Methods of elimination in quota preferential STV

[Bart Ingles]

LAYTON Craig wrote:
> 
> Bart Ingles wrote:
> 
> >True, if the voter gives her entire vote to a single candidate when that
> >candidate was in no danger of losing.  But candidate elimination removes
> >part of the incentive to vote for too few, in that you are less likely
> >to see all your candidates lose because you spread your vote too thin
> >(if your party is weaker than you thought, only one candidate would be
> >eliminated & the votes redistributed, instead of eliminating most or all
> >of them at once).
> >
> >So the problem should be less severe than with traditional limited vote
> >or cumulative vote.
> 
> The problem is pretty severe, even when the popular candidate receives no
> single votes (ie all those who vote for the popular candidate vote for
> others).  Example;
> 
> An electorate is electing 5 members.  There are four parties.
> 
> Pary A has 40% support
> Party B has 40% support
> Party C has 11% support
> Party D has 9% support
> 
> An election is held using your system.  Tiebreaker for two or more
> candidates in the same party, is the candidate further down the party ticket
> (ie with the higher number) is eliminated.  There won't be any ties between
> parties so we don't have to worry about that.
> 
> Parties A and B stand 5 candidates each: A1-A5, and B1-B5.  Parties C and D
> stand one each C1 & D1.
> 
> Every A and B voter votes for 3 candidates each.  Why three? Why not? They
> understand the electoral system enough to know that voting multiple times
> can help their party, but they also want to help their preferred party
> candidates win (after all, this is what individual candidate PR's all
> about).
> 
> A1 is very popular, and every A voter votes for him, and two others (A2-A5
> have an even spread).  B candidates have a perfectly even spread.  C and D
> voters vote for their own candidates only.
> 
> The voting goes like this;
> 20% A1, A2, A3
> 20% A1, A4, A5
> 8% B1, B2, B3
> 8% B3, B4, B5
> 8% B2, B4, B5
> 8% B1, B5, B3
> 8% B4, B1, B2
> 11% C1
> 9% D1
> 
> I won't bother with the rounds of voting, but candidates are eliminated in
> the following order;
> A5, A3, B5, B2, D1, A4, A2.
> 
> Candidates A1, B1, B3, B4, C1 are elected
> 
> Party A, with 40% support, gets 20% of the seats. Party B, with 40% support,
> gets 60% of the seats, and party C, with 11% support, gets 20% of the seats.
> 
> This is a pretty dodgy result.  In fact, if it was a limited vote (Single
> Non Transferrable Vote) with a similar voting pattern, A1, B1, B2, C1, D1
> would be elected.  This is actually a much better result, even though it
> isn't any more proportional.

No doubt there are situations where SNTV or plain cumulative voting (the
two are logically equivalent) give better results, just as there are
examples where FPTP makes more sense than a runoff system.  Where SNTV
would be worse is if some of the A1 voters knew enough to vote for other
candidates (say 20% A1, and 10% each A2 and A4), while the B voters
divided their votes equally.  Then the result would be A1, A2, A4, C1,
D1.  Elimination would at least keep the B voters from being hurt too
badly by that miscalculation.  

To do consistently better, you probably need quotas.  In fact, wouldn't
non-quota IRV would have the same problem as the method above?

About a year-and-a-half ago I posted an unranked quota-based method
similar to STV that would probably do better than the one above (it
wouldn't surprise me if this was also covered in the Bolger references):

---------------------------------------------------------
PROPORTIONAL APPROVAL

1.  Voters vote for any number of candidates, as in Approval.

2.  Initialize ACTIVE_BALLOTS to the number of voters, and OPEN_SEATS to
the number of seats open.
3.  Calculate the current quota (can use either Hare or Droop).  For
example, using Droop:
   CURRENT_QUOTA = [ACTIVE_BALLOTS / (OPEN_SEATS + 1)] + 1.
4.  Select an Approval winner, using votes on the currently active
ballots.
5.  Reduce the number of ballots ***containing the latest Approval
winner*** by an amount equal to CURRENT_QUOTA.  You can use either
Random Selection to discard ballots, or you can reduce the value of all
affected ballots, as with STV's Fractional Transfer.  If the winner had
less than a quota, simply drop all ballots containing a vote for the
winner.
6.  Reduce ACTIVE_BALLOTS by the number of ballots dropped in step 5.
7.  Reduce OPEN_SEATS by one.
8.  While there are more seats to fill, go back to step 3.
-----------------------------------------------------------


In the example above, the winners would be:
Candidate     Votes Consumed
  A1           1667
  B1           1667
  B4           1667
  A2           1166.5
  A4           1166.5


Bart