Brief Descriptions of Voting Methods, Part 3

[Bruce Anderson]

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