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The Webster method, also called the Sainte-Laguë method (French pronunciation: [sɛ̃t.la.ɡy]), is a highest averages apportionment method for allocating seats in a parliament among federal states, or among parties in a party-list proportional representation system.
By this definition, the Webster method is the least-biased apportionment method, [19] while Huntington-Hill exhibits a mild bias towards smaller parties. [18] However, other researchers have noted that slightly different definitions of bias, generally based on percent errors , find the opposite result (The Huntington-Hill method is unbiased ...
Webster's method is the unique apportionment method in which, for each pair of agents and , this difference is minimized (that is, moving a seat from to or vice versa would not make the difference smaller).
Apart from 1860, Congress deliberately chose after each census to set the size of the House at a level where Hamilton and Webster's methods gave the same apportionment. [39] This unofficial adoption of Webster's method was driven by the discovery of the Alabama paradox, which created an uproar in the House. [40]
Since Jefferson was the first method used for Congressional apportionment in the United States, this violation led to a substantial problem where larger states often received more representatives than smaller states, which was not corrected until Webster's method was implemented in 1842. Although Webster's method can in theory violate the quota ...
The converse is not true, however. Webster's method can be free of incoherence and maintain quota when there are three states. All sensible methods satisfy both criteria in the trivial two-state case. [4] [5] They show a proof of impossibility: apportionment methods may have a subset of these properties, but cannot have all of them:
Webster's method yields the same result (though this is not always the case). Otherwise, all other methods give a different number of seats to the parties. Notice how the D'Hondt method breaks the quota rule (shown in red text) and favors the largest party by "rounding" an ideal apportionment of 35.91 up to 37.
if, in addition, it is also strongly exact, [jargon] then it is a divisor method. Young proved that the unique apportionment method that is a coherent extension of the natural two-party apportionment rule of rounding to the nearest integer is the Webster method. [9]: 49–50, 190 [10]: Sub.9.10