Chapter 4, Problem 70E

Consider the problem of apportioning $M$ seats between two states, $A$ and $B$. Let $q^A$ and $q^B$ denote the standard quotas of $A$ and $B$, respectively, and assume that these quotas have decimal parts that are not equal to $0.5$.Explain why in this case

a. Hamilton’s and Webster’s methods must give the same apportionment.

b. the Alabama or population paradoxes cannot occur under Hamilton’s method.[Hint: Use the result of (a).]

c. violations of the quota rule cannot occur under Webster’s method.[Hint: Use the result of (a).]