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Pie charts illustrating the difference between a mere plurality (where the green/bottom area is less than 50% of the total area) and a majority (where the green/bottom area is greater than 50% of the total area of the pie chart).
Poll most votes, but less than half overall
A plurality vote (in Canada and the United States) or relative majority (in the United Kingdom and Commonwealth except Canada)[1] describes the circumstance when a candidate or proposition polls more votes than any other but does not receive more than half of all votes cast.[2]
For example, if from 100 votes that were cast, 45 were for Candidate A, 30 were for Candidate B and 25 were for Candidate C, then Candidate A received a plurality of votes but not a majority. In some votes, the winning candidate or proposition may have only a plurality, depending on the rules of the organization holding the vote.[3]
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Voting Theory: Plurality Method and Condorcet Criterion
Plurality voting
Survey: Plurality Method of Voting
Transcription
- WELCOME TO A LESSON ON THE
PLURALITY VOTING METHOD.
IN THIS LESSON WE'LL DEFINE
THE PLURALITY VOTING METHOD,
DETERMINE WINNERS OF ELECTIONS
USING THE PLURALITY METHOD,
DEFINE THE CONDORCET
FAIRNESS CRITERION
AND ALSO FIND
A CONDORCET WINNER.
THE PLURALITY VOTING METHOD
IS PROBABLY THE METHOD
YOU'RE MOST FAMILIAR WITH,
WHERE THE CHOICE
WITH THE MOST FIRST PREFERENCE
VOTES IS DECLARED THE WINNER.
TIES ARE POSSIBLE AND WOULD HAVE
TO BE SETTLED THROUGH
SOME SORT OF RUN OFF.
THIS METHOD IS SOMETIMES
MISTAKENLY
CALLED THE MAJORITY METHOD,
OR MAJORITY RULES,
BUT IT IS NOT NECESSARY
FOR A CHOICE
TO HAVE GAINED A MAJORITY
OF VOTES TO WIN,
WHERE A MAJORITY IS OVER 50%
OF THE VOTES.
SO IT IS POSSIBLE FOR A WINNER
TO HAVE A PLURALITY
WITHOUT HAVING A MAJORITY.
LET'S TAKE A LOOK AT A COUPLE
OF EXAMPLES.
THE SURVEY ASKED TO RANK
WHICH WEST COAST STATES
PEOPLE PREFER TO LIVE.
THE RESULTS ARE BELOW.
USE THE PLURALITY METHOD
TO SELECT THE WINNER.
WE'RE LOOKING AT THE PREFERENCE
TABLE HERE,
C = CALIFORNIA, O = OREGON,
AND W = WASHINGTON.
NOTICE THAT WE FIND THE SUM
OF THESE VALUES HERE,
WE CAN DETERMINE THE TOTAL VOTES
IS 300.
TO DETERMINE THE PLURALITY
WINNER WE'LL DETERMINE
HOW MANY FIRST CHOICE VOTES
CALIFORNIA RECEIVED,
THEN HOW MANY FIRST CHOICE VOTES
OREGON RECEIVED,
AND THEN HOW MANY FIRST CHOICE
VOTES WASHINGTON RECEIVED.
WELL, CALIFORNIA RECEIVED
75 + 94 FIRST CHOICE VOTES,
WHERE 75 + 94 = 169.
OREGON RECEIVED 51 + 12
FIRST CHOICE VOTES,
WHICH IS 63 FIRST CHOICE VOTES.
AND FINALLY,
WASHINGTON RECEIVED
43 + 25 OR 68
FIRST CHOICE VOTES.
SO IN THIS CASE,
NOTICE THAT CALIFORNIA RECEIVED
THE MOST FIRST CHOICE VOTES.
AND THEREFORE, CALIFORNIA
IS THE PLURALITY WINNER.
NOTICE HOW IN THIS CASE
CALIFORNIA RECEIVED 169 FIRST
CHOICE VOTES OUT OF 300,
WHICH IS APPROXIMATELY 56.3%,
WHICH IS MORE THAN 50%.
AND THEREFORE, CALIFORNIA WOULD
ALSO BE THE MAJORITY WINNER.
REMEMBER, A WINNER DOES NOT HAVE
TO BE A MAJORITY WINNER
TO BE THE PLURALITY WINNER.
LET'S TAKE A LOOK AT A SECOND
EXAMPLE,
WHERE HERE A SMALL GROUP
OF COLLEGE STUDENTS
RANK THE BEST DESTINATION
FOR SPRING BREAK
WHERE S = SAN DIEGO, L = LAKE
HAVASU, AND R = ROCKY POINT.
AGAIN, BY FINDING THE SUM
OF THESE VALUES
HERE WE CAN DETERMINE
THERE ARE A TOTAL OF 17 VOTES.
NOTICE, SAN DIEGO RECEIVED
A TOTAL OF 4 + 4, OR 8,
FIRST PLACE VOTES.
LAKE HAVASU RECEIVED A TOTAL
OF TWO FIRST PLACE VOTES.
AND ROCKY POINT RECEIVED A TOTAL
OF 5 + 2, OR 7,
FIRST PLACE VOTES.
AND SINCE SAN DIEGO RECEIVED
THE MOST FIRST CHOICE VOTES,
OR FIRST PLACE VOTES,
SAN DIEGO IS THE WINNER.
NOTICE IN THIS CASE, SAN DIEGO
RECEIVED A TOTAL
OF 8 FIRST PLACE VOTES OUT
OF 17,
WHICH IS APPROXIMATELY 47.1%.
SO NOTICE HOW HERE EVEN THOUGH
SAN DIEGO IS NOT THE MAJORITY
WINNER,
IT STILL IS THE WINNER USING
THE PLURALITY METHOD.
THIS LEADS US TO A DISCUSSION
ABOUT WHAT CAN BE WRONG ABOUT
THE PLURALITY VOTING METHOD.
IF THERE ARE THREE OR MORE
CHOICES IT IS POSSIBLE
THAT A CHOICE COULD LOSE,
BUT WHEN COMPARED IN A ONE
TO ONE COMPARISON
IT COULD BE PREFERRED
OVER THE PLURALITY WINNER.
AND THIS VIOLATES WHAT'S CALLED
A FAIRNESS CRITERION
WHERE THE FAIRNESS CRITERIA
ARE STATEMENTS
THAT SEEM LIKE THEY SHOULD BE
TRUE IN A FAIR ELECTION.
THE FIRST FAIRNESS CRITERION
WE'LL CONSIDER
IS CALLED THE CONDORCET
CRITERION
WHERE IF THERE IS A CHOICE,
IT IS PREFERRED IN EVERY
ONE TO ONE COMPARISON
WITH THE OTHER CHOICES.
THAT CHOICE SHOULD BE THE WINNER
AND WE CALL THIS WINNER
THE CONDORCET WINNER
OR CONDORCET CANDIDATE.
LET'S LOOK AT TWO MORE EXAMPLES.
THIS IS THE EXAMPLE
THAT WE SAW BEFORE
WHERE WE KNOW THE PLURALITY
WINNER WAS SAN DIEGO
WITH A TOTAL OF 8 VOTES,
BUT NOW WE WANT TO FIND
THE CONDORCET WINNER.
SO TO FIND THE CONDORCET WINNER
WE'LL DO A ONE TO ONE COMPARISON
WITH OUR THREE OPTIONS.
SO WE'LL COMPARE SAN DIEGO
VERSUS LAKE HAVASU.
WE'LL COMPARE SAN DIEGO VERSUS
ROCKY POINT.
AND WE'LL COMPARE LAKE HAVASU
VERSUS ROCKY POINT.
TO DO THE ONE TO ONE COMPARISON
WITH SAN DIEGO AND LAKE HAVASU
WE WOULD IGNORE ROCKY POINT.
SO WE'LL IGNORE ROCKY POINT
HERE, HERE, HERE, HERE,
AND HERE.
REMEMBER, WE HAVE A TOTAL OF 17
VOTES.
SO OF THE 17, SAN DIEGO IS
PREFERRED OVER LAKE HAVASU
4 + 4 + 5 TIMES, SO THAT WOULD
BE 8 + 5 = 13.
SO SAN DIEGO WINS OVER LAKE
HAVASU 13 TO 4.
NOW WE'LL COMPARE SAN DIEGO
TO ROCKY POINT
SO WE'LL IGNORE LAKE HAVASU.
SO NOTICE SAN DIEGO
BEATS ROCKY POINT HERE AND HERE,
BUT NOTICE HOW ROCKY POINT
WINS HERE, HERE, AND HERE.
AND THEREFORE, FOR SAN DIEGO
VERSUS ROCKY POINT THE VOTE
IS 8 TO 9.
NOTICE IN THIS ONE TO ONE
COMPARISON ROCKY POINT WINS.
AND THEN FINALLY,
WE WANT TO CONSIDER
LAKE HAVASU VERSUS ROCKY POINT.
SO NOW WE'LL IGNORE SAN DIEGO.
SO LAKE HAVASU'S PREFERRED OVER
ROCKY POINT HERE AND HERE
AND THEREFORE, LAKE HAVASU
VERSUS ROCKY POINT
WOULD BE 6 TO 11.
NOW, LOOKING AT THESE ONE TO ONE
COMPARISONS
NOTICE HOW ROCKY POINT BEATS
LAKE HAVASU HERE
AND ROCKY POINT ALSO BEATS SAN
DIEGO HERE.
THEREFORE ROCKY POINT ALWAYS
WINS IN A ONE TO ONE COMPARISON.
AND THEREFORE, ROCKY POINT
IS THE CONDORCET WINNER.
SO EVEN THOUGH SAN DIEGO
WAS THE PLURALITY WINNER,
UNDER THE CONDORCET
FAIRNESS CRITERION
ROCKY POINT
SHOULD BE THE WINNER.
LET'S TAKE A LOOK
AT ONE MORE EXAMPLE.
WE WANT TO FIND THE CONDORCET
WINNER, OR CONDORCET CANDIDATE,
IF THERE IS ONE.
SO THE CANDIDATES
ARE "A," B, AND C
SO WE'LL DO A ONE TO ONE
COMPARISON.
WE'LL HAVE "A" VERSUS B, "A"
VERSUS C, AND B VERSUS C.
NOTICE THE PLURALITY WINNER
WOULD BE C WITH A TOTAL OF 16
FIRST CHOICE VOTES.
SO FOR "A" VERSUS B
WE'LL IGNORE C.
SO "A" WOULD WIN OVER B
HERE AND HERE.
SO "A" VERSUS B
WOULD BE 31 TO 10.
NEXT, FOR "A" VERSUS C
WE'LL IGNORE B.
NOTICE, "A" WINS ONLY HERE SO
"A" VERSUS C WOULD BE 15 TO 26.
AND THEN FOR B VERSUS C
WE'LL IGNORE "A".
NOTICE HOW B WINS HERE
AND C WINS HERE AND HERE.
SO B VERSUS C WOULD BE 10 TO 31.
SO AGAIN, LOOKING AT THESE TWO
HERE NOTICE C WINS OVER B
AND HERE C ALSO WINS OVER "A"
AND THEREFORE CANDIDATE C
IS THE CONDORCET WINNER,
BUT NOTICE HOW C IS ALSO
THE PLURALITY WINNER HERE.
I HOPE YOU FOUND THIS HELPFUL.
In international institutional law, a "simple majority" (also a "majority") vote is more than half of the votes cast (disregarding abstentions) among alternatives; a "qualified majority" (also a "supermajority") is a number of votes above a specified percentage (e.g. two-thirds); a "relative majority" (also a "plurality") is the number of votes obtained that is greater than any other option; and an "absolute majority" is a number of votes "greater than the number of votes that possibly can be obtained at the same time for any other solution",[note 1] when voting for multiple alternatives at a time.[4][note 2]
Henry Watson Fowler suggested that the American terms "plurality" and "majority" offer single-word alternatives for the corresponding two-word terms in British English, "relative majority" and "absolute majority", and that in British English "majority" is sometimes understood to mean "receiving the most votes" and can therefore be confused with "plurality".[1][note 3]William Poundstone observes that systems which allow choosing by a plurality of votes are more vulnerable to the spoiler effect—where two or more similar choices each draw fewer votes than a dissimilar choice that would have lost to any individual similar choice on its own—than systems which require a majority.[5]
^For example, 50 voters elect six office holders from a field of 11 candidates, thereby casting 300 votes. The largest absolute majority in this scenario would be 50 voters casting all their ballots for the same six candidates, which at 300 votes would be substantially higher than the simple majority of 151 votes—a result that no individual candidate can achieve, since the most votes any one can receive is 50. With the smallest absolute majority in this scenario, the six winners would receive 28 votes each, totaling 168, and the runners-up would receive either 27 or 26 votes each.
^An "absolute majority" can also mean a "majority of the entire membership", a voting basis that requires that more than half of all the members of a body (including those absent and those present but not voting) to vote in favour of a proposition in order for it to be passed.
^"With three-cornered contests as common as they now are, we may have occasion to find a convenient single word for what we used to call an absolute majority... In America the word majority itself has that meaning while a poll greater than that of any other candidate, but less than half the votes cast is called a plurality. It might be useful to borrow this distinction..." —Henry Watson Fowler
^"plurality". Merriam-Webster Dictionary. Retrieved 2015-12-29. a number of votes that is more than the number of votes for any other candidate or party but that is not more than half of the total number of votes
^Robert, Henry M. III; Honemann, Daniel H.; Balch, Thomas J. (2011). Robert's Rules of Order Newly Revised (11 ed.). Da Capo Press. pp. 404–405. ISBN978-0-306-82021-2.
This page was last edited on 18 June 2022, at 01:12