[EM] Alternative Vote (or IRV) using residual approval weights

[Elisabeth Varin/Stephane Rouillon]

                Alternative Vote (or IRV) using residual approval
                weights

http://groups.yahoo.com/group/Electoral_systems_designers/message/73
                (Stephane Rouillon)

                How does it work?

                It works like IRV except for selecting the winner.

                The input is Demorep's truncated preferential and
                approval ballot.
                It can be simplified using a Z virtual candidate as
                limit.
                For example: A1(yes) > C2(yes) > E3(yes) > D4(no) >
                B5(no)
                becomes A > C > E > Z > D > B.
                Z is the reference limit for an acceptable candidate.

                Then we apply usual IRV without taking "Z" in account.
                In case of equality, each scenario is done,
                the final result is the average of the scenarios (well
weighted).
                When the candidate with the least 1st place vote is
eliminated,
                we check what is his residual approval rating.
                He receives one vote for each ballot where he is the
last active
                candidate higher than Z (if Z is mentionned).
                If Z is not mentionned we suppose it could be added at
the end.
                The winner is the candidate with the highest approval
rating,
                not necessarily the latest eliminated.

                An example with 7 ballots and 5 candidates:
                2: A > E > B > Z > D
                1: E > Z > D > C
                1: D > E > C
                1: C > A > Z > B > E > D
                1: C > B
                1: Z > E

                1st round:
                A: 2 votes
                B: no vote
                C: 2 votes
                D: 1 vote
                E: 2 votes

                B is eliminated => no residual approval weight

                2nd round:
                A: 2 votes
                C: 2 votes
                D:1 vote
                E: 2 votes

                D is eliminated => no residual approval weight

                3rd round:
                A: 2 votes
                C: 2 votes
                E: 3 votes

                Two scenarios (AA or BB):
                ------------------------
                A is eliminated => no residual approval weight

                4th round:
                C: 2 votes
                E: 5 votes

                C is eliminated => 2 votes as residual approval weight
                E receives 4 votes as residual approval weight
                The last voter counts as a blank vote (he approved none
                but expressed his opinion about a lesser evil)

                Other scenario (BB):
                -------------------
                C is eliminated => 1 residual approval weight

                4th round:
                A: 3 votes
                E: 3 votes

                Again two scenarios (CC or DD):
                ------------------------------
                A is eliminated => 1 vote as residual approval weight
                E receives 4 votes as residual approval weight
                The last voter counts as a blank vote (he approved none
                but expressed his opinion about a lesser evil)

                Other scenario (DD):
                -------------------
                E is eliminated => 2 residual approval weight
                A receives 3 votes as residual approval weight
                The last voter counts as a blank vote (he approved none
                but expressed his opinion about a lesser evil)

                Final results:
                -------------
                A receives 1 vote (0/2 + 1/(2*2) + 3/(2*2))
                B receives no vote
                C receives 1.5 vote (2/2 + 1/2)
                D receives no vote
                E receives 3.5 votes (4/2 + 4/(2*2) + 2/(2*2))
                Blank(none): 1 vote

                E wins.

                Any questions?

                Steph.

----
For more information about this list (subscribe, unsubscribe, FAQ, etc), 
please see http://www.eskimo.com/~robla/em