Inconsistency and the Alabama Paradox Consistency These are features of largest remainder method, but not of division methods. Two simple examples illustrate the problem: Consistency means that the interrelationship between parties is not changed by changing another party’s votes. For example, if one party’s vote is changed without changing the number of seats for that party, the number of seats for other parties should also remain the same. LR is not consistent, as is illustrated below, where four seats are to be distributed: The Alabama Paradox The Alabama paradox is the name for a situation where the total number of seats is increased, but where the number of seats given to a party is reduced.45 This is not intuitive. If the total number is increased one would expect that no party would win fewer seats than before the increase. The effect requires the rules based upon LR to be more complicated, for example to cover the situation where a party may win more seats than it has candidates. With a division method this paradox does not occur and the rules become very simple. In the example below the number of seats is increased from 10 to 11 whereby the party C will lose its seat and both the other parties will win one extra. Party Number of Votes With 10 seats LR Number of seats With 11 seats LR Number of seats A B C Total 703 243 54 1,000 7 2 1 10 8 3 11 Table 27 An example of the Alabama paradox where a party (Party C) loses a seat even if the total number to be distributed is increased from ten to eleven The same example with Sainte-Laguë would give: Situation 1 Party Number of Votes Number of seats A 233 2 B 135 2 C 32 0 Total 400 4 Number of Votes Number of seats Situation 2 Party 233 A B 135 1 C 0 0 400 4 Total Party Number of Votes With 10 seats SL Number of seats With 11 seats SL Number of seats A B C Total 703 243 54 1,000 7 2 1 10 7 3 1 11 Table 28 The same example as in table 5, but now using the division method Sainte-Laguë. Division methods do not produce results with the Alabama paradox. Table 29: An example showing the inconsistency when using LR. By changing the votes for Party C the inter-relationship between party A and Party B changes. By removing the votes of an entity which has not won any seats the distribution between the other two changes. Sainte-Laguë would give the distribution (3, 1, 0) in both cases. In the 2013 Zimbabwe elections there is a good example of the lack of consistency in Bulawayo, both for the National Assembly and the Senate elections. This is discussed in Section 12.2. 45 Or the total number of seats is reduced and the number of seats for a party is increased. 64 3 65