Some remarks on game theoretical approach to prediction of formation of parliamentary coalitions. The case of Polish elections of 1997

In this paper we apply a game theoretical approach to an analysis of results of pre-election polls in Poland. The last parliamentary elections in Poland took place in September 1997. We analyse the results of three groups of polls using the method of Shapley value of games with a priori unions. The Shapley value of games with a priori unions (also called the modified Shapley value) was introduced by Owen. Next, he and Carreras applied this method to analyse the Catalonian Parliament (1988) and the Euskarian Parliament (1996). The present author used this method as well to analyse selected elections and pre-election polls in Poland. I observed that the modified Shapley values for games based on results of elections and on results of polls were similar. Therefore, the hypothesis arose that modified Shapley values could be used to predict formation of parliamentary coalitions. In this paper we examine this hypothesis in the case of pre-election polls carried out prior to Polish parliamentary elections of 1997 in 1996 and 1997. The effective results of elections are shown in the paper and compared to the results of polls. The analysis does not apply to the actual election results. The conclusion is drawn from the analysis that the hypothesis mentioned may be true for these polls, which are made shortly before elections. If the period between a poll and the elections is sufficiently long, the modified Shapley values strongly depend on the construction of a poll. Furthermore, Shapley values and modified values for polls are open to an influence exerted by the introduction of a new party. The generalized paradox of size is observed. Hence, whether this method can be used for prediction long before elections is an open question. Mathematical definitions and properties of Shapley values of games with a priori union (modified Shapley values) are presented in the appendix.