[EM] IRV with approval

[Sean Harris]

Has anyone ever combined IRV with approval voting in order to eliminate
some of the problems associated with traditional IRV?

I have been searching but I haven't found anything quite like it yet.

The method I am thinking of would follow IRV except that instead of
dropping candidates with the least number of first choice votes, all
but the remaining lowest ranked votes would be treated as unweighted
approval votes for the sake of proceeding to the next round.

If this is a new idea, then I dub it Approval Recount Voting (ARV).


The mechanism is this:

Voters mark their choices for candidates in order of preference.

If a candidate receives an absolute majority of first choice votes
in the first round of counting, they are declared the winner.

If no candidate receives an absolute majority:

  - then choices N minus R are treated as approval votes where N
    is the number of candidates and R is the round of counting

  - the candidate with the least amount of approval is dropped from
    those ballots are redistributed according to their second choice

If a candidate receives an absolute majority of first and second 
choice votes in the second round of counting, they are declared 
the winner.

If no candidate receives an absolute majority then choices N minus R
are again treated as approval votes and candidates continue to be
dropped and ballots redistributed until a clear winner is found.

Given the example of selecting a state capital of Tennessee where:

    42% of voters choose           26% of voters choose
      1 Memphis                      1 Nashville
      2 Nashville                    2 Chattanooga
      3 Chattanooga                  3 Knoxville
      4 Knoxville                    4 Memphis

    15% of voters choose           17% of voters choose
      1 Chattanooga                  1 Knoxville
      2 Knoxville                    2 Chattanooga
      3 Nashville                    3 Nashville
      4 Memphis                      4 Memphis

Round 1 ranking

  Looking at first place votes we get:

  Memphis       42
  Nashville     26
  Knoxville     17
  Chattanooga   15

  No clear majority, so votes go to N minus R approval.

Round 1 approval

  Adding all but fourth place votes gives us:

  Nashville    100
  Chattanooga  100
  Knoxville     58
  Memphis       42

  Memphis has the least amount of approval and is therefore dropped.

Round 2 ranking

  Reevaluating the remaining votes gives us:

  Nashville     68
  Knoxville     17
  Chattanooga   15

  Nashville now has a clear majority and is therefore elected.

I don't see this a being technically superior to other voting systems,
only as an improvement on IRV in the same light as IRV is better than
FPTP.