Mean minimum political distance: Difference between revisions
Content added Content deleted
imported>DanBishop No edit summary |
imported>DanBishop No edit summary |
||
| Line 1: | Line 1: | ||
'''Mean minimum political distance (MMPD)''' is a [[political spectrum]] statistic defined as the mean distance between a voter and the nearest elected candidate. |
'''Mean minimum political distance (MMPD)''' is a [[political spectrum]] statistic defined as the mean distance between a voter and the nearest elected candidate. |
||
== Example == |
|||
{{stub}} |
|||
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 |
|||
<table border> |
|||
<tr> |
|||
<th>voters</th> |
|||
<th>position</th> |
|||
<th>nearest winner</th> |
|||
<th>distance</th> |
|||
<th>voters × distance</th> |
|||
</tr> |
|||
<tr align="right"> |
|||
<td>0.15</td> |
|||
<td>0.00</td> |
|||
<td>0.25</td> |
|||
<td>0.25</td> |
|||
<td>0.0375</td> |
|||
</tr> |
|||
<tr align="right"> |
|||
<td>0.20</td> |
|||
<td>0.25</td> |
|||
<td>0.25</td> |
|||
<td>0.00</td> |
|||
<td>0.0000</td> |
|||
</tr> |
|||
<tr align="right"> |
|||
<td>0.30</td> |
|||
<td>0.55</td> |
|||
<td>either</td> |
|||
<td>0.25</td> |
|||
<td>0.0750</td> |
|||
</tr> |
|||
<tr align="right"> |
|||
<td>0.20</td> |
|||
<td>0.75</td> |
|||
<td>0.75</td> |
|||
<td>0.00</td> |
|||
<td>0.0000</td> |
|||
</tr> |
|||
<tr align="right"> |
|||
<td>0.15</td> |
|||
<td>1.00</td> |
|||
<td>0.75</td> |
|||
<td>0.25</td> |
|||
<td>0.0375</td> |
|||
</tr> |
|||
<tr> |
|||
<th colspan="4">sum of voters × distance</th> |
|||
<td align="right">0.1500</td> |
|||
</tr> |
|||
</table> |
|||
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 === |
|||
''This section is a stub.'' |
|||
Revision as of 19:49, 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
This section is a stub.