The Webster/SainteLaguë method, often simply Webster method or
SainteLaguë method (French pronunciation: [sɛ̃t.la.ɡy]),
is a highest quotient method for allocating seats in partylist
proportional representation used in many voting systems. It is named
in Europe after the French mathematician
André SainteLaguë and in
United States after statesman and senator Daniel Webster. The method
is quite similar to the D'Hondt method, but uses different divisors.
In most cases the largest remainder method delivers almost identical
results. The
D'Hondt method gives similar results too, but favors
larger parties compared to the Webster/SainteLaguë method.[1] Often
there is an electoral threshold, that is a minimum percentage of votes
required to be allocated seats.
Webster first proposed the method in 1832 and in 1842 the method was
adopted for proportional allocation of seats in United States
congressional apportionment (Act of June 25, 1842, ch 46, 5 Stat.
491). It was then replaced by Hamilton method and in 1911 the Webster
method was reintroduced.[2] In France,
André SainteLaguë introduced
the method in his 1910 article. It seems that French and European
literature was unaware of Webster until after World War II.
The Webster/
SainteLaguë method is used in Bosnia and Herzegovina,
Iraq, Kosovo, Latvia, New Zealand,
Norway
Contents 1 Description of the method 2 Webster, SainteLaguë, and Schepers 3 Modified SainteLaguë method 4 Threshold for seats 5 See also 6 References 7 External links Description of the method[edit] After all the votes have been tallied, successive quotients are calculated for each party. The formula for the quotient is[1] quot = V 2 s + 1 displaystyle text quot = frac V 2s+1 where: V is the total number of votes that party received, and s is the number of seats that have been allocated so far to that party, initially 0 for all parties. Whichever party has the highest quotient gets the next seat allocated, and their quotient is recalculated. The process is repeated until all seats have been allocated. The Webster/ SainteLaguë method does not ensure that a party receiving more than half the votes will win at least half the seats; nor does its modified form.[5] For example, with seven seats available and the votes split 53,000, 24,000 and 23,000, the allocation would be three, two and two seats respectively: round (1 seat per round) 1 2 3 4 5 6 7 Seats won (bold) Party A seats after round 53,000 1 17,667 1 17,667 1 17,667 2 10,600 3 7,571 3 7,571 3 3 Party B seats after round 24,000 0 24,000 1 8,000 1 8,000 1 8,000 1 8,000 2 4,800 2 2 Party C seats after round 23,000 0 23,000 0 23,000 1 7,667 1 7,667 1 7,667 1 7,667 2 2 The below chart is an easy way to perform the calculation: denominator /1 /3 /5 /7 /9 /11 /13 Seats won (*) True proportion Party A 53,000* 17,666* 10,600* 7,571 5,888 4,818 4,076 3 3.71 Party B 24,000* 8,000* 4,800 3,428 2,666 2,181 1,846 2 1.68 Party C 23,000* 7,666* 4,600 3,285 2,555 2,090 1,769 2 1.61 The d'Hondt method differs by the formula to calculate the quotients ( quot = V s + 1 ) displaystyle left( text quot = frac V s+1 right) .[1]
Webster, SainteLaguë, and Schepers[edit]
Webster proposed the method in United States Congress in 1832 for
proportional allocation of seats in United States congressional
apportionment. In 1842 the method was adopted (Act of June 25, 1842,
ch 46, 5 Stat. 491). It was then replaced by Hamilton method and in
1911 the Webster method was reintroduced.[6]
According to some observers the method should be treated as two
methods with the same result, because Webster method is used for
allocating seats based on states' population and Saint Lague based on
parties' votes.[7] Webster invented his method for legislative
apportionment (allocating legislative seats to regions based on their
share of the population) rather than elections (allocating legislative
seats to parties based on their share of the votes) but this makes no
difference to the calculations in the method.
Webster's method is defined in terms of a
Droop quota as in the
largest remainder method; in this method, the quota is called a
"divisor". For a given value of the divisor, the population count for
each region is divided by this divisor and then rounded to give the
number of legislators to allocate to that region. In order to make the
total number of legislators come out equal to the target number, the
divisor is adjusted to make the sum of allocated seats after being
rounded give the required total.
One way to determine the correct value of the divisor would be to
start with a very large divisor, so that no seats are allocated after
rounding. Then the divisor may be successively decreased until one
seat, two seats, three seats and finally the total number of seats are
allocated. The number of allocated seats for a given region increases
from s to s + 1 exactly when the divisor equals the
population of the region divided by s + 1/2, so at each step
the next region to get a seat will be the one with the largest value
of this quotient. That means that this successive adjustment method
for implementing Webster's method allocates seats in the same order to
the same regions as the
SainteLaguë method would allocate them.
The German physician Hans Schepers, at the time Head of the Data
Processing Group of the German Bundestag, in 1980 suggested that the
distribution of seats according to d'Hondt be modified to avoid
putting smaller parties at a disadvantage.[8] German media started
using the term Schepers Method and later German literature usually
calls it SainteLaguë/Schepers.[8]
Modified SainteLaguë method[edit]
Some countries, e.g. Nepal,
Norway
HagenbachBischoff quota References[edit] ^ a b c d Lijphart, Arend (2003), "Degrees of proportionality of
proportional representation formulas", in Grofman, Bernard; Lijphart,
Arend, Electoral Laws and Their Political Consequences, Agathon series
on representation, 1, Algora Publishing, pp. 170–179,
ISBN 9780875862675 . See in particular the section
"SainteLague", pp. 174–175.
^ Balinski, Michel L.; Peyton, Young (1982). Fair Representation:
Meeting the Ideal of One Man, One Vote.
^ Ireland's Green Party website
^ "
House of Lords
External links[edit] Excel SainteLaguë calculator
Seats Calculator with the SainteLaguë method
Java implementation of Webster's method at cuttheknot
Elections
New Zealand
v t e Electoral systems Part of the politics and election series Singlewinner voting system Approval voting Borda count Bucklin voting Contingent vote Coombs' method Copeland's method Dodgson's method Exhaustive ballot Firstpastthepost voting Instantrunoff voting Kemeny–Young method Majority judgment Simple majoritarianism Minimax Condorcet Nanson's method Plurality Positional voting system Range voting Ranked pairs Schulze method Tworound system Proportional representation Mixedmember Partylist Single transferable vote Schulze STV CPOSTV Highest averages method SainteLaguë D'Hondt Largest remainder method Alternative vote Plus Closed list Open list Overhang seat Underhang seat Semiproportional representation Parallel voting Single nontransferable vote Cumulative voting Limited voting Proportional approval voting Sequential proportional approval voting Satisfaction approval voting Usage Table of voting systems by country Voting system criteria Comparison Condorcet criterion Condorcet loser criterion Consistency criterion Independence of clones Independence of irrelevant alternatives Independence of Smithdominated alternatives Laternoharm criterion Majority criterion Majority loser criterion Monotonicity criterion Mutual majority criterion Pareto efficiency Participation criterion Plurality criterion Resolvability criterion Reversal symmetry Smith criterion Voting system quotas Droop quota HagenbachBischoff quota Hare quota Imperiali quota Other Ballot
Election
