Mean minimum political distance: Difference between revisions
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=== Optimal Candidates === |
=== Optimal Candidates === |
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The minimum possible MMPD in a uniform linear spectrum is 1/(4n), which occurs when the candidate set {(2i+1)/(2n): 0≤i<n} is elected. |
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Revision as of 19:57, 4 November 2006
Mean minimum political distance (MMPD) is a political spectrum statistic defined as the mean distance between a voter and the nearest elected candidate.
Example
Assume a one-dimensional political spectrum with the voter distribution
- 15% at position 0
- 20% at position 0.25
- 30% at position 0.5
- 20% at position 0.75
- 15% at position 1
If the candidate set {0.25, 0.75} is elected, then
voters | position | nearest winner | distance | voters × distance |
---|---|---|---|---|
0.15 | 0.00 | 0.25 | 0.25 | 0.0375 |
0.20 | 0.25 | 0.25 | 0.00 | 0.0000 |
0.30 | 0.55 | either | 0.25 | 0.0750 |
0.20 | 0.75 | 0.75 | 0.00 | 0.0000 |
0.15 | 1.00 | 0.75 | 0.25 | 0.0375 |
sum of voters × distance | 0.1500 |
The MMPD of this example is 0.15.
Special cases
On a uniform linear political spectrum:
Random Ballots
This section is a stub.
Droop Multiples
Electing the candidates {i/(n+1): 1≤i≤n} gives an MMPD of (n+3)/(4(n²+2n+1)). As the number of seats approaches infinity, this is asymptotically equal to 1/(4n).
Optimal Candidates
The minimum possible MMPD in a uniform linear spectrum is 1/(4n), which occurs when the candidate set {(2i+1)/(2n): 0≤i<n} is elected.