[EM] STV for small committees: some exceptions and questions.

[Advance Copy]

- - - - - - - - - - - - - - - - - - - - - - - - 02/27/01
Dear Hugo Harth, you wrote:
>1) Successors:  [filling a vacancy]
>One way would be : For each candidate determine the successor by
>running STV on all the ballots but without this candidate.
>Proceed in a similar way for the second and third successors: omit
>the candidate and the successors already determined.

Don: Sorry, but you cannot do it this way, you cannot elect one successor
at a time, and even if you could, you cannot omit the first successor
already determined while you elect the second successor. Doing so would
take the votes that elected the first successor and free them up to elect
the second successor. The effect would be that some votes would be electing
two members, that's a no no.
     The following is how it should be done:
     1) Go back to the ballots of the last election.
     2) Eliminate the now vacant member or members.
     3) Check and eliminate any candidate that is not now available
        to fill the position.
     4) Protect all the remaining sitting members by making a rule
        that none of the sitting members can be eliminated during
        the re-run of the election.
     5) Run the ballots: The results will produce the same current
        sitting members plus new members to fill the vacancies.

>2) Ranking exhausted:
>The rule might be: distribute this ballot over the demanding
>stacks proportional to their size.
>What is proportional here? I would say, prior to the distribution
>of the (depleting) stack, not when the case occurs.

Don: Why is it necessary to do something with the exhausted ballots.
Consider them to be the same as if that voter did not show up for a runoff
election.
     But, if you must do something, proportionality is correct, but after
the stack is transferred, not prior.  For prior proportionality includes
the stack that is being transferred.  You cannot give a proportional part
of the vote to the stack which is being transferred, the same stack that
contains the exhausted ballot.  Can you not see that trying to do so will
put you into a math jam.

>3) Multiple candidates in the same rank:

Don: The main value of allowing multiple candidates in the same rank is to
turn voided ballots into valid ballots.  Depending on election equipment,
there are going to be people who will mark `same rank'. Yes, it is a
mistake the voter has made, but he should not lose his ballot because of
it.

>4) Multiple equal piles to be distributed:   [tie solution]
>The rule would be: distribute them all. There might be curious
>(but benign) effects, suppose 5 piles, none has reached the quotum,
> 3 lowest piles are equal, 3 candidates have to be elected.

Don: It is not correct to distribute them all, unless the sum of the three
piles is less than the one pile ahead of the three, then it would be proper
to eliminate all three. But that may not be the case.
     In your example of five piles, the three lowest equal piles may
contain a majority of the total votes. If the sum is at least larger than
the votes of the one pile ahead of the three lowest candidates, the routine
would be as follows:
     You conduct a special tally on the side, you tally the next choices of
all the ballots of only these three piles.  Whichever of these three
candidates has the lowest count is the candidate that is eliminated.
     The elimination of this candidate and the transfer of his ballots
should break the tie of the next two lowest candidates that were also
members of the three way tie.
     If the special tally did not break the three way tie, then you run a
second special tally on the next set of choices for these three candidates.

>yours sincerely,
>
>Hugo Harth

  Regards, Donald Davison - Host of New Democracy,  www.mich.com/~donald

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   |                         Q U O T A T I O N                         |
   |  "Democracy is a beautiful thing,                                 |
   |       except that part about letting just any old yokel vote."    |
   |                            - Age 10                               |
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