In my country there's an official center undertaking surveys of voting intention every 4 months. However, they provide only "direct" voting intention, and the statistics obtained are usually pretty far away from the final results in the election day (people voting right wing parties usually pretend they don't or just say they don't know what they are going to vote yet). So, if you want a good estimator of the real voting intention you have to correct the data collected (in my country it is called "cooking" the survey, but I don't know how is it called outside), using in some way the information given by the deviations in previous elections.
Do you know any paper or reference that studies this cooking corrections with some mathematical rigor? Or can explain how this corrections are developed?
There are two issues. The first is that the data contains outliers. For example some voters may be giving misleading information. This corresponds to an in accurate statistical modeling. That an assumed statistical model deviates in reality and only the amount of devations can be estimated. The whole things that I described above lie in the area of robust estimation. You can google for that. On the other hand, there might be some data which is useful however it might have been misinterpreted and misunderstood. For such a data a correction model can be estimated with some unknown parameters. For example a parameter $\theta$ which indicates the correlation between the voters vote for the right wing although they are supposed not to vote according to the survey. The number of such parameters can be increased for all possible misinterpretations. Then the model with free parameters are fitted to the outcome of the voting results. This process determines the parameters and explains the questions why? The corrected model can be re-applied in the next elections. Such a correction can be repeated and eventually the parameters which do not change its value would be the stable and consistent ones for which a singe corrections is enough. However, some other parameters will be dynamic and should be estimated after each election.