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The largest remainder method is one way of allocating seats proportionally for representative assemblies with party list voting systems. It is a contrast to the highest averages method. Party-list proportional representation systems are a family of voting systems used in multiple-winner elections (e. ...
Voters at the voting booths in the US in 1945 Voting systems are methods (algorithms) for groups of people to select one or more options from many, taking into account the individual preferences of the group members. ...
The highest averages method is one way of allocating seats proportionally for representative assemblies with party list voting systems. ...
Method
The largest remainder method requires the number of votes for each party to be divided by a quota representing the number of votes required for a seat, and this gives a notional number of seats to each, usually including an integer and either a fraction or alternatively a remainder. Each party receives seats equal to the integer. This will generally leave some seats unallocated: the parties are then ranked on the basis of the fraction or equivalently on the basis of the remainder, and parties with the larger fractions or remainders are each allocated one additional seat until all the seats have been allocated. This gives the method its name. A quota is a prescribed number or share of something. ...
The integers consist of the positive natural numbers (1, 2, 3, …) the negative natural numbers (−1, −2, −3, ...) and the number zero. ...
In common usage a fraction is any part of a unit. ...
In mathematics, the result of the division of two integers usually cannot be expressed with an integer quotient, unless a remainder —an amount left over— is also acknowledged. ...
Quotas There are several possibilities for the quota. The most common are: the Hare quota and the Droop quota. The Hare quota is a formula used to calculate the minimum number, or quota, of votes required to capture a seat in some forms of single transferable vote or largest remainder method party-list proportional representation voting systems. ...
The Droop Quota is the formula that is used to calculate the minimum number, or quota, of votes required to capture a seat in a multi-member constituency using Proportional Representation through the Single Transferable Vote (PR.STV). ...
The Hare Quota is defined as follows
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The Hamilton method of apportionment is actually a largest-remainder method which is specifically defined as using the Hare Quota, named after Alexander Hamilton. It is used for legislative elections in Namibia and in the territory of Hong Kong. It was historically applied for congressional apportionment in the United States during the nineteenth century. A portrait of Alexander Hamilton by John Trumbull, 1792. ...
The membership of the United States House of Representatives changes each decade following the decennial United States Census. ...
Alternative meaning: Nineteenth Century (periodical) (18th century — 19th century — 20th century — more centuries) As a means of recording the passage of time, the 19th century was that century which lasted from 1801-1900 in the sense of the Gregorian calendar. ...
The Droop quota is the integer part of The Droop Quota is the formula that is used to calculate the minimum number, or quota, of votes required to capture a seat in a multi-member constituency using Proportional Representation through the Single Transferable Vote (PR.STV). ...
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and is applied in elections in South Africa.
The Hare quota tends to be slightly more generous to less popular parties and the Droop quota to more popular parties. Which is more proportional depends on what measure of proportionality is used.
The Imperiali quota The Imperiali quota is a formula used to calculate the minimum number, or quota, of votes required to capture a seat in some forms of single transferable vote or largest remainder method party-list proportional representation voting systems. ...
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is rarely used since it suffers from the problem that it may result in more candidates being elected than there are seats available; this will certainly happen if there are only two parties. In such a case, it is usual to increase the quota until the number of candidates elected is equal to the number of seats available, in effect changing the voting system to a highest averages system with the Jefferson apportionment formula. The dHondt method is a method for allocating seats in party-list proportional representation. ...
Pros and cons It is very easy for the average voter to understand how Largest Remainder allocates seats. Provided the Hare quota is used, it gives no advantage to lists with either a large or a small proportion of the votes - to that it extent it is neutral. However, whether a list gets an extra seat or not is highly dependent on how the votes are distributed among other parties; it is quite possible for a party to make a slight percentage gain yet lose a seat. A related paradox is that increasing the number of seats may cause a party to lose a seat. The Sainte-Laguë method avoids these paradoxes but is less easy for the average voter to understand. The Sainte-Laguë method of the highest average (also known as Websters method or divisor method with standard rounding) is one way of allocating seats proportionally for representative assemblies with party list voting systems. ...
Technical evaluation and paradoxes The largest remainder method is the only apportionment that satisfies the quota rule; in fact, it is designed to satisfy this criterion. However, it comes at the cost of paradoxical behaviour. The Alabama paradox is defined as when an increase in seats apportioned leads to decrease in the number of seats a certain party holds. Suppose we want to apportion 25 seats between 6 parties in the proportions 1500:1500:900:500:500:200. The two parties with 500 votes get three seats each. Now allocate 26 seats, and it will be found that the these parties get only two seats apiece. For other meanings of Paradox, see Paradox (disambiguation). ...
The Alabama paradox was the first of the apportionment paradoxes to be discovered. ...
With 25 seats, we get:
| Party | A | B | C | D | E | F | Total | | Votes | 1500 | 1500 | 900 | 500 | 500 | 200 | 5100 | | Seats | | | | | | | 25 | | Hare Quota | | | | | | | 204 | | Quotas Received | 7.35 | 7.35 | 4.41 | 2.45 | 2.45 | 0.98 | | | Automatic seats | 7 | 7 | 4 | 2 | 2 | 0 | 22 | | Remainder | 0.35 | 0.35 | 0.41 | 0.45 | 0.45 | 0.98 | | | Surplus seats | 0 | 0 | 0 | 1 | 1 | 1 | 3 | | Total Seats | 7 | 7 | 4 | 3 | 3 | 1 | 25 | With 26 seats, we have: | Party | A | B | C | D | E | F | Total | | Votes | 1500 | 1500 | 900 | 500 | 500 | 200 | 5100 | | Seats | | | | | | | 26 | | Hare Quota | | | | | | | 196 | | Quotas Received | 7.65 | 7.65 | 4.59 | 2.55 | 2.55 | 1.02 | | | Automatic seats | 7 | 7 | 4 | 2 | 2 | 1 | 23 | | Remainder | 0.65 | 0.65 | 0.59 | 0.55 | 0.55 | 0.02 | | | Surplus seats | 1 | 1 | 1 | 0 | 0 | 0 | 3 | | Total Seats | 8 | 8 | 5 | 2 | 2 | 1 | 26 |
Examples These examples take an election to allocate 10 seats where there are 100,000 votes.
Hare quota | Party | Yellows | Whites | Reds | Greens | Blues | Pinks | Total | | Votes | 47,000 | 16,000 | 15,800 | 12,000 | 6,100 | 3,100 | 100,000 | | Seats | | | | | | | 10 | | Hare Quota | | | | | | | 10,000 | | Votes/Quota | 4.70 | 1.60 | 1.58 | 1.20 | 0.61 | 0.31 | | | Automatic seats | 4 | 1 | 1 | 1 | 0 | 0 | 7 | | Remainder | 0.70 | 0.60 | 0.58 | 0.20 | 0.61 | 0.31 | | | Highest Remainder Seats | 1 | 1 | 0 | 0 | 1 | 0 | 3 | | Total Seats | 5 | 2 | 1 | 1 | 1 | 0 | 10 |
Droop quota | Party | Yellows | Whites | Reds | Greens | Blues | Pinks | Total | | Votes | 47,000 | 16,000 | 15,800 | 12,000 | 6,100 | 3,100 | 100,000 | | Seats | | | | | | | 10 | | Droop Quota | | | | | | | 9,091 | | Votes/Quota | 5.170 | 1.760 | 1.738 | 1.320 | 0.671 | 0.341 | | | Automatic seats | 5 | 1 | 1 | 1 | 0 | 0 | 8 | | Remainder | 0.170 | 0.760 | 0.738 | 0.320 | 0.671 | 0.341 | | | Highest Remainder Seats | 0 | 1 | 1 | 0 | 0 | 0 | 2 | | Total Seats | 5 | 2 | 2 | 1 | 0 | 0 | 10 |
See also - List of democracy and elections-related topics
Politics is the process and method of gaining or maintaining support for public or common action: the conduct of decision-making for groups. ...
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