Vote-ratio monotonicity

Vote-ratio,^: Sub.9.6 weight-ratio, or population-ratio monotonicity^: Sec.4 is a property of some apportionment methods. It says that if the entitlement for ${\displaystyle A}$ grows at a faster rate than ${\displaystyle B}$ (i.e. ${\displaystyle A}$ grows proportionally more than ${\displaystyle B}$), ${\displaystyle A}$ should not lose a seat to ${\displaystyle B}$.^: Sub.9.6 More formally, if the ratio of votes or populations ${\displaystyle A/B}$ increases, then ${\displaystyle A}$ should not lose a seat while ${\displaystyle B}$ gains a seat. An apportionment method violating this rule may encounter population paradoxes.

A particularly severe variant, where voting for a party causes it to lose seats, is called a no-show paradox. The largest remainders method exhibits both population and no-show paradoxes.^: Sub.9.14