- WELCOME TO AN INTRODUCTION TO VOTING.
IN THIS LESSON WE WILL DEFINE A PREFERENCE BALLOT
AND A PREFERENCE TABLE AND ALSO WE'LL CREATE A PREFERENCE TABLE.
BUT BEFORE WE DO THIS, LET'S DISCUSS SOME OF THE ISSUES
THAT CAN ARISE WHEN SELECTING A WINNER OF AN ELECTION.
SOMETIMES VOTING IS MORE INVOLVED THAN JUST ELECTING
WHO GETS THE MOST VOTES.
THERE ARE SEVERAL METHODS
FOR DETERMINING A WINNER OF AN ELECTION.
A CERTAIN METHOD FOR SELECTING A WINNER
MAY BE MORE APPROPRIATE BASED UPON THE TYPE OF ELECTION.
FOR EXAMPLE, THE METHOD OF ELECTING A PRESIDENT
FAIRLY MIGHT BE DIFFERENT THAN A GROUP OF FRIENDS
FAIRLY DECIDING WHAT MOVIE TO WATCH.
LET'S CONSIDER AN EXAMPLE TO SEE WHY ISSUES CAN ARISE
WHEN SELECTING WINNERS OF ELECTIONS.
LET'S BEGIN BY CONSIDERING THE FOLLOWING RESULTS
FROM A STUDENT BODY PRESIDENTIAL ELECTION.
NOTICE HOW THE CANDIDATES ARE LISTED IN THE FIRST ROW
FROM "A" THROUGH E AND THE SECOND ROW TELLS US
THE NUMBER OF FIRST PLACE VOTES.
NOTICE IF WE ADD THIS SECOND ROW,
THIS TELLS US THERE ARE A TOTAL OF 450 VOTES.
AND SINCE CANDIDATE E HAS THE MOST VOTES AT 102,
E SHOULD WIN RIGHT?
WELL, NOTICE THAT IN ORDER TO HAVE A MAJORITY,
OR MORE THEN 50%, SOMEBODY WOULD HAVE TO HAVE
MORE THEN 225 VOTES.
WELL, NOTICE THAT NO CANDIDATE HERE EVEN COMES CLOSE
TO HAVING A MAJORITY OF THE VOTES.
NOW, LETS ASSUME THAT THE VOTERS RANK THE CANDIDATES
FROM THEIR FIRST CHOICE THROUGH THEIR FIFTH CHOICE
AND HERE ARE THE RESULTS.
AND THIS IS CALLED A PREFERENCE TABLE,
WHICH WE'LL DEFINE IN JUST A MOMENT.
IF WE FOCUS ON CANDIDATE E FOR A MOMENT,
NOTICE HOW EXCEPT FOR THE 102
WHO VOTED E AS THEIR FIRST CHOICE,
MOST VOTERS REALLY SEEMED TO DISLIKE THE CANDIDATE
BECAUSE CANDIDATE E IS RANKED FIFTH FOR EVERYONE ELSE.
IF WE COMPARE CANDIDATE E TO CANDIDATE B,
NOTICE HOW 98 PEOPLE VOTED B AS THEIR FIRST CHOICE,
ONLY FOUR LESS THEN E.
BUT EVERYONE ELSE THAT DIDN'T VOTE B FIRST RANKED B SECOND.
SO WE COULD SAY THAT B IS NOT DISLIKED BY ANYBODY,
SO MAYBE THAT MEANS THAT B SHOULD WIN.
IT'S SITUATIONS LIKE THESE THAT LEAD TO INTERESTING DISCUSSIONS
ABOUT VOTING THEORY AND VOTING METHODS.
AND IN THIS SERIES OF VIDEOS
WE'LL BE DISCUSSING VARIOUS VOTING METHODS,
BUT FOR THIS INTRODUCTORY VIDEO LETS BEGIN BY DEFINING
A PREFERENCE BALLOT AND A PREFERENCE SCHEDULE
OR A PREFERENCE TABLE.
A PREFERENCE BALLOT IS A BALLOT
IN WHICH THE VOTERS RANK THE CHOICES IN ORDER OF PREFERENCE.
AND A PREFERENCE SCHEDULE, OR TABLE,
IS WHEN THESE INDIVIDUAL BALLOTS ARE TYPICALLY COMBINED
INTO ONE PREFERENCE SCHEDULE OR TABLE,
WHICH SHOWS THE NUMBER OF VOTERS IN THE TOP ROW
THAT VOTED FOR EACH OPTION.
LET'S TAKE A LOOK AT AN EXAMPLE.
A COLLEGE SURVEYS STUDENTS ABOUT A POSSIBLE NEW DESIGN
FOR THEIR WEBSITE.
THE THREE SITES ARE LABELED A, B, AND C
AND THE INDIVIDUAL BALLOTS ARE SHOWN BELOW.
SO THESE BALLOTS HERE WOULD BE CALLED THE PREFERENCE BALLOTS.
NOTICE HOW THE BALLOTS RANK THE CHOICES
FROM FIRST THROUGH THIRD.
WE'RE FIRST ASKED HOW MANY STUDENTS VOTED.
WELL, NOTICE HOW WE HAVE THREE ROWS OF 7
SO WE CAN SAY THAT 21 STUDENTS VOTED.
AND THEN FROM THESE BALLOTS WE CAN CREATE A PREFERENCE TABLE
WHERE WE'LL LIST THE CHOICES FROM FIRST THROUGH THIRD
THEN THE NUMBERS OF VOTERS IN THE FIRST ROW
THAT VOTED FOR EACH ORDER.
AND SINCE THERE ARE THREE CHOICES,
THERE ARE A TOTAL OF THREE FACTORIAL, OR SIX,
POSSIBLE ORDERS OF PREFERENCE.
WE CAN ALSO USE ACCOUNTING PRINCIPLE
AND SAY THERE ARE THREE OPTIONS FOR THE FIRST CHOICE,
TWO OPTIONS FOR THE SECOND CHOICE,
AND ONE OPTION FOR THE THIRD CHOICE
GIVING US A TOTAL OF SIX DIFFERENT ORDERS
FOR THE CHOICES.
LET'S BEGIN BY LISTING THE SIX POSSIBLE ORDERS.
SO IF WE START WITH "A", B, C.
LETS NOW LIST "A", C, B.
NOW LET'S START WITH B, SO WE COULD HAVE B, "A", C
AND THEN B, C, "A".
AND NOW WE'LL START WITH C.
WE COULD HAVE C, "A", B AND THEN C, B, "A".
AND NOW WE'LL COUNT THE NUMBER OF VOTES
FOR EACH PARTICULAR ORDER.
LET'S BEGIN BY LOOKING FOR THE ORDER OF "A", B, C.
THERE'S ONE, TWO, THREE, FOUR, AND FIVE.
NOW WE'LL LOOK FOR "A", C, B.
THERE'S ONE, TWO, THREE,
SO THERE'S THREE VOTERS FOR THE ORDER "A", C, B.
NOW WE'LL LOOK FOR B, "A", C.
THERE'S ONE, TWO, IT LOOKS LIKE THERE'S ONLY TWO.
AND NOW WE'LL LOOK FOR B, C, "A".
THERE'S ONE, TWO, THREE, AND FOUR.
NOW WE'LL LOOK FOR C, "A", B.
THERE'S ONE, TWO, THREE, SO TOTAL OF THREE,
WHICH LEAVES ONE, TWO, THREE, FOUR THAT VOTED FOR C, B, "A".
NOW TO MAKE SURE WE DIDN'T MISS ANY,
LET'S GO AHEAD AND FIND THIS SUM TO MAKE SURE THE SUM IS 21.
SO WE HAVE 5 + 3 + 2 = 10 + 4 + 3 + 4 = 21.
SO AGAIN, THESE ARE THE PREFERENCE BALLOTS
AND THIS IS THE PREFERENCE TABLE.
SO BASED UPON THE VOTING METHOD,
WE WOULD NORMALLY USE THIS PREFERENCE TABLE HERE
TO GATHER THE INFORMATION NEEDED TO SELECT THE WINNER.
I HOPE YOU FOUND THIS INTRODUCTION HELPFUL.