The paper has two aims. First, it is a presentation of Satoshi Kanazawa's model of voting behaviour, a theory of voting based on principles of stochastic learning. The model, drawing on Michael W. Macy's general theory of stochastic learning, is an attempt at resolution of the so-called 'paradox of voter turnout', one of the most inconvenient puzzles of rational choice theory. Second, in the article Kanazawa's main propositions are applied to the phenomenon of participation and abstention in the parliamentary elections of 1991 and 1997 in Poland. Using Polish General Social Surveys data the author presents evidence suggesting partial suitability of Kanazawa's theory for the analysis of electoral participation and abstention in Poland. The model, emphasising past voting behaviour as a determinant of participation and abstention, has, however, serious limitations which he shows using the case of the 1997 parliamentary election. At the same time, referring to the research on the so-called 'bandwagon effect', the author proposes an extension of Kanazawa's theory. The research on the 'bandwagon effect' indicates that voters may also refer to future elections and this may distort the process of stochastic learning. In this context, Kanazawa's proposition appears incomplete and unfinished which makes room for further research. .