[EM] IRV with approval

Sean Harris harris.sean at gmail.com
Wed May 18 06:51:25 PDT 2005

```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.

```