Sequential proportional approval voting

Transcription

- 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.