- WELCOME TO A LESSON ON INSTANT RUNOFF VOTING, ABBREVIATED IRV.
IN THIS LESSON WE'LL DEFINE INSTANT RUNOFF VOTING,
AND ALSO APPLY INSTANT RUNOFF VOTING TO DETERMINE THE WINNER
OF AN ELECTION.
INSTANT RUNOFF VOTING,
ALSO CALLED PLURALITY WITH ELIMINATION,
IS A MODIFICATION OF THE PLURALITY METHOD
THAT ATTEMPTS TO ADDRESS THE ISSUE OF INSINCERE VOTING,
AND WE DISCUSSED THIS IN THE PREVIOUS LESSON.
IN IRV VOTING IS DONE WITH PREFERENCE BALLOTS
AND A PREFERENCE SCHEDULE IS GENERATED.
THE CHOICE WITH THE LEAST FIRST PLACE VOTES IS ELIMINATED
FROM THE ELECTION, AND ANY VOTES FOR THAT CANDIDATE
ARE REDISTRIBUTED TO THE VOTER'S NEXT CHOICE.
THIS CONTINUES UNTIL A CHOICE HAS A MAJORITY,
OR OVER 50% OF THE VOTES.
SO LET'S TAKE A LOOK AT A MORE DETAILED EXAMPLE.
HERE WE HAVE A PREFERENCE SCHEDULE.
WE'RE GOING TO DETERMINE THE WINNER
USING INSTANT RUNOFF VOTING, OR IRV.
BEFORE WE DO THIS THOUGH,
NOTICE HOW IF WE FIND THE SUM OF THIS ROW HERE
WE CAN DETERMINE THERE ARE A TOTAL OF 35 VOTES,
AND THEREFORE, FOR A MAJORITY
A CANDIDATE MUST HAVE AT LEAST 18 VOTES.
ALSO NOTICE USING THE BASIC PLURALITY METHOD,
THE WINNER WOULD BE CANDIDATE B.
NOTICE B HAS 5 + 5 + 6, OR 16 FIRST CHOICE VOTES,
GIVING IT MORE THAN ANY OTHER CANDIDATE.
WHERE CANDIDATE "A" HAS 0 FIRST PLACE VOTES, CANDIDATE C HAS 8,
CANDIDATE D HAS 9, AND CANDIDATE E HAS 2.
NOW TO FIND THE WINNER USING THE INSTANT RUNOFF METHOD,
WE WOULD ELIMINATE CANDIDATE "A", SINCE CANDIDATE "A"
HAS 0 FIRST CHOICE VOTES.
SO WE CAN EITHER CROSS OFF "A", AS I AM HERE,
OR JUST DELETE "A" FROM THE TABLE,
WHICH WOULD LOOK LIKE THIS.
NOTICE IN THIS CASE BY ELIMINATING CANDIDATE "A"
WE DON'T ASSIGN ANY FIRST CHOICE VOTES TO ANY OTHER CANDIDATES.
SO NOW WE MOVE ALONG TO THE SECOND STEP,
ELIMINATE CANDIDATE E THAT HAS 2 FIRST PLACE VOTES.
SO WE ELIMINATE CANDIDATE E, OR DELETE E FROM THE TABLE.
THE TABLE WOULD LOOK LIKE THIS.
NOTICE HOW BY ELIMINATING CANDIDATE E,
THESE 2 VOTES ARE NOW ASSIGNED TO CANDIDATE D.
SO "A" HAS 0, B HAS 16, C STILL HAS 8, BUT NOW D HAS 11 VOTES,
AND NOW E HAS 0.
NOW FOR THE NEXT STEP NOTICE CANDIDATE C HAS THE LEAST VOTES,
SO NOW WE'LL ELIMINATE CANDIDATE C, OR JUST DELETE C.
NOTICE BY DOING THIS THESE 8 VOTES NOW GO TO CANDIDATE D.
SO "A" STILL HAS 0, B STILL HAS 16, C NOW HAS 0,
BUT NOTICE HOW D HAS 18,
WHICH NOW GIVES D A MAJORITY OF THE VOTES.
18 DIVIDED BY 35 IS APPROXIMATELY 51.4%,
AND THEREFORE D WINS USING THE INSTANT RUNOFF METHOD.
NOW, LET'S DISCUSS WHAT CAN GO WRONG
WHEN USING THE INSTANT RUNOFF METHOD.
INSTANT RUNOFF VOTING CAN VIOLATE THE CONDORCET CRITERION,
AS WE SAW IN OUR PREVIOUS LESSON
WHEN WE WERE DISCUSSING INSINCERE VOTING.
LET'S GO AHEAD AND REVISIT THIS EXAMPLE
JUST TO EMPHASIZE WHAT CAN GO WRONG.
HERE WAS THE INITIAL ELECTION RESULTS
USING THE BASIC PLURALITY METHOD.
THE WINNER WAS CANDIDATE "A".
THEN DOING THE ONE-TO-ONE COMPARISON
WE NOTICED THAT CANDIDATE C,
OR THE INDEPENDENT CANDIDATE, WOULD WIN.
BUT THEN IF WE APPLY THE INSTANT RUNOFF METHOD,
NOTICE HOW CANDIDATE C HAS THE LEAST FIRST PLACE VOTES.
SO IF WE ELIMINATE CANDIDATE C USING THE INSTANT RUNOFF METHOD,
WE CAN SEE THAT THE DEMOCRAT WINS WITH A MAJORITY OF 57.9%
OF THE VOTES.
SO THIS IS AN EXAMPLE OF WHERE THE INSTANT RUNOFF METHOD
CAN VIOLATE THE CONDORCET CRITERION.
HOWEVER, IT IS IMPORTANT TO EMPHASIZE
THAT THE INSTANT RUNOFF METHOD DOES ADDRESS INSINCERE VOTING.
THOSE VOTERS THAT WERE TEMPTED TO VOTE FOR THE DEMOCRAT,
CANDIDATE B, CAN NOW VOTE FOR THEIR PREFERRED CANDIDATE,
CANDIDATE C, OR THE INDEPENDENT,
KNOWING THAT IF THEIR CANDIDATE IS ELIMINATED
THEIR VOTE WOULD GO TO THEIR SECOND CHOICE, OR CANDIDATE B.
I HOPE YOU FOUND THIS HELPFUL.