Brief Descriptions of Voting Methods, Part 3
Bruce Anderson
landerso at ida.org
Sun Jun 2 04:40:58 PDT 1996
A. Some Elemental Direct and Sequential Deletion Methods (continued):
Random: selects a unique winner by randomly (i.e., independently and uniformly)
picking one candidate from among those (remaining) under consideration.
B. Some Procedures for Creating New (Compound) Voting Methods from Previously
Defined Voting Methods:
If M1 and M2 are two (not necessarily distinct) ranked-ballot voting methods,
then define M1//M2 to be the ranked-ballot voting method that applies M2 to the
set of winners according to M1 (using the preference orders as expressed on the
voters ballots restricted to that set of M1-winners).
If M1 is a ranked-ballot voting method, then define [M1] to be the ranked-ballot
voting method given by:
M1//M1//...//M1,
where ...//M1 means to continue to apply M1 until further applications of M1
produce no further changes.
If M1 and M2 are two (necessarily) distinct ranked-ballot voting methods, then
define (M1^M2) to be the ranked-ballot voting method that selects the
candidate(s) that win(s) according to both M1 and M2, if one or more such
candidates exist; and, otherwise, selects any candidate that: 1) is a winner
according to either one of the two methods, and 2) pairwise beats or ties at
least one candidate that is a winner according to the other method.
C. Some Compound Voting Methods:
Black: is Beats-all//Borda.
Complete-Champion: is [Anderson]//[Bucklin-ext]//Random.
Consensus-Champion: is [Anderson]//[Plurality-ext]//Random.
Niemi-Riker: is (Copeland^Borda).
Regular-Champion: is [Copeland]//[Plurality-ext]//Random.
Qualified-Champion: is [Fishburn]//[Anderson]//[Bucklin-ext]//Random.
Qualified-Kemeny: is [Fishburn]//[Kemeny]//[Bucklin-ext]//Random.
D. On Names:
Approval, Arrow-Raynaud, Black, Borda, Bucklin, Condorcet, Coombs, Dodgson,
Fishburn, Hare, Kemeny, Nanson, Niemi-Riker, Plurality, Plurality-with-runoff,
Random, Schwartz, and Young have been used has names of voting methods in the
open voting theory literature. Mike and I defined Beats-all and Smith. I
defined the others.
Clearly, the voting methods described here (i.e., in Parts 1, 2, and 3 here)
represent only a small sample of the many possible ranked-ballot voting methods.
Bruce
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