[EM] local CPO-STV

[James Green-Armytage]

Dear election methods fans,

Here is my proposal for a computationally cheaper (although slightly
compromised, of course) version of CPO-STV. It could be called "local
CPO-STV," or CPO-STV lite

Perhaps I am wrong, but I see this method as being marginally better than
sequential STV, while maintaining a fairly moderate computational cost.

_______________________________



Part one: Identify non-viable candidates and outcomes. (For a detailed
version of this, see my July 24 posting entitled "CPO-STV shortcuts".)

1. Outcomes that fail to contain candidates who have surpluses can be
dismissed from consideration.

2. There are n seats to be won. Take the n candidates with the highest top
choice vote totals, and call it the "n set". The one with the lowest
number of top choice votes has r top choice votes. 
	If any candidate is not ranked on at least r ballots, then they can be
eliminated, and any outcomes containing them can be dismissed from
consideration. 
	If any candidate is not ranked above at least one member of the n set, on
at least r ballots, then they can be eliminated, and any outcomes
containing them can be dismissed from consideration.

Note: The first round of such eliminations can take place after initial
surpluses are transferred. If the elimination of candidates causes another
surplus transfer that raises the value of r, then another round of
elimination can take place, which may in turn set off another round of
surplus transfers, and so on, until either type of round produces no
change.

Part two: Begin with an initial outcome, and search for an outcome with
local stability through one-candidate substitutions.

3. Do an initial STV count, producing an initial outcome ("outcome A").

4. Compare outcome A with one-candidate substitutions from A (all possible
one-candidate substitutions, except for those already dismissed from
consideration in part one). If outcome A beats all of its one-candidate
substitutions, then it has local stability and is declared to be the final
result.

5. If outcome A is beaten or tied by another outcome or other outcomes
("outcome B", "outcome C", etc.), such outcomes are added to the "set of
contending outcomes", or "contender set". 

6. All outcomes in the contender set are compared with all of their
one-candidate substitutions, excepting those that have been dismissed from
consideration, and those which are already in the contender set. 
	If any such one-candidate substitution outcomes beat or tie the member of
the contender set that they are being compared with, then they are added
to the contender set.

7. When no members of the contender set are beaten or tied by a
one-candidates substitution not already in the set, then the set is closed.

8. All candidates in the contender set are compared to one another, and
the winning outcome is decided by a Condorcet completion method (probably
either beatpath or ranked pairs).