Disproportionality

1
Disproportionality Median Correspondence

• What are we trying to measure with
  disproportionality?
• How votes are translated into legislative
  representation
• Quality of representation
• But what the translation of votes into seats
  really tell us?
• Does high disproportionality always imply poor
  representation?

2
Disproportionality as a measure of representation

• Votes are a rough measure of preferences
• Measure at a district level to explain national
  phenomena
• The meaning of a vote depends on the available
  alternatives (parties)

3
Disproportionality in the Majoritarian Vision

• Majoritarian Vision
• Representation does not matter
• Responsibility
• Accountability

4
Median Correspondence

• What is a median?
• Citizen/Voter Median
• Legislative Median
• If the two medians are the same -gt policy
  outcomes ought to reflect citizens will
• Minimizes the number of unhappy voters.

5
Classifying Electoral Systems

• What aspect of an electoral system is likely to
  influence it representativeness?
• The harder it is to win a seat in the legislator
  the less likely it is to be representative
• Electoral thresholds, e.g., make it more
  difficult.
• Effective threshold
• Average of votes needed to win a seat under a)
  least favorable circumstances and b) most
  favorable circumstances
• T 50/(M1) 50/(2M)

6
Electoral Threshold Disproportionality

• Positive relationship well documented
• Examples
• Effective threshold in the Netherlands
• dHondt quota .6666666666
• Effective threshold
• Effective threshold in SMD
• Least favorable 50
• Most favorable ?

7
A Simple Model

• Voter preferences measured on 10-point scale
• Shape of preference distribution
• Assume 10 parties each identified with a point
  on the scale
• What happens as we increase the threshold?

8
A simple model

• No threshold Low disproportionality, similar
  variance, close correspondence between medians
• High threshold High Disproportionality, smaller
  variance in legislature, close correspondence
  between medians

1 2 3 4 5 6 7 8 9 10 4 5 12 13 19 12 12 12
4 6
9
The Simple Model

• Actors not strategic
• of parties influences by threshold/
  proportionality
• How will strategic actions influence model?
• Coxs M1 rule -gt decreases disprop.
• Disproportionality measured at district level
  interpreted at the national level -gt
  disproportionality may cancel out. More likely to
  effect SMD than PR

10
Coordination and convergence failures

• Cancellation effects may not occur if
• Patterns of winning/losing are consistent across
  district
• Parties fail to converge on median voter
• -gt SMD may or may not display high levels of
  disproportionality

11
Electoral Rules Correspondence

• In PR systems theory predicts that parties will
  spread themselves out across political spectrum
  -gt Median correspondence should hold
• Fails
• parties to large, or they fail to take
  appropriate positions (on left or right only)
• No party takes the median voters positions

12
Correspondence in SMD

• If classic two party competition then there is
  no problem
• Non correspondence may occur if
• gt2 parties
• Median convergence at district level

13
Empirical Test

• Does type of electoral system influence median
  correspondence?
• To test we need
• Measure of citizens preferences
• Measure of legislative parties positions
• Surveys Voters self-placement on a left-right
  ideological continuum
• Expert surveys Place political parties on a 10
  (or 11) point scale
• Test Compare medians.

14
Results

• PR systems
• Medians are close (mean difference.6)
• Not monotonic in threshold, but standard
  deviation is large
• SMD systems
• Medians are much further away (mean
  difference1.5)
• Not consistent with theoretical expectations