 435 in the U.S. House, 650 in the UK Commons, 577 in the French Assemblée nationale — because legislatures rarely vote themselves larger. And nearly every federal or regional system also guarantees each constituent unit at least one seat, no matter how thinly populated, on the principle that representation cannot reach zero.

These two rules coexist easily enough when populations are roughly even. They collide when a unit's population, divided proportionally, would entitle it to a fraction well below one. The guaranteed minimum then awards it a full seat it has not arithmetically earned. That seat has to come from somewhere, and the only legal source is the pool available to larger units.

The displacement is not evenly shared. Divisor methods — which allocate seats by successively dividing each unit's population and rounding — quietly absorb the cost inside the rounding step, favouring whichever rounding rule is in use. Largest-remainder methods handle it more visibly: the quota is calculated, the minimum is applied, and whatever seats the minimums consumed are simply subtracted before remainders are distributed among the rest.

The real-world stakes are measurable. In the European Parliament, small member states have long held seats well above their strict population share, a deliberate political settlement called degressive proportionality — representation that shrinks, but not in strict proportion to population. The overhang is explicit and acknowledged. In systems where the minimum is not openly debated, the same effect arrives quietly through the arithmetic, and goes largely unnoticed until a mid-sized region realises it has lost a seat to a much smaller neighbour.

A fixed chamber size with guaranteed minimums is not a paradox — it is a political choice encoded as arithmetic. The question is only how transparently the trade-off is recorded.