There exists various possible methods to distribute seats 
proportionally between states (or parties) in a parliament. In the first 
half of the talk I will describe some often used methods and discuss their 
pros and cons (it's all in the rounding).

One easy method is called Hamilton's method (also known as the method of 
largest reminder or Hare's method). It suffers from a drawback called the 
Alabama paradox, which e.g made USA abandon it for the distribution of 
seats in the house of representatives between states. It is still in use 
in many other countries including Sweden.

In the second half of the talk I will describe a joint work with Svante 
Janson (Uppsala Univ.) where we study the probability that the Alabama 
paradox will happen. We give, under certain assumptions, a closed formula 
for the probability that the Alabama paradox occurs given the vector 
$p_1,\dots,p_m$ of relative sizes of the states.