Editing Highest averages method (section)

===Webster (Sainte-Laguë) method===
{{Main article|Sainte-Laguë method}}

The Sainte-Laguë or Webster method, first described in 1832 by American statesman and senator [[Daniel Webster]] and later independently in 1910 by the French mathematician [[André Sainte-Laguë|André Sainte-Lague]], uses the fencepost sequence {{Math|1=post(''k'') = ''k''+.5}} (i.e. 0.5, 1.5, 2.5); this corresponds to the standard [[Rounding|rounding rule]]. Equivalently, the odd integers (1, 3, 5...) can be used to calculate the averages instead.<ref name="Pukelsheim-2017-1" /><ref name="Sainte-2024" />

The Webster method produces more proportional apportionments than Jefferson's by almost every metric of misrepresentation.<ref name="Pennisi-1998" /> As such, it is typically preferred to D'Hondt by political scientists and mathematicians, at least in situations where manipulation is difficult or unlikely (as in large parliaments).<ref name="Balinski-1980" /> It is also notable for minimizing [[seat bias]] even when dealing with parties that win very small numbers of seats.<ref name="Pukelsheim-2017-2" /> The Webster method can theoretically violate the [[quota rule|ideal frame]], although this is extremely rare for even moderately-large parliaments; it has never been observed to violate quota in any [[United States congressional apportionment]].<ref name="Balinski-1980" />

In small districts with no [[Electoral threshold|threshold]], parties can [[vote management|manipulate]] Webster by splitting into many lists, each of which wins a full seat with less than a [[Hare quota]]'s worth of votes. This is often addressed by modifying the first divisor to be slightly larger (often a value of 0.7 or 1), which creates an [[electoral threshold|implicit threshold]].<ref name="Pukelsheim-2017-8" />