[EM] Closed list and open primary

[Michael Allan]

Here's a puzzle of party strategy.  A continuous open primary (0)
ranks all possible candidates by primary votes received.  The assembly
size is 12, so the predicted election bar (---) is below candidate
(Fi).  Candidates are divided by known party preference (H, J) and
independents (i1).  This division yields the default nomination
scenario (1).  Ah, Bh, Dh and Eh are expected to accept the nomination
of the left party, while Bj and Ej accept that of the right.  The
remainder go to the open party (i1).  The open party is apolitical and
nominates anyone, but is constrained to list in primary order (0).

      (0)  |       (1)       |       (2) P
           |                 |
      all  |   H    i1   J   |   H    i1   J
      ---  |  ---  ---  ---  |  ---  ---  ---
   30  Ah  |   Ah            |   Ah
   29  Ai  |        Ai       |        Ai
   14  Bh  |   Bh            |   Bh
   14  Bi  |        Bi       |        Bi
   14  Bj  |             Bj  |             Bj
   13  Ci  |        Ci       |        Ci
   10  Dh  |   Dh            |   Dh
   10  Di  |        Di       |        Di
    9  Eh  |   Eh            |    -   Eh
    8  Ei  |        Ei       |        Ei
    8  Ej  |             Ej  |             Ej
    8  Fi  |        Fi       |        -
      ---  |  ---  ---  ---  |  ---  ---  ---
    6  Gh  |                 |   Gh
    5  Gi  |                 |
    4  Hh  |                 |
    4  Hi  |                 |
    4  Hj  |                 |
    4  Li  |                 |
      ---  |  ---  ---  ---  |  ---  ---  ---
           |   63 + 82 + 22  |   60 + 83 + 22
           |                 |
           |          = 167  |          = 165

    Figure [NB].  Two nomination scenarios.
    http://zelea.com/w/Stuff:Votorola/p/assembly_election/multi-winner#NB


Scenario (2) differs in that Eh accepts the nomination of the open
party instead of H.  But she remains left in orientation, so the left
is now predicted to elect 5 instead of 4.  This is by assumption P:

   P: Electors use their votes on election day to elect the seating of
      PARTIES that was predicted in the primary and the default
      nomination scenario (0, 1).  So H seats 4 regardless of the
      actual nomination scenario (1, 2 or 3).

Suppose the left and right compete in this.  Scenario (3) shows both
increasing their seat counts by 50%, which is the most they can do.


      (0)  |       (3) P     |       (4) C
           |                 |
      all  |   H    i1   J   |   H    i1   J
      ---  |  ---  ---  ---  |  ---  ---  ---
   30  Ah  |   Ah            |   Ah
   29  Ai  |        Ai       |        Ai
   14  Bh  |   -    Bh       |   -    Bh
   14  Bi  |        Bi       |        Bi
   14  Bj  |        Bj   -   |        Bj   -
   13  Ci  |        Ci       |        Ci
   10  Dh  |   -    Dh       |   -    Dh
   10  Di  |        -        |        Di
    9  Eh  |   Eh            |   Eh
    8  Ei  |        -        |        Ei
    8  Ej  |             Ej  |             Ej
    8  Fi  |        -        |        Fi
      ---  |  ---  ---  ---  |  ---  ---  ---
    6  Gh  |   Gh            |
    5  Gi  |                 |
    4  Hh  |   Hh            |
    4  Hi  |                 |
    4  Hj  |             Hj  |
    4  Li  |                 |
      ---  |  ---  ---  ---  |  ---  ----  --
           |   49 + 94 + 12  |   39 + 120 + 8
           |                 |
           |          = 155  |          = 167

    Figure [FC].  Two electoral assumptions.
    http://zelea.com/w/Stuff:Votorola/p/assembly_election/multi-winner#NB


The same nomination scenario (3) is repeated in (4), but here the
electoral assumption is changed from P to C:

   C: Electors use their votes on election day to elect the seating of
      CANDIDATES that was predicted in the primary (0).  So they
      follow the candidates into the open party, and Ah to Fi are
      elected regardless.

The truth must be somewhere between P and C (3 and 4); each is true to
some extent.  They therefore work together to take bites out of the
parties: first P attracts the better candidates (or at least gives
them political cover to escape the party), while C takes an electoral
bite out of the party in consequence.  The measure of that bite is the
effect on candidate strength (summed at bottom).  It's a smaller bite
if i1 is small to begin with, but it grows with each election cycle.
So what could party H do to avoid being eaten up like this?

-- 
Michael Allan

Toronto, +1 416-699-9528
http://zelea.com/