[EM] An example of BTR-STV

[Anthony O'Neal]

(This is the election I pulled out of the Wikipedia article for CPO-STV. I
just didn't feel like making up an election where the results from CPO-STV
and STV differ right now.  If you want to see how the results for the
CPO-STV and STV results were arrived upon, then go to the article)

(PS, does anyone know what the BTR part of BTR-IRV means?  Honestly, I can't
figure it out, but that's what Warren on Rangevoting.com calls it.  I'm
thinking of changing the name to Majority Elimination by IRV, or ME-IRV, and
ME-STV, but if BTR makes more sense...)


The votes are:

25 votes: Andrea
34 votes: Carter > Brad > Delilah
7 votes: Brad > Delilah
8 votes: Delilah > Scott
5 votes: Delilah > Scott
21 votes: Scott> Delilah

STV elects Andrea, Carter, and Deliliah.  CPO-STV elects Andrea, Carter, and
Scott.

Now let's compute the score for BTR-STV:

Add up first place votes:

25 for Andrea
34 for Carter
7 for Brad
13 for Delilah
21 for Scott

Now for this election, using the Hagenbach-Bischoff quota of votes/seats +
1, the amount needed to get elected is 25 votes.  So Andrea and Carter are
immediately declared elected, as their amount of votes exceeds the quota.

So Carter's 9 surplus votes need to be transferred, and they are transferred
to Brad.

Now let's add up the tally:

25 for Andrea (elected)
25 for Carter (elected)
15 for Brad
13 for Delilah
21 for Scott

No one has enough votes to be elected, so let's go through the elimination
round.  The elimination round in BTR-STV is to take the N + 1 (where N is
the number of seats that STILL need to be elected in the election)
candidates that have the least votes, and then compare them by having each
voter attach themselves to the candidate of the least whom they rank
highest.

There are is only one seat left that needs to be filled, so we take the two
with the least votes, and they are Delilah and Brad and compare them:

Note: at this point I am confused about the direction the election needs to
take.  If we don't count Carter's 25 consumed votes in this imaginary
elimination round, Delilah wins (as in CPO-STV).  If we do, Brad wins (and
Deliliahs votes are transferred to Scott, and Scott wins).  I'm going to
show how both ways happen, and I'll find out the correct way to do it later.

Counting consumed votes:

Delilah: 34 people prefer Delilah to Brad
Brad: 41 people prefer Brad to Delilah

Therefore, Delilah is eliminated, and 8 of her votes transfer to Brad, and 5
of her votes transfer to Scott.  Scott would then have 21 votes and he would
be elected.  This is the same result as normal STV

Not counting the consumed votes:

Delilah: 34 people prefer Delilah to Brad
Brad: 15 people prefer Brad to Delilah

Brad is eliminated, and all 15 of his votes are transferred to Delilah, so
Delilah would now have 28 votes and would be eleected.



I believe that the second method, not counting already consumed voters, is
the proper method, but this may just be bias since I'm trying to paint my
method out to be simialar to CPO-STV.  I have presented both, so if any of
you know more about the subject feel free to point me in the right
direction.


-Anthony O'Neal
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