[EM] Iterative quota voting

[Jim & Mary Ronback]

Iterative Quota Voting

I am very uncomfortable with complexity of the process used for 
transferring surplus marks of the candidates in the STV counting 
process. That counting process is very difficult for most voters to 
follow. In BC they could easily be swayed to vote against BC-STV on 17 
May 2005 even though it is a big improvement over First Past The Post. 
Thus I was inspired to propose a different and simpler counting method 
which avoids fractions and incorporates some aspects of approval voting. 
For lack of a better name, it is called "iterative quota voting" (IQV). 
Perhaps it resembles some existing voting methods already, but since I'm 
new to this endeavour, it may be old hat to some of you.

So here it goes:
Voters can mark their ballots preferentially from 1 up to N for any of C 
candidates vying for N seats.  The preference numbers on the ballot have 
to start at 1. The numbers should have no gaps, but repetitions are 
allowed, e.g., two or more candidates may have the same number. This 
latter feature provides a notion of approval voting, if  more than one 
candidate is acceptable at a given preference level to a given voter. He 
can only put one mark against a given candidate.
For round r,
The quota Qr = ((Mr/Cr)/(Nr+1)) +1 where 
Mr is the number of marks (labeled 1 through r, including repetitions) 
for the remaining candidates on all the ballots
Cr is the number of candidates remaining
Nr is the number of vacant seats remaining
Note: the quota at each round is based on counting the marks on all the 
ballots, not the number of ballots.

Once a candidate has exceeded the quota at a given round, as a voter, 
all I'm concerned about is that the remaining marks ("1" to "number of 
round") for the remaining candidates on my, and everyone else's, ballot 
are counted at full value on the subsequent rounds. Once candidates have 
been selected, i.e., passed the quota, the next round can be considered 
as a brand new election for the remaining seats using a new quota.

Once a candidate(s)' count has passed the quota, all marks ("1" up to 
"N") against their name(s) are excluded on the next round. Thus for 
round two, a new quota is calculated based on the number of remaining 
seats and number of candidates left and the total numbers of marks 
labeled "1" and "2" on all the ballots for these remaining candidates. 
Those candidates whose count of "1's" and "2's" exceed the new quota are 
elected and all their marks are excluded in the next round and a new 
quota is calculated based on the number of remaining seats, the 
remaining candidates left and the total number of marks labeled "1", "2" 
and "3" for the remaining candidates. And so on, until all the seats are 
filled.

Could this still be considered a variant of iterative approval voting or 
is it something else? I think it is fair since it ensures that at each 
round, all marks ("1" through "number of round")  for each remaining 
candidate are counted at full value. This process would be simpler to 
explain to the voters, since it avoids fractions and there are a fewer 
number of decisions in the process.  Once all the seats have been filled 
by round r <= y, any marks labeled "y+1" or greater are no longer 
needed, except to record the number and value of the marks the losers 
obtained. Those marks (1 to y >=  last round +1) which belong to the 
losers, after all the seats have been filled, have no further influence 
on those who already were elected. Votes that really "count" in 
selecting winners have not been discarded. No ballots have been 
discarded in the counting process.

Each mark on all the ballots is considered at full value at a given 
round like in approval voting, as opposed to the STV process a voter's 
ballot has only the total weight of one vote equal to 1, no matter how 
many preferences he marks on his ballot. Thus his vote may be divided 
into two fractions, one for the winner of the round and passing a 
fractional surplus of his one vote to the other preferences on his 
ballot. In the IQV approach,  a voter has  up to N votes of equal 
weight  but  these votes are only  progressively counted  at each round 
based on their preference value.

It would be interesting to see how results based on this approach would 
differ from BC-STV results.

We should not underestimate the power of simplicity in being able to 
convince the voter of the merits of a counting process which is easy to 
visualize. The counting process should be simply enough that the 
majority of voters/ scrutineers can easily do it manually (especially 
whenever electrical power is not available for computers).

Yours democratically,

Jim Ronback
Tsawwassen, BC

PS Comments would be appreciated for my edification.