The legal term apportionment (French: apportionement; Mediaeval Latin: apportionamentum, derived from Latin: portio, share), also called delimitation,[1] is in general the distribution or allotment of proper shares,[2] though may have different meanings in different contexts. Apportionment can refer to estate, the amount of compensation received by a worker[3] and in respect of time.
This term may be employed roughly and sometimes has no technical meaning; this indicates the distribution of a benefit (e.g. salvage or damages under the Fatal Accidents Act 1846, § 2), or liability (e.g. general average contributions, or tithe rent-charge), or the incidence of a duty (e.g. obligations as to the maintenance of highways).[2]
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Apportionment: Hamilton's Method
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What is Apportionment?
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Introduction to Apportionment
Transcription
- WELCOME TO A LESSON ON HAMILTON'S METHOD OF APPORTIONMENT. ALEXANDER HAMILTON PROPOSED THE METHOD THAT NOW BEARS HIS NAME. HIS METHOD WAS APPROVED BY CONGRESS IN 1791, BUT WAS VETOED BY PRESIDENT WASHINGTON. IT WAS LATER ADOPTED IN 1852, AND USED THROUGH 1911. SINCE HE WAS INTERESTED IN THE QUESTION OF CONGRESSIONAL REPRESENTATION, WE'LL USE THE LANGUAGE OF STATES AND REPRESENTATIVES. HAMILTON'S METHOD PROVIDES A PROCEDURE TO DETERMINE HOW MANY REPRESENTATIVES EACH STATE SHOULD RECEIVE. SO THE FIRST STEP IN HAMILTON'S METHOD IS TO 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 DIVISOR, OR DIVISOR. STEP TWO, WE DIVIDE EACH STATE'S POPULATION BY THE DIVISOR TO DETERMINE HOW MANY REPRESENTATIVES IT SHOULD HAVE. WE WOULD RECORD THIS ANSWER TO SEVERAL DECIMAL PLACES, AND THIS ANSWER IS CALLED THE QUOTA. SINCE WE CAN ONLY ALLOCATE WHOLE REPRESENTATIVES, HAMILTON RESOLVES THE WHOLE NUMBER PROBLEM AS FOLLOWS: STEP THREE, WE CUT OFF THE DECIMAL PARTS OF ALL THE QUOTAS, AND THESE ARE CALLED THE LOWER QUOTAS. THEN WE ADD THE LOWER QUOTAS. THIS SUM WILL ALWAYS BE LESS THAN OR EQUAL TO THE TOTAL NUMBER OF REPRESENTATIVES. STEP FOUR, ASSUMING THAT THE TOTAL FROM STEP THREE WAS LESS THAN THE TOTAL NUMBER OF REPRESENTATIVES, ASSIGN THE REMAINING REPRESENTATIVES ONE EACH TO THE STATES WHOSE DECIMAL PART OF THE QUOTA WERE LARGEST UNTIL THE DESIRED TOTAL IS REACHED. WE DO WANT TO MAKE SURE THAT EACH STATE ENDS UP WITH AT LEAST ONE REPRESENTATIVE. LET'S TAKE A LOOK AT OUR FIRST EXAMPLE. AGAIN, THE FIRST STEP, WE WANT TO FIND THE DIVISOR, OR STANDARD DIVISOR. SO WE TAKE THE SUM OF THE POPULATION FROM ALL THE STATES, WHICH IS 189,000, AND DIVIDE BY THE TOTAL OF SEATS IN CONGRESS, WHICH IS 30. NOTICE HOW THIS GIVES US A DIVISOR OF 6,300. AND NOW, TO FIND THE QUOTAS WE TAKE EACH STATE POPULATION AND DIVIDE BY 6,300. SO FOR STATE "A" THE QUOTA WOULD BE 27,500 DIVIDED BY 6,300. IF WE ROUND TO FOUR DECIMAL PLACES, THE QUOTA FOR STATE "A" WOULD BE APPROXIMATELY 4.3651. FOR STATE B WE WOULD HAVE 38,300 DIVIDED BY 6,300, SO THE QUOTA FOR STATE B WOULD BE APPROXIMATELY 6.0794, AND SO ON. TO SAVE SOME TIME WE WON'T SHOW ALL THIS DIVISION. SO HERE ARE OUR QUOTAS TO FOUR DECIMAL PLACES, AND NOW FOR THE INITIAL APPORTIONMENT OR INITIAL ASSIGNMENT OF THE SEATS IN CONGRESS, WE REMOVE THE DECIMAL PARTS OF THE QUOTA. WHICH MEANS STATE "A" WOULD RECEIVE 4, STATE B WOULD RECEIVE 6, STATE C WOULD RECEIVE 7, AND STATE D WOULD RECEIVE 12. WE NOTICE HOW THE SUM HERE IS 29, AND WE HAVE A TOTAL OF 30 SEATS. WE NOW ASSIGN THE REMAINING SEAT TO THE STATE WHOSE QUOTA HAS THE LARGEST DECIMAL PART. NOTICE STATE "A" HAS THE LARGEST DECIMAL PART AT .3651, AND THEREFORE STATE "A" RECEIVES ONE MORE SEAT. WHICH MEANS FOR THE FINAL APPORTIONMENT STATE "A" RECEIVES 5 SEATS, STATE B RECEIVES 6, STATE C RECEIVES 7, AND STATE D RECEIVES 12. NOTICE HERE THE TOTAL IS 30. WE'VE USED ALL THE SEATS IN CONGRESS. AND HERE'S THE RESULT IN A NICE TABLE. LET'S TAKE A LOOK AT A SECOND EXAMPLE. HERE A TEACHER WISHES TO DISTRIBUTE 10 IDENTICAL PIECES OF CANDY AMONG 4 STUDENTS, BASED UPON HOW MANY PAGES OF A BOOK THEY READ LAST MONTH, USING HAMILTON'S METHOD. THE TABLE BELOW LISTS THE TOTAL NUMBER OF PAGES READ BY EACH STUDENT. SO IN THIS PARTICULAR QUESTION WE'RE ASKED TO FIND THE DIVISOR, THE QUOTA FOR ANTONIO, AND THE INITIAL APPORTIONMENT FOR ANTONIO. BUT WE'LL ACTUALLY GO AHEAD AND GO THROUGH THIS ENTIRE PROCESS FOR THIS PROBLEM. SO THE FIRST STEP IS TO FIND THE DIVISOR, SO WE'LL SET THIS UP AS A TABLE AS WE SEE HERE. NOTICE HOW WE ALREADY FOUND THE SUM OF THE TOTAL NUMBER OF PAGES, WHICH IS 1,120, AND THERE ARE 10 PIECES OF CANDY TO APPORTION. SO OUR DIVISOR IS 1,120 DIVIDED BY 10, OR 112. SO TO FIND THE QUOTA WE'LL TAKE THE NUMBER OF PAGES EACH STUDENT READ AND DIVIDE BY 112. SO THE QUOTE FOR ALAN WOULD BE 580 DIVIDED BY 112, WHICH WOULD BE APPROXIMATELY 5.1786. FOR ANTONIO THE QUOTA WOULD BE 230 DIVIDED BY 112, GIVING A QUOTA OF APPROXIMATELY 2.0536, AND SO ON. SO AGAIN, HERE ARE OUR QUOTAS. WE FOUND FROM THE PREVIOUS SLIDE THE DIVISOR IS 112, AND THE QUOTA FOR ANTONIO WE NOW KNOW IS 2.0536. AND NOW FOR THE INITIAL APPORTIONMENT WE REMOVE THE DECIMALS FROM THE QUOTA. SO ALAN WOULD RECEIVE 5 PIECES, ANTONIO WOULD RECEIVE 2, ALEX WOULD RECEIVE 1, AND LUCAS WOULD ALSO RECEIVE 1. SO THE INITIAL APPORTIONMENT FOR ANTONIO, WHICH IS WHAT OUR QUESTION ASKED FOR, IS 2. BUT NOTICE HOW THERE ARE 10 PIECES OF CANDY, AND THIS ONLY ADDS TO 9. SO GOING BACK TO THE ORIGINAL QUOTAS, SINCE ALEX HAS THE LARGEST DECIMAL PART IN HIS QUOTA, HE WOULD RECEIVE THE EXTRA PIECE OF CANDY. AND THEREFORE THE FINAL APPORTIONMENT WOULD BE 5, 2, 2, AND 1. NOTICE HOW HERE THE TOTAL IS 10 PIECES, SO WE'VE USED ALL THE CANDY. AND AGAIN, HERE IS THE RESULT IN A NICE TABLE. HAMILTON'S METHOD DOES SATISFY WHAT IS CALLED THE QUOTA RULE. THE QUOTA RULE SAYS THAT THE FINAL NUMBER OF REPRESENTATIVES A STATE GETS SHOULD BE WITHIN ONE OF THAT STATE'S QUOTA. SINCE WE'RE DEALING WITH WHOLE NUMBERS FOR OUR FINAL ANSWERS, THAT MEANS THAT EACH STATE SHOULD EITHER GO UP TO THE NEXT WHOLE NUMBER ABOVE ITS QUOTA OR GO DOWN TO THE NEXT WHOLE NUMBER BELOW ITS QUOTA. AND THEN FINALLY, THERE IS SOME CONTROVERSY WHEN USING HAMILTON'S METHOD. AFTER SEEING HAMILTON'S METHOD, MANY PEOPLE FIND THAT IT MAKES SENSE, AND IT'S NOT THAT DIFFICULT TO USE. SO WHY WOULD ANYONE WANT TO USE ANOTHER METHOD? WELL, THE PROBLEM IS THAT HAMILTON'S METHOD IS SUBJECT TO SEVERAL WHAT WE CALL PARADOXES. THREE OF THEM HAPPENED ON SEPARATE OCCASIONS WHEN HAMILTON'S METHOD WAS USED TO APPORTION THE UNITED STATES HOUSE OF REPRESENTATIVES. AND THOSE THREE PARADOXES ARE NUMBER ONE, THE ALABAMA PARADOX, TWO, THE NEW STATES PARADOX, AND THREE, THE POPULATION PARADOX. WE'LL TALK ABOUT EACH OF THESE IN FUTURE LESSONS. I HOPE YOU FOUND THIS HELPFUL.
Apportionment in respect of estate
Apportionment in respect of estate may result either from the act of the parties or from the operation of law.[2]
Apportionment by act of the parties
Where a lessee is evicted from, or surrenders or forfeits possession of part of the property leased to him, he becomes liable at common law to pay only a rent apportioned to the value of the interest which he still retains. So where the person entitled to the reversion of an estate assigns part of it, the right to an apportioned part of the rent incident to the England,[4] and in many of the British colonies.[5] In the cases just mentioned there is apportionment in respect of estate by act of the parties.[2]
Apportionment by operation of law
Apportionment by operation of law may be brought about where by act of law a lease becomes inoperative as regards its subject-matter, or by the "act of God", as, for instance, where part of an estate is submerged by the encroachments of the sea. To the same category belongs the apportionment of rent which takes place under various statutes (e.g. the Lands Clauses Consolidation Act 1845 (8 & 9 Vict. c. 18), section 119, when land is required for public purposes; the Agricultural Holdings Act 1883, section 41, in the case of a tenant from year to year receiving notice to quit part of a holding; and the Irish Land Act 1903 (3 Edw. 7. c. 37), section 61, apportionment of quit and crown rents).[2]
Apportionment in respect of time
| Apportionment Act 1834 | |
|---|---|
| Act of Parliament | |
 | |
| Long title | An Act to amend an Act of the Eleventh Year of King George the Second, respecting the Apportionment of Rents, Annuities, and other periodical Payments. |
| Citation | 4 & 5 Will. 4. c. 22 |
| Dates | |
| Royal assent | 16 June 1834 |
At common law, there was no apportionment of rent in respect of time. Such apportionment was, however, in certain cases allowed in England by the Distress for Rent Act 1737, and the Apportionment Act 1834 (4 & 5 Will. 4. c. 22), and is now allowed generally. Under that statute (section 2) all rents, annuities, dividends and other periodical payments in the nature of income are to be considered as accruing from day to day and to be apportionable in respect of time accordingly. It is provided, however, that the apportioned part of such rents, etc., shall only be payable or recoverable in the case of a continuing payment, when the entire portion of which it forms part itself becomes payable, and, in the case of a payment determined by re-entry, death or otherwise, only when the next entire portion would have been payable if it had not so determined (§ 3). Persons entitled to apportioned parts of rent have the same remedies for recovering them when payable as they would have had in respect of the entire rent; but a lessee is not to be liable for any apportioned part specifically. The rent is recoverable by the heir or other person who would, but for the apportionment, be entitled to the entire rent, and he holds it subject to distribution (section 4).
| Apportionment Act 1870 | |
|---|---|
| Act of Parliament | |
 | |
| Long title | An Act for the better Apportionment of Rents and other periodical Payments. |
| Citation | 33 & 34 Vict. c. 35 |
| Dates | |
| Royal assent | 1 August 1870 |
Status: Current legislation | |
| Text of statute as originally enacted | |
| Text of the Apportionment Act 1870 as in force today (including any amendments) within the United Kingdom, from legislation.gov.uk. | |
The Apportionment Act 1870 (33 & 34 Vict. c. 35) extends to payments not made under any instrument in writing (section 2), but not to annual sums made payable in policies of insurance (section 6). Apportionment under the act can be excluded by express stipulation.[2]
The apportionment created by this statute is "apportionment in respect of time." The cases to which it applies are mainly cases of either:
- apportionment of rent due under leases where at a time between the dates fixed for payment the lessor or lessee dies, or some other alteration in the position of parties occurs; or
- apportionment of income between the representatives of a limited owner and the remainder-man when the limited interest determines at a time between the date when such income became due.[2]
Apportionment of rent
With regard to the former of these classes, it may be noticed that although apportioned rent becomes payable only when the whole rent is due, the landlord, in the case of the bankruptcy of an ordinary tenant, may prove for a proportionate part of the rent up to the date of the receiving order;[6] and that a similar rule holds good in the winding up of a company;[7] and further that the act of 1870 applies to the liability to pay, as well as to the right to receive, rent.[8] Accordingly, where an assignment of a lease is made between two half-yearly rent-days, the assignee is not liable to pay the full amount of the half-year's rent falling due on the rent-day next after the date of the assignment, but only an apportioned part of that half-year's rent, computed from the last mentioned date.[2][9] If someone pays a ground rent on a leasehold property or a rentcharge on a freehold property that is also payable on other neighbouring properties, they can apply to the Department for Communities and Local Government for an 'order of apportionment' that legally separates their share of the ground rent or rentcharge.[10]
Apportionment of income
With regard to the apportionment of income, the only points requiring notice here are that all dividends payable by public companies are apportionable, whether paid at fixed periods or not, unless the payment is, in effect, a payment of capital (§ 5).[2]
See also
- Formulary apportionment, is a method of allocating profit earned or loss incurred
- Fair division
- Entitlement (fair division)
- Proportional cake-cutting with different entitlements
References
- ^ "legislative apportionment | government | Britannica". www.britannica.com. Retrieved 16 May 2022.
- ^ a b c d e f g h i One or more of the preceding sentences incorporates text from a publication now in the public domain: Renton, Alexander Wood (1911). "Apportionment". In Chisholm, Hugh (ed.). Encyclopædia Britannica. Vol. 2 (11th ed.). Cambridge University Press. pp. 226–227.
- ^ "Apportionment". Investopedia. Retrieved 16 May 2022.
- ^ Law of Property Amendment Act 1859, § 3; Conveyancing Act 1881, § 12.
- ^ For example, Ontario, Rev. Stats., 1897, c. 170, § 9; Barbados, No. 12 of 1891, § 9.
- ^ Bankruptcy Act 1883, Sched. ii. r. 19.
- ^ In South Kensington Co-operative Stores, 1881, 17 Ch.D. 161.
- ^ Wilson, 1893, 62 L.J.Q.B. 628, 632.
- ^ Glass v. Patterson, 1902, 2 Ir.R. 660.
- ^ "Rentcharges - GOV.UK". www.gov.uk. Retrieved 2018-02-21.
This page was last edited on 23 March 2024, at 10:39