- IN THIS EXAMPLE, WE'RE GIVEN A PREFERENCE TABLE
AND ASKED SEVERAL QUESTIONS.
LOOKING AT THE PREFERENCE TABLE,
NOTICE HOW THE FIRST ROW TELLS US A NUMBER OF VOTERS
WHILE THE SECOND THROUGH FIFTH ROWS TELL US THE VOTERS' FIRST,
SECOND, THIRD AND FOURTH CHOICES.
LOOKING AT THE CHOICES, NOTICE HOW THE CANDIDATES
ARE "A," D, F AND G.
FIRST QUESTION IS, "HOW MANY VOTERS VOTED IN THIS ELECTION,"
WHICH WOULD BE THE SUM OF THIS FIRST ROW,
SO WE HAVE 11 + 19 + 10 + 3 + 2 + 12 + 4 WHICH IS EQUAL TO 61.
SO A TOTAL OF 61 VOTERS VOTED THIS ELECTION.
NEXT, WE'RE ASKED, "HOW MANY FIRST-PLACE VOTES
ARE NEEDED FOR A MAJORITY?"
A MAJORITY IS MORE THAN HALF,
SO WE WANT TO BEGIN BY FINDING HALF OR 50% OF 61.
TO FIND 50% OF 61, WE WOULD CONVERT 50% TO A DECIMAL
WHICH IS 0.5 OR 0.50, THEN MULTIPLY BY 61,
THIS WOULD GIVE US 30.5.
OF COURSE, WE CAN'T HAVE A FRACTIONAL PART OF A VOTE
AND ALSO A MAJORITY IS MORE THAN HALF,
AND THEREFORE WE HAVE TO ROUND THIS UP TO 31.
THEREFORE 31 FIRST-PLACE VOTES ARE NEEDED FOR A MAJORITY.
I DO WANT TO POINT OUT THAT IF THERE WERE A TOTAL OF 60 VOTERS,
HALF OF 60 WOULD BE 30
BUT 30 WOULD NOT BE ENOUGH VOTES
BECAUSE WE HAVE TO HAVE MORE THAN HALF OR MORE THAN 50%,
SO WE'D STILL HAVE TO HAVE 31 FIRST-PLACE VOTES
FOR A MAJORITY IF THERE WERE ONLY 60 VOTERS.
NEXT, "WHICH CANDIDATE OR CHOICE HAS THE MOST FIRST-PLACE VOTES?"
WE CAN DETERMINE THIS BY ANALYZING
THE FIRST AND SECOND ROWS.
NOTICE HOW CANDIDATE D RECEIVED 11 FIRST-CHOICE VOTES
BUT CANDIDATE "A" RECEIVED 19 + 10 + 4 OR 33 FIRST-CHOICE VOTES,
F RECEIVED 3 + 2 OR 5 AND G RECEIVED 12,
AND THEREFORE "A" RECEIVED THE MOST FIRST-PLACE VOTES.
NEXT, WE'RE ASKED, "WHICH CANDIDATE OR CHOICE
HAS THE LEAST FIRST-CHOICE VOTES?"
HERE WE HAVE TO BE A LITTLE CAREFUL,
BECAUSE IF A CANDIDATE DID NOT SHOW UP HERE IN THIS ROW,
MEANING THEY DID NOT RECEIVE ANY FIRST-CHOICE VOTES,
THAT WOULD BE THE CANDIDATE WITH THE LEAST FIRST-PLACE VOTES.
BUT EVERY CANDIDATE DOES APPEAR IN THIS ROW
THEREFORE EVERY CANDIDATE DID RECEIVE
AT LEAST SOME FIRST-CHOICE VOTES.
LOOKING AT CANDIDATE F,
F RECEIVED ONLY 3 + 2 OR 5 FIRST-PLACE VOTES
WHICH IS THE LEAST, SO THIS WOULD BE CANDIDATE F.
NEXT, WE'RE ASKED,
"WHICH CANDIDATE OR CHOICE HAD THE MOST LAST-PLACE VOTES,"
WHICH IN THIS CASE WOULD BE THE MOST FOURTH-CHOICE VOTES.
SO ANALYZE THIS ROW HERE, "A" RECEIVED A TOTAL OF 11 + 2
OR 13 FOURTH-CHOICE VOTES,
BUT NOTICE CANDIDATE D RECEIVED 19 + 10 OR 29
FOURTH-CHOICE VOTES, G RECEIVED 3 + 4 OR 7,
AND F RECEIVED 12.
SO CANDIDATE D RECEIVED THE MOST FOURTH-CHOICE
OR LAST-PLACE VOTES.
AND THEN FINALLY, "WHICH CANDIDATE OR CHOICE
HAS THE LEAST LAST-PLACE VOTES?"
AGAIN, THERE WAS A CANDIDATE MISSING FROM THIS ROW HERE
THAT GIVES US THE FOURTH-CHOICE VOTES.
THAT CANDIDATE WOULD RECEIVE ZERO FOURTH-CHOICE VOTES
AND THEREFORE WOULD BE THE CANDIDATE FOR THIS QUESTION.
BUT AGAIN EVERY CANDIDATE DOES APPEAR IN THIS ROW,
AND NOTICE CANDIDATE G RECEIVED 3 + 4 OR 7 FOURTH-CHOICE VOTES
AND THEREFORE G RECEIVED THE LEAST LAST PLACE
OR FOURTH-CHOICE VOTES.
I HOPE YOU FOUND THIS HELPFUL.