Exhausted
Ballots and Continuing Candidates under RCV
I have
heard that with Ranked Choice Voting it is possible for a winning
candidate to win with fewer than a majority of votes. Is this true?
According to the San Francisco charter, the
ìwinnerî in ranked choice voting is defined as the one who wins a
majority of what is called "continuing ballots."
Continuing ballots are those where all the rankings have not
exhausted, where the voter is still participating in the runoff. If a
voter uses all of his or her three rankings on candidates who don't have a
chance of winning, that ballot will ëexhaustí and not be a
'continuing' ballot. So it's possible that the winner may end up with a
majority that is less than the majority of all voters who initially voted,
but it is still a majority of continuing ballots.
This is analogous to a situation where some voters donít return to vote
for the December runoff. But considering the fact that voter turnout
usually decreased between the November election and the December runoff 
often by anywhere from 30 to 50%  more voters likely will participate in
the final decisive runoff under ranked choice voting than under the
previous December runoff system.
Here's a mock election that will illustrate "continuing ballots"
and "exhausted ballots."
Candidates

1st
round

A

32

B

24

C

20

D

15

E

9

Total

100

Candidate E is in last place and does not make the initial runoff.
Let's say of E's nine votes, 5 go to C and 4 got to A.
Now the vote totals stand:
Candidates

1st
round

2^{nd}

A

32

(+4)=36

B

24

24

C

20

(+5)=25

D

15

15

E

9

(9)
out

Total

100

100

Now D is in last place
and is eliminated from the runoff. Let's
say of 15 D voters, 5 ranked A as their next choice, 5 ranked B, and 5
ranked E. But E has been
eliminated, so of these 5 voters, let's say their next (third)ranked
candidate is: 3 rank B and 2 rank A. Now the vote totals stand:
Candidates

1st
round

2^{nd}

3^{rd}

A

32

(+4)=36

(+5+2)=43

B

24

24

(+5+3)=32

C

20

(+5)=25

25

D

15

15

(15)
out

E

9

(9)
out

Out

Total

100

100

100

We're down to three
candidates, so one of the candidates is about to win, when the current
last place candidate, Candidate C, is eliminated. But here's where the
'continuing candidate' factor comes in.
Candidate C is in last place and is eliminated from the runoff.
Of the 25 voters who were voting for C, let's say 5 rank A as their
next choice, 10 rank B, and 10 rank Candidate D as their next choice. But
Candidate D has been eliminated from the runoff, so for those ballots it
goes to each voterís next ranked candidate. Let's say of these 10, 7
ranked Candidate E as their next (third) choice, and three ranked
Candidate B. But Candidate E also has been eliminated from the runoff.
Since that is those voters third ranking, they have no more runoff choices
to give their vote to and so those seven votes go into what is called an
ìexhausted pile.î They are ballots that do not ëcontinue,í and the
voters of these ballots do not participate in the final runoff.
That means that the winner is candidate A with 48 votes  slightly less
than a majority of the original 100 ballots, but 51.6% of the 93
continuing ballots, with 7 ballots exhausted.
This is analogous to those 7 voters not returning for the December runoff,
which of course in most December runoffs happened in large numbers.
But with RCV, the dropoff  as indicated by the number of
ëcontinuing ballotsí  will be much less than with December runoffs.
Here are the final vote totals:
Candidates

1st
round

2^{nd}

3rd

4^{th}

A

32

(+4)=36

(+5+2)=43

(+5)=48

B

24

24

(+5+3)=32

(+10+3)=45

C

20

(+5)=25

25

(25)
out

D

15

15

(15)
out

out

E

9

(9)
out

out

out

Total

100

100

100

93+7
exhausted=100

Compiled
by Steven Hill, (415) 6655044, [email protected]
