Mean minimum political distance: Difference between revisions

imported>DanBishop
imported>DanBishop
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=== Random Ballots ===
 
The mathematically expected MMPD for ''n'' winners randomly selected from uniform(0,1) is (n+3)/(2(n+1)(n+2)), which is 1/3 for a single winner, and asympotically 1/(2n) as the number of seats approaches infinity.
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=== Droop Multiples ===
 
Electing the candidates {i/(n+1): 1≤i≤n} gives an MMPD of (n+3)/(4(n²+2n+1)²). As the number of seats''n'' approaches infinity, this is asymptotically equal to the optimal value of 1/(4n).
 
=== Optimal CandidatesWinners ===
 
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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