- WELCOME TO A LESSON
ON JEFFERSON'S METHOD OF APPORTIONMENT.
AFTER WASHINGTON VETOED HAMILTON'S METHOD,
THOMAS JEFFERSON PROPOSED A NEW METHOD
CALLED JEFFERSON'S METHOD.
IT WAS USING CONGRESS FROM 1791 THROUGH 1842.
THE METHOD DOES TEND TO FAVOR LARGE STATES,
AND JEFFERSON HAPPENED TO LIVE IN VIRGINIA,
THE LARGEST STATE AT THE TIME.
JEFFERSON'S METHOD DIFFERS FROM HAMILTON'S METHOD
ON HOW TO RESOLVE A SITUATION
WHEN THE LOWER QUOTA OR INITIAL QUOTA
IS LESS THAN THE ACTUAL SEATS AVAILABLE.
SO THE FIRST THREE STEPS OF JEFFERSON'S METHOD
IS THE SAME AS HAMILTON'S METHOD.
STEP ONE DETERMINE HOW MANY PEOPLE
EACH REPRESENTATIVE SHOULD REPRESENT.
WE DO THIS BY DIVIDING THE TOTAL POPULATION OF ALL THE STATES
BY THE TOTAL NUMBER OF REPRESENTATIVES.
THIS ANSWER IS CALLED THE STANDARD DEVISOR
OR JUST A DEVISOR.
STEP TWO WE DIVIDE EACH STATE'S POPULATION BY THE DIVISOR
TO DETERMINE HOW MANY REPRESENTATIVES IT SHOULD HAVE.
WE RECORD THIS ANSWER TO SEVERAL DECIMAL PLACES
AND THIS ANSWER IS CALLED THE QUOTA.
STEP THREE WE CUT OFF THE DECIMAL PART OF ALL THE QUOTAS.
THESE VALUES ARE THE LOWER QUOTAS OR INITIAL APPORTIONMENT.
WE ADD THESE WHOLE NUMBERS.
THIS ANSWER WILL ALWAYS BE LESS THAN OR EQUAL TO
THE TOTAL NUMBER OF REPRESENTATIVES.
IF IT'S EQUAL TO THE TOTAL NUMBER OF REPRESENTATIVES
WE WOULD BE DONE.
BUT IF IT'S NOT THEN WE GO TO STEP FOUR.
STEP FOUR SAYS IF THE TOTAL FROM STEP THREE
IS LESS THAN THE TOTAL NUMBER OF REPRESENTATIVES
WE ACTUALLY REDUCE THE DEVISOR
AND RECALCULATE THE QUOTA AND INITIAL ALLOCATION.
SO IF WE HAVE LEFT OVER REPRESENTATIVES
WE ACTUALLY MODIFY THE DEVISOR
RATHER THAN USING THE DECIMAL PARTS OF THE QUOTAS
AS WE DO WHEN USING HAMILTON'S RULE.
SO IF WE HAVE LEFT OVER REPRESENTATIVES
WE ACTUALLY CHANGE THE DEVISOR.
REMEMBER IN HAMILTON'S RULE
WE RELY ON THE DECIMAL PARTS OF THE QUOTA.
SO FOR JEFFERSON'S METHOD WE REDUCE THE DEVISOR
AND RECALCULATE THE QUOTA AND ALLOCATION.
WE CONTINUE DOING THIS UNTIL THE TOTAL FROM STEP THREE
IS EQUAL TO THE TOTAL NUMBER OF REPRESENTATIVES.
THE DEVISOR WE END UP USING IS CALLED THE MODIFIED DEVISOR
OR ADJUSTED DEVISOR.
SO LET'S LOOK AT AN EXAMPLE.
A COLLEGE OFFERS TUTORING IN MATH, ENGLISH, CHEMISTRY,
AND BIOLOGY.
THE NUMBER OF STUDENTS ENROLLED IN EACH SUBJECT IS LISTED BELOW.
IF THE COLLEGE CAN ONLY AFFORD TO HIRE 21 TUTORS,
DETERMINE HOW MANY TUTORS SHOULD BE ASSIGNED TO EACH SUBJECT
USING JEFFERSON'S METHOD.
SO THE FIRST STEP IS TO FIND THE TOTAL ENROLLMENT,
WHICH WE SEE HERE IS 890.
AND SINCE WE HAVE 21 TUTORS TO ALLOCATE,
WE FIND THE STANDARD DEVISOR BY TAKING 890 AND DIVIDING BY 21.
SO THE STANDARD DEVISOR IS APPROXIMATELY 42.3810.
AND NOW TO FIND THE QUOTA FOR EACH SUBJECT,
WE TAKE THE ENROLLMENT FOR EACH SUBJECT
AND DIVIDE BY OUR STANDARD DEVISOR.
LET'S GO AHEAD AND SHOW A COUPLE OF THESE.
SO TO FIND THE QUOTA FOR MATH
WE WOULD HAVE 360 DIVIDED BY 42.3810.
TO THREE DECIMAL PLACES
THE QUOTA WOULD BE APPROXIMATELY 8.494.
THE QUOTA FOR ENGLISH WOULD BE 315 DIVIDED BY 42.3810,
WHICH WOULD BE APPROXIMATELY 7.433.
WE WOULD DO THE SAME FOR CHEMISTRY AND BIOLOGY.
SO HERE WE SEE THE QUOTAS FOR THE FOUR DISCIPLINES.
AND NOW TO FIND THE INITIAL APPORTIONMENT
OR INITIAL ALLOCATION,
REMEMBER WE DROP THE DECIMAL PART OF THE QUOTA.
SO MATH GETS 8, ENGLISH GETS 7, CHEMISTRY GETS 3,
AND BIOLOGY GETS 1.
BUT NOTICE HOW USING THE INITIAL APPORTIONMENT,
NOTICE HOW THE TOTAL IS 19 AND WE HAVE A TOTAL OF 21 TUTORS.
SO NOW WE'RE GOING TO MODIFY THE STANDARD DEVISOR
OR REDUCE THE STANDARD DEVISOR,
RECALCULATE THESE QUOTAS
UNTIL WE FIND AN INITIAL APPORTIONMENT HERE
THAT DOES SUM TO 21.
SO LET'S GO AHEAD AND REDUCE THIS TO LET'S SAY 42
AND THEN RECALCULATE THESE QUOTAS.
SO IF WE USE AND MODIFY DEVISOR 42,
NOW WE'RE GOING TO TAKE THE ENROLLMENT OF EACH SUBJECT
AND DIVIDE BY 42.
AND LET'S GO AHEAD AND SHOW A COUPLE OF THESE.
SO, AGAIN, FOR MATH WITH THE MODIFIED DEVISOR
WE'D HAVE 360 DIVIDED BY 42,
WHICH IS APPROXIMATELY 8.571.
FOR ENGLISH WE'D HAVE 315 DIVIDED BY 42,
WHICH IS EQUAL TO 7.5.
I THINK YOU GET THE IDEA,
BUT NOTICE HOW IF WE CUT OFF THE DECIMAL PARTS OF THE QUOTA,
NOTICE HOW WE HAVE 8, 7, 3, 1.
BUT STILL NOTICE HOW THE TOTAL HERE IS 19 NOT 21.
SO NOW WE NEED TO REDUCE THE DEVISOR AGAIN.
LET'S GO AHEAD AND TRY 40 AND SEE WHAT HAPPENS.
WE CAN SEE FROM THE COMPLETED TABLE
WITH A MODIFIED DEVISOR OF 40 EVERYTHING WORKS OUT PERFECTLY.
OKAY, LET'S GO AHEAD AND SHOW SOME OF THE DIVISION
TO FIND THESE QUOTAS.
THIS TIME I SHOW THE QUOTA FOR CHEMISTRY,
WHICH WOULD BE 135 DIVIDED BY 40, WHICH IS EXACTLY 3.375.
AND OF COURSE FOR BIOLOGY 80 DIVIDED BY 40 WOULD BE 2.
SO USING THESE QUOTAS AND IGNORING THE DECIMALS
WE HAVE AN ALLOCATION OF 9, 7, 3, 2,
WHICH DOES GIVE US A SUM OF 21 TUTORS.
THEREFORE, WE NOW HAVE THE FINAL ALLOCATION
USING JEFFERSON'S METHOD.
AND, AGAIN, OUR FINAL MODIFIED DEVISOR WAS 40.
LET'S TAKE A LOOK AT A SECOND EXAMPLE.
THE LEGISLATURE IN A STATE HAS 57 SEATS.
A PORTION OF THESE SEATS TO 6 COUNTIES BELOW
USING JEFFERSON'S METHOD.
FIRST STEP WE FIND THE TOTAL POPULATION OF ALL THE STATES
WHICH IS GIVEN HERE, 1,000,229,000.
WE HAVE 57 STATES TO A PORTION,
SO THE STANDARD DEVISOR'S GOING TO BE THE TOTAL POPULATION
DIVIDED BY 57 WHICH IS GIVEN HERE TO THREE DECIMAL PLACES.
AND NOW TO FIND THE QUOTA FOR EACH COUNTY
WE'LL TAKE THE POPULATION OF THE COUNTY
AND DIVIDE BY OUR STANDARD DEVISOR,
WHICH, AGAIN, HAS ALREADY BEEN DONE HERE,
BUT LET'S GO AHEAD AND CHECK THE FIRST TWO.
SO WE HAVE 283,000 DIVIDED BY 21,651.404,
WHICH WOULD GIVE US APPROXIMATELY 13.071,
WHICH WE SEE HERE.
AND THEN FOR GRANT WE WOULD HAVE 153,000 DIVIDED BY 21,651.404,
WHICH GIVES A QUOTA OF APPROXIMATELY 7.067, AND SO-ON.
SO NOW FOR THE INITIAL APPORTIONMENT
WE IGNORE THE DECIMAL PART OF THE QUOTA,
SO WE HAVE 13, 7, 4, 15, 10, AND 5.
NOTICE HERE THE TOTAL IS 54,
BUT WE HAVE 57 SEATS TO A PORTION.
SO FOR THE NEXT STEP WE REDUCE THE STANDARD DEVISOR,
RECALCULATE THE QUOTA, AND REPEAT THE PROCESS.
WE REPEAT THE PROCESS UNTIL THIS ALLOCATION HERE
SUMS TO THE TOTAL OF SEATS WHICH WOULD BE 57.
SO WE NEED TO REDUCE THIS.
YOU MIGHT BE ASKING HOW FAR TO REDUCE IT,
AND THAT'S THE CHALLENGE OF JEFFERSON'S METHOD.
LET'S REDUCE THE DEVISOR TO 20,000
AND, AGAIN, RECALCULATE THE QUOTAS
WHICH I'VE ALREADY DONE.
AGAIN, WE TAKE EACH STATE POPULATION,
DIVIDE BY 20,000 TO GET THESE QUOTAS HERE.
AND NOW FOR THE ALLOCATION WE REMOVE THE DECIMAL PART,
SO WE HAVE 14, 7, 5, 17, 11, AND 5.
NOTICE HERE WE REDUCED THE DEVISOR TOO MUCH
BECAUSE NOW THE ALLOCATION IS FOR 59 SEATS
AND WE ONLY HAVE 57.
SO NOW WE NEED TO INCREASE THE DEVISOR
AND THE CHALLENGE IS HOW MUCH DO WE INCREASE THE DEVISOR.
LET'S SAY WE'D INCREASE THE DEVISOR TO 20,200,
RECALCULATE THE QUOTAS, REMOVE THE DECIMAL PART FOR ALLOCATION.
SO WITH A DEVISOR OF 20,200
WE HAVE AN ALLOCATION OF 14, 7, 5, 17, 11, AND 5.
AGAIN, NOTICE HOW WE HAVE TOO MANY SEATS.
THIS IS 59 AND WE ONLY HAVE 57,
WHICH MEANS WE NOW INCREASE THE DEVISOR AGAIN.
SO LET'S TRY 20,300.
USING THE DEVISOR OF 20,300 WE WOULD HAVE THESE QUOTAS.
AND MOVING THE DECIMAL PART WE'D HAVE 13, 7, 5, 17, 10, AND 5,
WHICH DOES GIVE US A SUM OF 57 SEATS.
SO WE'RE FINALLY DONE
AND THIS WOULD BE THE FINAL ALLOCATION
USING JEFFERSON'S RULE.
SO AS YOU CAN SEE, THE CHALLENGE ON JEFFERSON'S RULE
IS COMING UP WITH THE CORRECT DEVISOR
SO THAT ONCE WE CALCULATE THE NEW QUOTAS
AND REMOVE THE DECIMAL PART
THE ALLOCATION SUMS TO THE NUMBER OF SEATS AVAILABLE.
I HOPE YOU FOUND THIS EXPLANATION HELPFUL.