Voting Theory: Approval Voting


– WELCOME TO A LESSON
ON APPROVAL VOTING. IN THIS LESSON
WE WILL DEFINE APPROVAL VOTING, AND ALSO DETERMINE AN ELECTION
WINNER USING APPROVAL VOTING. NORMALLY WE THINK OF DEMOCRATIC
VOTING AS ONE PERSON, ONE VOTE. HOWEVER, SINCE NO VOTING SYSTEM
IS PERFECT, VARIOUS VOTING METHODS USE
DIFFERENT TECHNIQUES TO TRY TO FAIRLY SELECT
A WINNER. MOST VOTING SYSTEMS REQUIRE
RANKING OF CANDIDATES, BUT NOT ALL VOTING METHODS. FOR EXAMPLE, APPROVAL VOTING
DOES NOT ASK VOTERS TO RANK THE CANDIDATES. VOTERS APPROVE OR DISAPPROVE
OF EACH CANDIDATE. THE CANDIDATE WITH THE MOST
APPROVAL IS THE WINNER. LET’S BEGIN BY LOOKING
AT AN EXAMPLE. THE TABLE ABOVE SUMMARIZES
THE RESULTS OF AN APPROVAL VOTE AMONG CANDIDATES
“A”, B, C, AND D. EACH COLUMN SHOWS THE NUMBER
OF PEOPLE WITH A CERTAIN APPROVAL VOTE. APPROVALS ARE MARKED WITH AN X. WE WANT TO FIND THE WINNER UNDER
THE APPROVAL VOTING METHOD. SO IF WE START WITH CANDIDATE
“A”, NOTICE HOW CANDIDATE “A” WAS APPROVED BY 24 + 21 + 25,
OR 70 VOTERS. LOOKING AT CANDIDATE B, CANDIDATE B WAS APPROVED BY
24 + 23 + 22, OR 69 VOTERS, CANDIDATE C WAS APPROVED
BY 24 + 21 + 22, OR 67 VOTERS, AND FINALLY, CANDIDATE D
WAS APPROVED BY 24 + 22 + 25, OR 71 VOTERS. AND BECAUSE CANDIDATE D RECEIVED
THE MOST APPROVAL, CANDIDATE D WINS. LET’S TAKE A LOOK
AT A SECOND EXAMPLE. CONSIDER THREE CANDIDATES
RUNNING FOR MAYOR. LET’S ASSUME CANDIDATE “A” AND CANDIDATE B HAVE SIMILAR
POLITICAL VIEWS. 35% APPROVE ONLY OF C, 32% APPROVE “A” FIRST
AND B SECOND, 32% APPROVE B FIRST AND “A”
SECOND, AND 1% APPROVE ONLY “A”. SO NOTICE CANDIDATE “A”
IS APPROVED BY THIS 32%, THIS 32%, AND THIS 1%. SO 32% + 32% + 1%=65% APPROVAL
RATING. CANDIDATE B WOULD BE APPROVED
BY THIS 32% AND THIS 32%. SO 32% + 32%=64% APPROVAL
RATING. AND THEN CANDIDATE C
IS APPROVED BY 35%. AND THEREFORE, UNDER THE
APPROVAL VOTING METHOD, NOTICE HOW CANDIDATE “A”
WOULD WIN WITH 65% APPROVAL. NOW, LET’S TALK ABOUT WHAT’S
WRONG WITH THE APPROVAL VOTING METHOD. SOMETIMES APPROVAL VOTING
TENDS TO ELECT THE LEAST DISLIKED CANDIDATE. TO ILLUSTRATE THIS,
LET’S LOOK AT THIS EXAMPLE HERE. USING THIS PREFERENCE SCHEDULE, IF WE ASSUME THE VOTERS FIRST TWO CHOICES ARE CONSIDERED
APPROVED, LET’S FIND THE WINNER USING
THE APPROVAL VOTING METHOD. SO AGAIN, WE’RE ONLY FOCUSING
ON THESE FIRST TWO CHOICES. NOTICE THAT CANDIDATE “A” IS
ONLY APPROVED HERE BY 39 VOTERS. IF WE LOOK AT CANDIDATE B, AGAIN, WE’RE COUNTING APPROVAL
AS THE FIRST OR SECOND CHOICE, AND THEREFORE CANDIDATE B
IS APPROVED BY 39 + 8 + 3, OR ALL OF THE VOTERS. AND THEREFORE CANDIDATE B
IS APPROVED BY 50 VOTERS, AGAIN, OR ALL OF THE VOTERS. IF WE LOOK AT CANDIDATE C, NOTICE HOW CANDIDATE C IS
APPROVED BY 8 + 3, OR 11 VOTERS. SO UNDER APPROVAL VOTING
CANDIDATE B WOULD WIN, WHICH MAY NOT SEEM RIGHT. BECAUSE NOTICE HOW ONLY 8 VOTERS
SELECTED B AS THEIR FIRST CHOICE, WHILE 39 VOTERS SELECTED “A”
AS THEIR FIRST CHOICE. SO “A” ACTUALLY HAS THE MAJORITY
OF THE FIRST CHOICE VOTES, AND THEREFORE
WOULD HAVE A MAJORITY WIN. BUT UNDER THE APPROVAL VOTING
METHOD, CANDIDATE B WINS. SO YOU CAN SEE WHY SOMETIMES
THE APPROVAL VOTING METHOD SELECTS THE LEAST DISLIKED
CANDIDATE AS THE WINNER. NOBODY REALLY DISLIKES B, BUT ONLY 8 VOTERS ACTUALLY
REALLY WANT B TO WIN. APPROVAL VOTING CAN ALSO
BE SUSCEPTIBLE TO STRATEGIC OR INSINCERE
VOTING, WHERE INSINCERE VOTING
IS WHEN A VOTER DOES NOT VOTE THEIR TRUE
PREFERENCE, TO TRY TO INCREASE THE CHANCE OF A PARTICULAR CANDIDATE
OF WINNING. LET’S GO BACK AND TAKE A LOOK AT
ONE OF THE PREVIOUS EXAMPLES. AS WE SAW EARLIER USING APPROVAL
VOTING, D WINS WITH THE MOST APPROVAL
VOTES. HOWEVER, IF THREE VOTERS
WHO APPROVE OF “A” AND D, OR THREE VOTERS FROM THIS COLUMN
HERE, REMOVE THEIR APPROVAL FOR D, LET’S SEE HOW THIS WOULD AFFECT
THE RESULTS OF THIS ELECTION. SO AGAIN, THREE OF THE VOTERS
HERE, THAT APPROVE OF BOTH “A” AND D, ARE GOING TO REMOVE THEIR
APPROVAL FOR D, AND ONLY APPROVE CANDIDATE “A”. WHICH WILL LEAVE 22 VOTES THAT
APPROVE OF “A” AND D, AND 3 VOTES THAT APPROVE
FOR ONLY “A”. NOTICE HOW THIS SUM HERE
IS STILL 25 FROM THE PREVIOUS PREFERENCE
SCHEDULE. SO NOW USING THIS TABLE TO FIND
THE WINNER, NOTICE HOW CANDIDATE “A”
STILL RECEIVES 24 + 21 + 25, OR 70 APPROVAL VOTES. CANDIDATE B STILL HAS 24 + 23 +
22, OR 69 APPROVAL VOTES, CANDIDATE C STILL HAS
24 + 21 + 22, OR 67 APPROVAL VOTES, BUT BECAUSE 3 VOTERS REMOVED
THEIR APPROVAL FOR CANDIDATE D, NOTICE NOW CANDIDATE D, THE PREVIOUS WINNER,
HAS 24 + 22 + 22, OR ONLY 68 APPROVAL VOTES. SO BECAUSE OF THE INSINCERE
VOTING, NOTICE HOW CANDIDATE D
IS NO LONGER THE WINNER. NOW CANDIDATE “A” IS THE WINNER
UNDER APPROVAL VOTING. SO AS YOU CAN SEE FROM THIS
EXAMPLE, IN SOME CASES APPROVAL VOTING
CAN BE SUSCEPTIBLE TO STRATEGIC
OR INSINCERE VOTING. I HOPE YOU FOUND THIS HELPFUL.  

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Comments

  1. Your example doesn't actually demonstrate a majority criterion violation. The majority criterion applies when a method fails to select a winner that has greater than 50% of first-choice votes. The sample provided showed a candidate with a mere 39% plurality of first-choice votes. As for the outcome, 61% preferred B over A. And Approval Voting chose B over A. It's hard to see this outcome as "what is wrong with Approval Voting."

    Your videos have a clear visual, by the way. They look nice.

  2. My gratitude for the time and effort put into your videos, they have significantly aided in my learning of voting theory 🙂

  3. Thanks for talking about this. Most people i know aren't even aware there are other ways to vote. They don't understand there are pro's and con's. We need to continue talking about voting systems and educating the pubic that this discussion is going on. I hope soon we settle on a new voting system int the US that satisfies our highly suspicious public.

  4. I'm glad you brought up the negatives of this system. I really don't see how "approval voting" is susceptible to strategic voting. As I understand strategic voting, it is to artificially adjust your ballot to influence an election in a different way. IRV or alternative voting is perhaps most susceptible to this, because there are occasions in IRV where putting your favourite candidate 2nd will actually cause him to win, and campaigning for your party to get extra 1st votes can cause the candidate to paradoxically lose. This is an artificial scenario that also affects plurality. But with approval voting I don't see how three people removing support for D artificially influence the election. It causes D to lose plane and simple, which was an expected outcome of anyone withdrawing support, now if removing 3 votes from D somehow caused D to win, then that seems artificial. In Plurality you can trick a win in your election by drawing voters to a third party causing a lesser favoured candidate to win, this I think would be classified as strategic voting (or strategic campaigning) in Approval voting if r were to "artificially" introduce a third party candidate, it wouldn't necessarily draw support away from the main candidate, unless they were insincere. I do agree with you about insincerity, but again looking at the other forms of voting I think insincerity would affect the election about the same in each form, but we can't necessarily judge mig election based on intentions, or we might introduce a 3 month later "buyers remorse" election to give voters the opportunity to "undo" their choice, lol.

  5. First of all, thanks a lot for putting the effort to make this series.
    However, I think you have misunderstood approval voting. There are no rankings in approval voting, you just have to mark the candidates that you approve (in no order). And the issues you brought up about this system are also not correct:
    1. Keeping in mind that there are no orders in approval voting, in example 3, we see that all voters have approved all the candidates! I guess you were aware of that and that's why you only looked at the first two rows. and Again if we remove the notion of ranking, B has the majority of approvals and is fairly the winner.
    2. In the last example, what you brought up is not strategic voting, because those 3 voters had the chance to approve both A and D but chose to no approve D. Strategic voting takes place when you don't have the opportunity to vote equally for two or more different candidates, which is not the case with approval voting.
    Again thanks a lot for these videos, really helpful.

  6. Nice video!

    I just don't get what you're trying to show with the last example. First, D was the winner with 71 approval votes and A was second with 70. Then 3 voters remove only their approval for D. So A wins. Why is the drawback of approval voting in this case?

  7. Where did the 24, 21, etc. voter numbers come from? This almost looks like Part 2 of the tutorial. Where is Part 1 then?

  8. It doesn't make sense to include ranked choice preferences @3:04 as an example. All of the candidates received the same amount of APPROVALS in that example. LOL

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