The figure below shows the posterior densities for our beliefs about each of the justices’ ideal points, updated through the most recent vote cast. Our model restricts former Chief Justice Rehnquist to have an ideal point of 1 and former Justice O’Connor to have an ideal point of 0. This makes it easy to get rough comparisons between them and the current justices. We added verticle lines at 0 and 1 to show the positions of Justice O’Connor and Chief Justice Rehnquist, respectively.
The more the densities for two justices overlap, the less able we are to say for sure which is more conservative and which is more liberal. For some justices, however, we are virtually certain about their ranking relative to their colleagues. We can be almost certain, for example, that Justices Thomas is more conservative than the other justices.