When Sleeping Beauty First Awakes

Ever since its introduction, the Sleeping Beauty Problem has been fought over by the halfers against the thirders. We distinguish three interpretations of the original problem as described in Adam Elga's seminal paper on the subject. Elga's intended interpretation leads to the position of the thirders; but the other readings result in that of the halfers. We show that all three of these results can be obtained by making use of objective probabilities in a four-dimensional rather than a threedimensional space. Our reasoning avoids various problems, not only of Dutch Book and other subjectivist approaches, but also of earlier treatments in terms of objective probabilities.