[EM] Month Approval election results

[Tom Ruen]

This is a first draft analysis on the Month Approval election held over the
last week.

I asked people to vote for their favorite months, as many or few as they
liked. I said if none had a majority approval, the top approval candidate
would win, and if more than 2 had a majority approval, then there would be a
runoff among them.

There were a total of 57 ballots cast. Most of the them were from friends
and coworkers (In continental extreme climate of Minnesota!), but there were
about a dozen by email on the EM and IRV-freewheeling email lists.

The approval results are:
Total Ballots=57
Sep   28 ( 49.12%)
May   27 ( 47.37%)
Jul   23 ( 40.35%)
Oct   21 ( 36.84%)
Jun   20 ( 35.09%)
Aug   20 ( 35.09%)
Apr   17 ( 29.82%)
Nov   14 ( 24.56%)
Dec   13 ( 22.81%)
Feb   11 ( 19.30%)
Mar   10 ( 17.54%)
Jan   10 ( 17.54%)

September officially wins this election by a hair over May.

My main interest was to compare this to plurality, although I didn't ask
voters to also specify their top vote to compare the results. I can,
however, show a similar election I held a couple months ago with ranked
ballots. (Note: In that election, I allowed tied ranked, and I count them by
dividing a full vote equally among the candidates in the tie. This causes
some fractional votes.)

Plurality vote (top rank votes): (previous election)
Total Ballots=105
Sep=20.0 (19.0%)
May=16.3 (15.5%)
Aug=12.3 (11.7%)
Jul=10.1 (9.6%)
Apr=9.5 (9.0%)
Oct=8.3 (7.9%)
Feb=6.0 (5.7%)
Jan=6.0 (5.7%)
Dec=5.3 (5.1%)
Nov=5.0 (5.0%)
Jun=4.3 (4.3%)
Mar=2.0 (1.9%)

Condorcet ranking: [2=win, 1=tie, 0=lose] (same previous election)
Total Ballots=105
    S M A J J O A D N F M J
    e a p u u c u e o e a a
    p y r n l t g c v b r n
Sep - 2 2 2 2 2 2 2 2 2 2 2
May 0 - 2 2 2 2 2 2 2 2 2 2
Apr 0 0 - 2 2 2 2 2 2 2 2 2
Jun 0 0 0 - 2 1 2 2 2 2 2 2
Jul 0 0 0 0 - 2 2 2 2 2 2 2
Oct 0 0 0 1 0 - 2 2 2 2 2 2
Aug 0 0 0 0 0 0 - 2 2 2 2 2
Dec 0 0 0 0 0 0 0 - 2 2 2 2
Nov 0 0 0 0 0 0 0 0 - 2 2 2
Feb 0 0 0 0 0 0 0 0 0 - 2 2
Mar 0 0 0 0 0 0 0 0 0 0 - 2
Jan 0 0 0 0 0 0 0 0 0 0 0 -

These results can't be compared with the approval election since the voter
base is different, but you can see a few things. All three methods agreed in
the top two places, so this is a pretty easy election considering the number
of candidates. Also the approval ordering is closer (than Plurality) to the
Condorcet ordering. (IRV gives the same ordering as Condorcet in this ranked
election if I eliminate winners and repeat the process.)

This to me is a demonstration that simple approval voting can go a long way
in expressing overall voter preference.

In the plurality election, only 19% supported September first. The approval
election demonstrates that September's support runs much deeper than this
core, even without a runoff.

Here's some other statistics on the approval election:
57 Ballots/voters.
214 votes (3.75 votes/voter)
Votes/ballot distribution:
Votes    Voters
0            1        (No months liked!)
1            7
2            18
3            12
4            4
5            1
6            3
7            4
8            2
9            1
10          2
11          1
12          1        (All months liked!)

With only 57 voters, there are 3 candidates between 40-50% approval. I
decided to look at the distribution of ballots among these 3 candidates.
These 3 candidates perhaps represent the top of 3 coalitions - Spring,
Summer, and Fall.

Ballot frequency count: (8 types of ballots)
M J S
A U E
Y L P  Frequency
 0 0 0   15  30.6% (No preference known)
 1 0 0    3   6.1%
 0 1 0    8  16.3% (Summer lovers)
 0 0 1    4   8.2%
 1 1 0    3   6.1%
 1 0 1   12  24.5% (Spring/Fall overlapping)
 0 1 1    3   6.1%
 1 1 1    9  18.4% (Spring/Summer/Fall overlap)

69.4% support at least one of these 3.
55.1% support at least two of these 3.
18.4% support all 3 choices!

And looking only at the top two candidates:
Ballot frequency count: (4 types of ballots)
 M S
 A E
 Y P  Frequency
 0 0   23  43.4%
 1 0    6  11.3%
 0 1    7  13.2%
 1 1   21  39.6%

This is illuminating. 56.6% of voters supported either September or May, and
39.6% support BOTH! Only 24.5% have made a clear decision among the top two
choices. This means 75% of voters have not openly decided among which of
these two strongest approval candidates to support!

My simple and obvious conclusion is that a single round of Approval is not
overly decisive election among 12 strong candidates when voters are voting
blindly and cautiously.

I might suggest a runoff it warranted if less than 50% of voters bullet
voted. If this is true, then round up the average voters/voter to a whole
number (3.75) and that can be the threshold for the runoff.

In this election, 7/57 (12%) bullet voted, therefore we could take the top
(3.75 rounded up) 4 candidates and hold a runoff among them.

Generally, I would suggest "Approval w/runoff" could be implemented by
calling for a bullet threshold. If enough voters bullet vote, then they are
saying they are satisfied by the election choices. This threshold could be
90%, 75%, 50%, or whatever you like. Forced elimination does not even need
to be part of the process since voters will naturally reduce their votes in
later rounds.

Well, I'd be happy to hear comments or thoughts about this election and your
conclusions.

Sincerely,
Tom Ruen