## Journal of Applied Probability

- J. Appl. Probab.
- Volume 49, Number 3 (2012), 773-794.

### The probability of the Alabama paradox

Svante Janson and Svante Linusson

#### Abstract

Hamilton's method is a natural and common method to distribute seats
proportionally between states (or parties) in a parliament. In the USA it has
been abandoned due to some drawbacks, in particular the possibility of the
Alabama paradox, but it is still in use in many other countries. In this paper
we give, under certain assumptions, a closed formula for the asymptotic
probability, as the number of seats tends to infinity, that the Alabama paradox
occurs given the vector *p*_{1},..., *p*_{m}
of relative sizes of the states. From the formula we deduce a number of
consequences. For example, the expected number of states that will suffer from
the Alabama paradox is asymptotically bounded above by 1 / e and on average
approximately 0.123.

#### Article information

**Source**

J. Appl. Probab., Volume 49, Number 3 (2012), 773-794.

**Dates**

First available in Project Euclid: 6 September 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.jap/1346955333

**Digital Object Identifier**

doi:10.1239/jap/1346955333

**Mathematical Reviews number (MathSciNet)**

MR3012099

**Zentralblatt MATH identifier**

1282.91092

**Subjects**

Primary: 60C05: Combinatorial probability

Secondary: 91B12: Voting theory

**Keywords**

Alabama paradox election method apportionment proportional allocation Hamilton's method method of largest remainder

#### Citation

Janson, Svante; Linusson, Svante. The probability of the Alabama paradox. J. Appl. Probab. 49 (2012), no. 3, 773--794. doi:10.1239/jap/1346955333. https://projecteuclid.org/euclid.jap/1346955333