– WELCOME TO A LESSON ON THE

BORDA COUNT METHOD OF VOTING. IN THIS LESSON WE’LL DEFINE

THE BORDA COUNT METHOD, THEN DETERMINE WINNERS

OF ELECTIONS USING THE BORDA COUNT METHOD. BORDA COUNT IS A VOTING METHOD

NAMED AFTER JEAN CHARLES DE BORDA, WHO

DEVELOPED THE SYSTEM IN 1770. IN THIS METHOD POINTS ARE

ASSIGNED TO CANDIDATES BASED UPON THEIR RANKING,

WHERE CANDIDATES RECEIVE 1 POINT FOR LAST, 2 POINTS FOR SECOND

TO THE LAST, AND SO ON. SO FOR EXAMPLE, IF THERE WERE

FOUR CHOICES, FIRST CHOICE VOTES

WOULD BE WORTH 4 POINTS, SECOND CHOICE VOTES

WORTH 3 POINTS, THIRD CHOICE VOTES

WORTH 2 POINTS, AND FINALLY FOURTH CHOICE VOTES

WOULD BE WORTH 1 POINT. THEN THE POINTS OF THE BALLOTS

ARE TOTALED, AND THE CANDIDATE

WITH THE LARGEST POINT TOTAL IS THE WINNER. LET’S LOOK AT AN EXAMPLE. HERE’S THE PREFERENCE TABLE

FOR A CAMPING CLUB THAT IS DECIDING WHERE TO GO ON

THEIR NEXT TRIP, WHERE “A” REPRESENTS THE ARCHES,

G REPRESENTS THE GRAND CANYON, Y REPRESENTS YOSEMITE,

AND Z=ZION. NOTICE HOW WE HAVE FOUR CHOICES

HERE, AND THEREFORE FIRST PLACE, OR FIRST CHOICE,

WOULD RECEIVE 4 POINTS, SECOND PLACE WOULD RECEIVE 3

POINTS, THIRD PLACE 2 POINTS, AND FOURTH PLACE 1 POINT. WHICH MEANS EVERY VOTE

IN THIS FIRST ROW WOULD BE WORTH 4 POINTS, EVERY VOTE IN THE SECOND CHOICE

ROW IS WORTH 3 POINTS, AND SO ON. SO TO FIND THE TOTAL POINTS, WE’LL SET THIS UP USING A LARGER

TABLE, AS WE SEE HERE. AGAIN, ALL OF THESE FIRST PLACE

VOTES HERE ARE WORTH 4 POINTS EACH FOR EACH CANDIDATE,

OR IN THIS CASE EACH LOCATION. SO LOOKING AT THIS FIRST ROW

FOR A MOMENT, NOTICE HOW 12 VOTERS VOTED

YOSEMITE FIRST. SO YOSEMITE RECEIVES 12 x 4

OR 48 POINTS. LOOKING AT THE SECOND COLUMN

HERE, NOTICE HOW FIVE VOTERS VOTED

THE GRAND CANYON FIRST, AND THEREFORE THE GRAND CANYON

RECEIVED 5 x 4 OR 20 POINTS. THE SECOND CHOICE ROW HERE IS

WORTH 3 POINTS FOR EVERY VOTE. THE THIRD CHOICE ROW

IS WORTH 2 POINTS, AND THE FOURTH CHOICE ROW

IS WORTH 1 POINT. SO YOU MAY WANT TO PAUSE

THE VIDEO NOW JUST TO VERIFY

THAT I DID CALCULATE THESE POINTS CORRECTLY. LET’S GO AHEAD AND FIND THE

TOTAL FOR EACH CHOICE. LET’S FIRST FIND THE POINTS

FOR THE ARCHES, SO WE’LL LOOK FOR ALL THE “A”s. SO IN THE FIRST ROW WE HAVE

AN “A” HERE AND HERE, THE SECOND ROW WE HAVE AN “A”

HERE, THE THIRD ROW WE HAVE AN “A”

HERE AND HERE, AND THE FOURTH ROW WE HAVE AN

“A” HERE. SO “A” RECEIVES 36 + 24 + 12 +

10 + 20 + 12 POINTS, OR 114 POINTS. NEXT WE’LL FIND THE POINTS FOR

THE GRAND CANYON, SO WE’LL FIND ALL OF THE Gs. FIRST ROW WE HAVE A G HERE,

SECOND ROW WE HAVE A G HERE, THIRD ROW WE HAVE A G HERE,

HERE, AND HERE, AND THE FOURTH ROW WE HAVE A G

HERE. SO THE GRAND CANYON RECEIVES 20 + 30 + 24 + 8 + 18 + 6,

OR 106 POINTS. NEXT, FOR YOSEMITE WE HAVE A Y

HERE IN THE FIRST ROW, SECOND ROW WE HAVE A Y HERE AND

HERE, THIRD ROW WE HAVE A Y HERE, AND FOURTH ROW WE HAVE A Y

HERE AND HERE. SO YOSEMITE RECEIVES 48 + 15 +

27 + 12 + 4 + 10, OR 116 POINTS. AND THEN FINALLY ZION IS HERE

IN THE FIRST ROW AND HERE, SECOND ROW WE HAVE A Z

HERE AND HERE. THERE ARE NO Zs IN THE THIRD

ROW, BUT THE FOURTH ROW WE HAVE A Z

HERE AND HERE. SO ZION RECEIVES 16 + 40 + 36 +

18 + 5 + 9 POINTS, WHICH IS 124 POINTS. AND SINCE ZION

HAS THE MOST POINTS, UNDER THE BORDA COUNT METHOD

ZION IS THE WINNER. NOW LET’S TALK ABOUT THE FLAW, OR WHAT’S WRONG WITH THE BORDA

COUNT METHOD. ONE POTENTIAL FLAW OF BORDA

COUNT IS A CANDIDATE COULD RECEIVE A MAJORITY OF THE FIRST CHOICE

VOTES, AND STILL LOSE THE ELECTION. TO ILLUSTRATE THIS, LET’S TAKE

A LOOK AT ANOTHER EXAMPLE. LET’S CONSIDER THE FOLLOWING

PREFERENCE SCHEDULE. FIRST, NOTICE IN THIS ELECTION

THERE ARE A TOTAL OF 20 VOTES, AND NOTICE HOW CANDIDATE “A”

RECEIVES 9 + 2, OR 11 OF THE 20 VOTES,

WHICH WOULD BE 55%, OR A MAJORITY WIN. NOTICE CANDIDATE B RECEIVES

8 FIRST CHOICE VOTES, OR 40% OF THE FIRST CHOICE

VOTES, AND CANDIDATE C ONLY RECEIVES 1,

OR 5% OF THE FIRST CHOICE VOTES. SO “A” WOULD WIN BY MAJORITY. BUT NOW LET’S FIND THE WINNER

OF THIS ELECTION BY USING THE BORDA COUNT METHOD. FIRST, SINCE THERE ARE THREE

CANDIDATES, FIRST CHOICE VOTES

ARE WORTH 3 POINTS, SECOND CHOICE VOTES

ARE WORTH 2 POINTS, AND THIRD CHOICE VOTES

ARE WORTH 1 POINT. I DIDN’T SHOW AS MUCH WORK HERE, BUT NOTICE HOW LOOKING AT THIS

FIRST COLUMN 9 VOTERS VOTED “A” FIRST, SO “A” RECEIVES 9 x 3,

OR 27 POINTS. IN THIS COLUMN 2 VOTERS VOTED

“A” FIRST, SO “A” RECEIVES ANOTHER 2 x 3,

OR 6 POINTS. HERE B IS VOTED FIRST BY 8

VOTERS, SO B RECEIVES 8 x 3,

OR 24 POINTS, AND SO ON. EVERY VOTE IN THE SECOND ROW

IS WORTH 2 POINTS, SO B RECEIVES 18 POINTS HERE,

SINCE 9 x 2=18, AND SO ON. SO NOW LET’S FIND THE TOTAL

NUMBER OF POINTS FOR EACH CANDIDATE. “A” RECEIVES 27 + 6 + 8 + 1

OR 42 POINTS. REMEMBER “A” WAS THE MAJORITY

WINNER. BUT NOW IF WE TAKE A LOOK

AT CANDIDATE B, B RECEIVES 24 + 18 + 2 + 2, WHICH NOTICE HOW IT COMES

TO 46 POINTS. NOTICE HOW CANDIDATE B

HAS MORE POINTS THAN “A”, EVEN THOUGH “A” IS THE MAJORITY

WINNER. AND THEN FINALLY CANDIDATE C

RECEIVES 3 + 4 + 16 + 9, OR 32 POINTS. SO NOTICE HOW, AGAIN,

B WOULD WIN USING BORDA COUNT, WHICH BRINGS UP ANOTHER FAIRNESS

CRITERION, THE MAJORITY CRITERION. IF A CHOICE HAS A MAJORITY

OF FIRST PLACE VOTES, THAT CHOICE

SHOULD BE THE WINNER. BORDA COUNT IS SOMETIMES

DESCRIBED AS A CONSENSUS

BASED VOTING SYSTEM, SINCE IT CAN SOMETIMES CHOOSE

A MORE BROADLY ACCEPTABLE OPTION OVER ONE WITH MAJORITY SUPPORT. THIS IS A DIFFERENT APPROACH

THAN PLURALITY AND INSTANT RUNOFF VOTING THAT

FOCUS ON FIRST CHOICE VOTES. BORDA COUNT CONSIDERS

VOTERS ENTIRE RANKING TO DETERMINE THE OUTCOME. BECAUSE OF THIS CONSENSUS

BEHAVIOR, BORDA COUNT, OR SOME VARIATION OF IT, IS COMMONLY USED IN SELECTING

SPORTS AWARDS. VARIATIONS ARE USED TO DETERMINE THE MOST VALUABLE PLAYER

IN BASEBALL, TO RANK TEAMS IN THE NCAA, AND ALSO TO AWARD THE HEISMAN

TROPHY. I HOPE YOU FOUND THIS HELPFUL.

If I pass this test and Graduate college, It will be thanks to you.

Is there, by chance, a method of the Borda count that includes a "0" ranking for choices that voters just cannot abide? I think that would be an excellent addition.

Like in this video example – What if I reeeally wanted to go to the Yosemite so…

I rank Yosemite first, giving it 4 points.

I think the Grand Canyon would also be cool so I give that my 3 points.

I don't know anything about Arches, really, so since it's a 3rd choice, would need to rank it with 2 pts. (rather than skipping a rank to give it a 1, I would think. (Now that I think of it, I didn't consider how to deal with potential "skips" and that may be an issue with voting. Will have to think about that one.)

But I can't stand the idea of going to Zion so I give it a "0" in order to purposefully denote my stance against the idea and lower the point count for the choice.

Is there a method that considers that?

Further, can one make a "0" rank or "non-vote" for more than one option? Say I want to vote "0" for Zion

andArches…That being said, would it be better to offer a ranking system of top-down, bottom-up to distinguish the ones you like best to least and also the ones you really don't like most to least? Would that require a "null" voting rank to put a buffer between the two options "preferred" and "not-preferred". Maybe it should be a 10 pt. down through 1 pt. ranking (unless there are more voting option; perhaps double the count or the votes?)

Or would a negative point ranking system work for the "non-preferred" candidates? If so, would (or could) those count against the other candidates overall positive votes?

Not sure about that last one. At least with governmental elections, anyway. Sounds like it could be used as a weapon, so to speak. It's already convoluted. And I definitely fear the potential for fraud & tampering.

So, perhaps it would be best to stick to zeroes. But that means that the entire candidate list from all parties (including 3rd parties, etc.) would, of course, have to be ranked.

Sorry… Got lost in thinking "out loud" so to speak. : )

Thank you SO much for making his video!!!! I totally understand this topic now! Right on time for my test thursday. Thank you so much!

Thanks so much for making this video!

thanks so much for the video, helped a lot. Where can I download the power-point?

What happens in the case of a tie?

You outsmarted my teacher appreciate it!!