D'Hondt method

The D'Hondt method, also called the Jefferson method or the greatest divisors method, is an apportionment method for allocating seats in parliaments among federal states, or in proportional representation among political parties. It belongs to the class of highest-averages methods. The method was first described in 1792 by future U.S. president Thomas Jefferson. It was re-invented independently in 1878 by Belgian mathematician Victor D'Hondt, which is the reason for its two different names. Proportional representation systems aim to allocate seats to parties approximately in proportion to the number of votes received. For example, if a party wins one-third of the votes then it should gain about one-third of the seats. In general, exact proportionality is not possible because these divisions produce fractional numbers of seats. As a result, several methods, of which the D'Hondt method is one, have been devised which ensure that the parties' seat allocations, which are of whole numbers, are as proportional as possible. Although all of these methods approximate proportionality, they do so by minimizing different kinds of disproportionality. The D'Hondt method minimizes the largest seats-to-votes ratio. Empirical studies based on other, more popular concepts of disproportionality show that the D'Hondt method is one of the least proportional among the proportional representation methods. The D'Hondt favours large parties and coalitions over small parties due to strategic voting. In comparison, the Sainte-Laguë method, reduces the disproportional bias towards large parties and it generally has a more equal seats-to-votes ratio for different sized parties. The axiomatic properties of the D'Hondt method were studied and they proved that the D'Hondt method is a consistent and monotone method that reduces political fragmentation by encouraging coalitions. A method is consistent if it treats parties that received tied votes equally. By monotonicity, the number of seats provided to any state or party will not decrease if the house size increases.