D'Hondt Method - D'Hondt and Jefferson

D'Hondt and Jefferson

The d'Hondt method is equivalent to the Jefferson method (named after the U.S. statesman Thomas Jefferson) in that they always give the same results, but the method of calculating the apportionment is different. Jefferson devised the method in 1792 for the U.S. congressional apportionment pursuant to the First United States Census, with the objective being the proportional distribution of seats in the House of Representatives among the states rather than distributing seats in a legislature among parties pursuant to an election (the problems are functionally equivalent if one puts states in the place of parties and population in place of votes). Jefferson's method uses a quota, as in the largest remainder method, but the quota (called a divisor) is adjusted as necessary so that the resulting quotients, disregarding any fractional remainders, sum to the required total (so the two methods share the additional property of not using all numbers, whether of state populations or of party votes, in the apportioning of seats). One of a range of quotas will accomplish this, and applied to the above example of party lists this extends as integers from 85,001 to 93,333, the highest number always being the same as the last average to which the d'Hondt method awards a seat if it is used rather than the Jefferson method, and the lowest number being the next average plus one.