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
Select target paragraph3
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