4.15 D’Hondt method

Remark: the result of D’Hondt apportionment \(\equiv\) the result of Jefferson apportionment

• In D’Hondt (DH) algorithm, we use the following formula to distribute seats:

\[ quotient_{DH} = \frac{v_i}{s^*_i + 1} \]

where: \(v_i\) is the total number of votes that \(i-\)th party received and \(s^*_i\) is the number of seats that a party has been allocated so far, initially 0 for all parties.

• D’Hondt method requires (see the example in: https://docs.google.com/spreadsheets/d/1QslIHty8AT_R7nLXiliYg4QQE2f0b7WqjWaG-eKFziw/edit?usp=sharing) the total numbers of votes received by parties to be divided first by one, then by two, then by three, and so on as necessary. The resulting quotients are then ranked by size, with the order determining entitlement to the seats available.