[EM] Request for help: complex election

[Nikhil Nair]

Hi,

A British charity that I chair is looking for a new election method for
its Board of Trustees.  The scenario is a little more complex than typical
political elections, and I haven't been able to find anything on how this
should be tackled.

I'm aware that you may be mainly interested in established single-winner
methods, but hope that some of you will be willing to have a think about
this, as I'm sure you have far more expertise in such matters than us.

So, without further ado, on to the details.

There are up to 8 trustees, elected to two-year terms, with up to 4 being
elected each year.  So far, half have been elected by the membership
(currently 800, but with the last turnout only around 10%), and the other
half by the Council (around 15 people, with a much better knowledge of the
candidates etc.).

We'd like to merge the two elections, so that up to 4 trustees are elected
by *both* membership and Council.  The Board works on a "one person, one
vote" basis, so we're looking at a mutli-winner, dual-electorate election
of unaffiliated individuals (i.e. no parties).  As such, clearly no
proportional representation systems are appropriate.

A few specific factors:

- The turnout of the membership could change drastically from one year to
  the next, so the system would have to be able to cope with that.

- If there are insufficient good candidates, we'd rather elect fewer than
  4, rather than have a poor individual on the Board.

- We'd like to weight the result slightly, so that the Council (with
  greater understanding) gets a greater say; probably something like
  60:40.

In addition, as there's quite a lot of complexity involved already, it's
important that the system we propose is easy to understand - otherwise, it
will never get passed at our AGM.

So, are there any established systems which would do the job here?  If so,
could you either tell me about them, or point me in the right direction to
read more?

If not, I've had an idea which I think will work.  However, as I'm
relatively new to this field, there may be fatal flaws which I haven't
noticed - I'd value your input.

My idea is this:

Let's say that M_n people vote from the membership, and C_n from the
Council, in total.  If candidate i gets M_v,i votes from the membership,
and C_v,i from the council, we take the percentages of turnout, i.e.
   M_p,i = 100 * M_v,i / M_n
   C_p,i = 100 * C_v,i / C_n
Now, if either M_p,i or C_p,i is less than a threshold (probably 20%), the
candidate is disqualified (i.e. both membership and Council have a veto to
prevent poor candidates getting through).  Otherwise, candidates i's final
score is a simple weighted average:
   V_i = p * C_p,i + (1 - p) * M_p,i
probably with p=0.6, to favour the Council.

Eventually, the top 4 scoring non-disqualified candidates would be
elected, or less if fewer survived disqualification.

How does this look?

A few issues:

1.  How does an individual (from either membership or
Council) vote?  According to our precedent, it would be "vote for up to 4
people", so they wouldn't have to vote for a fourth if they thought there
were only three good candidates one year.  Would it be better to allow
them to vote for as many as they like, i.e. an approval-based system?

2.  It seemed better to avoid ranking, as:

(a) Things would get rather complicated, for instance someone who everyone
voted for in 3rd or 4th place should surely be one of the four elected,
whereas this might not happen in some rank-based systems.

(b) It really ought to make a difference if, say, the fourth placed person
got 70% of the vote from the membership, or only 30%.  If percentages were
used, this would carry through when averaged with the score from the
Council, whereas the information would be lost in a ranking system.

I'd value your input, and look forward to hearing from you!

Nikhil.