Different
apportionment methods such as
Sainte-Laguë method and
D'Hondt method differ in the seats-to-votes ratio for individual parties.
Seats-to-votes ratio for Sainte-Laguë method The Sainte-Laguë method optimizes the seats-to-votes ratio among all parties i with the
least squares approach. Disproportionality, the difference of the parties' seats-to-votes ratio and the ideal seats-to-votes ratio for each party, is squared, weighted according to the vote share of each party and summed up: error = \sum_i {v_i*\left(\frac{s_i}{v_i}-1\right)^2} It was shown that this error is minimized by the Sainte-Laguë method.
Seats-to-votes ratio for D'Hondt method The D'Hondt method approximates proportionality by minimizing the largest seats-to-votes ratio among all parties. \delta^* = \min_{\mathbf{s} \in \mathcal{S}} \max_i a_i, where \mathbf{s} is a seat allocation from the set of all allowed seat allocations \mathcal{S}. == Notes ==