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.

 

A:

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

 

------------------------------------------
Peter Furniss
Chief 
Scientist, Choreology Ltd
web: http://www.choreology.com
email: 
phone: 
+44 870 739 0066
mobile: +44 7951 536168