Largest remainders method
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The largest remainders methods
When using the
Method
The largest remainder method requires the numbers of votes for each party to be divided by a quota representing the number of votes required for a seat. Usually, this is given by the total number of votes cast, divided by the number of seats. The result for each party will usually consist of an
This will generally leave some remainder seats unallocated. To apportion these seats, the parties are then ranked on the basis of their fractional remainders, and the parties with the largest remainders are each allocated one additional seat until all seats have been allocated. This gives the method its name.
Quotas
There are several possible choices for the electoral quota; the choice of quota affects the properties of the , with smaller quotas leaving fewer seats left over for small parties to pick up, and larger quotas leaving more seats.
The two most common quotas are the Hare quota and the Droop quota. The use of a particular quota with the largest remainders method is often abbreviated as "LR-[quota name]", such as "LR-Droop".[2]
The Hare (or simple) quota is defined as follows:
It is used for legislative elections in
The Droop quota is given by:
and is applied to elections in South Africa.
The Hare quota is more generous to less popular parties and the Droop quota to more popular parties. Specifically, the Hare quota is
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+1=11 | ||||||
| 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 |
Pros and cons
It is easy for a voter to understand how the largest remainder method allocates seats. The Hare quota gives no advantage to larger or smaller parties, while the Droop quota is biased in favor of larger parties.[9] However, in small legislatures with no threshold, the Hare quota can be manipulated by running candidates on many small lists, allowing each list to pick up a single remainder seat.[10]
However, whether a list gets an extra seat or not may well depend on how the remaining votes are distributed among other parties: it is quite possible for a party to make a slight percentage gain yet lose a seat if the votes for other parties also change. A related feature is that increasing the number of seats may cause a party to lose a seat (the so-called
Technical evaluation and paradoxes
The largest remainder method satisfies the
With 25 seats, the results are:
| 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, the results are:
| 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 |
References
- ISBN 978-0-321-56803-8.
- ISBN 978-0-19-153151-4.
- ^ "2". Proposed Basic Law on Elections and Referendums - Tunisia (Non-official translation to English). International IDEA. 26 January 2014. p. 25. Retrieved 9 August 2015.
- ISBN 9783319232614. Retrieved 2017-08-17.
- ^ "Archived copy" (PDF). Archived from the original (PDF) on 2015-09-24. Retrieved 2011-05-08.
{{cite web}}: CS1 maint: archived copy as title (link) - ^ "Archived copy" (PDF). Archived from the original (PDF) on 2006-09-01. Retrieved 2006-09-01.
{{cite web}}: CS1 maint: archived copy as title (link) - ^ "Archived copy" (PDF). Archived from the original (PDF) on 2007-09-26. Retrieved 2007-09-26.
{{cite web}}: CS1 maint: archived copy as title (link) - ^ "Lipjhart on PR formulas".
- ^ "Notes on the Political Consequences of Electoral Laws by Lijphart, Arend, American Political Science Review Vol. 84, No 2 1990". Archived from the original on 2006-05-16. Retrieved 2006-05-16.
- ^ See for example the 2012 election in Hong Kong Island where the DAB ran as two lists and gained twice as many seats as the single-list Civic despite receiving fewer votes in total: New York Times report
- ^
Balinski, Michel; H. Peyton Young (1982). Fair Representation: Meeting the Ideal of One Man, One Vote. Yale Univ Pr. ISBN 0-300-02724-9.
External links
- Hamilton method experimentation applet at cut-the-knot