Estimating parliamentary composition through electoral polls

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