[EM] Month Approval election results

[Bart Ingles]

Tom Ruen wrote:
> 
> 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.

This was an interesting demonstration, although I don't agree that the
closeness between May and September was the fault of approval voting. 
Even among those who did express a preference for one or the other,
there was only a 2 percentage-point difference.

Among the rest of the voters, there is no particular reason to expect
them to break one way or the other on May vs. September -- if you were
to hold a runoff between them, the voters may, for lack of a real
preference, base their decision on something like alphabetical or
numeric order, or position on the ballot.



> 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.

I don't understand this -- although I recall you stating a belief that
the best approval strategy is to bullet vote.  Is it that you suspect
that voters who don't bullet vote don't really know what they are doing?

The presence of a runoff election would tend to negate approval's
inherent ability to reject low-utility candidates, even without forced
elimination.

A suggestion for future elections might be to solicit a rating (on a
scale of 0..10 or so) along with the actual votes.  Then you could see
how well a method does at choosing the overall highest-rated candidate. 
You could also use the ratings to derive approval or ranked votes using
various strategies. 

Bart



> 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