[EM] A much simpler proportional Condocet Method - BTR-STV

[raphfrk at netscape.net]

> Now, first I'm going to introduce to you the idea of the proportional 
Condorcet winner.
> The are several of these in an election, and the majority Conorcet 
winner is always
> among them. A proportional Condorcet winner is the Condorcet winner 
of the
> minority of the electorate. For instance, in a four seat election the 
a Proportional
> Condorcet winner would be the Condorcet winner of 25% of the 
populace.

That is not a very clear definition.  Are you saying that a candidate 
is a proportional
condorcet winner if there exists a set of votes amounting to 25% (or 
more) of the
electorate in which he counts as a condorcet winner ?

If so, then in a 4 seat constituency, there is potentially more than 4 
proportional
condorcet winners.

For example (just listing first preferences)

A: 15%
B: 15%
C: 14%
D: 14%
E: 14%
F: 14%
G: 14%

Any of the candidates in the above election is a proportional condorcet 
winner.  The 25%
that each candidate would pick would be his own supporters and 11% of 
the vote from
some other supporter.  He would be the condorcet winner as 14% rank him 
first and at
most 11% rank any other candidate ahead of him.  This means that there 
could be 7
proportional condorcet winners in a 4 seat constituency (maybe more).  
At least 3
of them must be eliminated.

> Now, this method that I'm proposing differs slightly. It uses a 
normal STV method
> for transferring the surplus votes. Then in the elimination of 
undervotes round,
> instead of eliminating the one with the least votes and then 
transferring their
> votes, you take a set of the least-vote getters equivalent to the 
amount of seats
> in the election, plus 1, and eliminate the one who is the least 
preferred on the
> ranked ballots by the the electorate, then transfer that person 
votes. Therefore,
> a proportional Condorcet winner will never be eliminated, and they 
will always rise
> to the top.

You haven't said how the least preferred is to be determined (condorcet 
loser?).
So, in a 4 seat constituency, the bottom 5 candidates are compared and 
the
condorcet loser of that election is determined based on all the votes.  
Since, I
don't know what you mean by proportional condorcet winner, I don't know
what your claim that none of them can be eliminated actually means.

In any case, there is an interesting effect if you use the Droop quota 
for electing
candidates.  After a candidate is elected, and their votes transferred, 
you can
consider the remainder of the election as an election for one fewer 
seats.

For example, if there was a 4 seater, the rounds might go like:

Round 1:  nobody elected (20% required)
Bottom 5 candidates are compared

Round 2: candidate gets >20% so is elected
votes redistributed

Election now considered a 3 seat election.
Votes remaining: 80% of the original
Target is droop quota = 80%/(3+1) = 20% of original vote so stays 
constant

Round 3: nobody elected
Bottom 4 candidates are compared (instead of 5)

and so on.


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