Estimating parliamentary composition through electoral polls

Any electoral system has an electoral formula that converts vote proportions into parliamentary seats. Pre-electoral polls usually focus on estimating vote proportions and then applying the electoral formula to give a forecast of the parliament's composition. We here describe the problems arising from this approach: there is always a bias in the forecast. We study the origin of the bias and some methods to evaluate and to reduce it. We propose some rules to compute the sample size required for a given forecast accuracy. We show by Monte Carlo simulation the performance of the proposed methods using data from Spanish elections in last years. We also propose graphical methods to visualize how electoral formulae and parliamentary forecasts work (or fail).