We describe a novel language-independent approach to the task of determining the polarity, positive or negative, of the author's opinion on a specific topic in natural language text. In particular, weights are assigned to attributes, individual words or word bi-grams, based on their position and on their likelihood of being subjective. The subjectivity of each attribute is estimated in a two-step process, where first the probability of being subjective is calculated for each sentence containing the attribute, and then these probabilities are used to alter the attribute's weights for polarity classification. The evaluation results on a standard dataset of movie reviews shows 89.85% classification accuracy, which rivals the best previously published results for this dataset for systems that use no additional linguistic information nor external resources.