Our estimation technique allows us to make probability statements about our beliefs regarding justices’ locations. We update these beliefs after every vote cast, learning more and more about the likely location of the justices’ ideological positions. The scale is set so that former Justice O’Connor and Chief Justice Rehnquist have ideal points at 0 and 1, respectively.
The graph below displays 95% credible intervals for Justice Alito and Chief Justice Roberts, updated after each vote. We can be 95% certain that these ideal points are located in each of these credible intervals. Note that the graph begins when Chief Justice Roberts joins the court. The credible intervals for Justices Alito, Sotomayor, and Kagan do not appear until each begins casting votes.
As more and more votes are cast, we gain more information about the Justices’ ideal points and our credible intervals shrink, indicating our increased certainty regarding their positions. The dots in the center of the intervals represent the mean of our posterior, which can be thought of as our “best guess” at a given point in time about the Justice’s ideal point.