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Subject: stv with quota

Title: Message
I promised/threatend/joked on Monday's call that I'd send a summary of the full glory of single transferable vote with quota to this group.
This is useful where it is desirable/necessary to have multiple selections with various sub-groups represented. So Northern Ireland, student unions, and the sandwiches for a family picnic are suitable. It's very easy to deal with for the voter, rather complicated for the returning officer.
It predefined how many representatives (or packets of sandwiches) are being chosen. (let this be R)
There are no restrictions on how many candidates there are, or how many from a party (in fact one of the virtues of this system is that "party" does not need to be defined in the system)
All voters assign preferences to as many candidates as they wish (usually by putting numbers against the name, 1= first choice, but small children could arrange the filling pots in order)   Voters do not need to assign preferences to all candidates, but they must make them unambiguous (a voter can't say several are equal rank), but getting a later preference wrong does not invalidate an earlier one (so ham=1, honey=2, cheese=3, peanut butter =3 , salmon=5) has valid first and second preferences, but no valid 3rd or beyond)  [writing this paragraph I found one should avoid the word "rank" - is rank 2 higher or lower than rank 1 ?]
Once the votes are in, they (or strictly those with a valid first preference) are counted.(let this be V)
Now we establish the quota, which is V/(R+1). Let this be Q
All votes are sorted by first preference.
If the candidate with the highest value of votes is now over the quota, they are declared elected.
    If there are now R elected representatives, end the procedure.
    If there are not yet R elected, compare the votes of the just-elected candidate (let this be E) are compared to the quota Q.
    If E == Q, discard all these votes, and go to A:
    If E > Q, reduce these votes value to  (E-Q)/E of their current value, and reallocate to next preference; go to A
If no candidate is over quota, take the votes of the candidate with the lowest value of votes and reallocate according to next preference; go to A
The procedure is usually described as assigning an initial value of 100 to the votes, so quota is 100 *V /(R+1), and the value rounds down to a whole number, but in concept you can work it with floating point and an initial value of 1.0.
The case where R=1 (which is what we've just had for the ws-bpel name) is a degenerate form of this, as the procedure terminates as soon as someone is elected and the reallocation of a successful candidates votes never happens.  But in other cases, that's the neat bit, because it means a popular party doesn't use up all its strength on their best candidate.
Actually, the sandwich example would have to treat the fillings as parties, with "ham A", "ham B" etc.
Peter Furniss
Chief Scientist, Choreology Ltd
web: http://www.choreology.com
email: peter.furniss@choreology.com
phone: +44 870 739 0066
mobile: +44 7951 536168

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