You would be best advised to not oversimplify the dynamics of the Supreme Court.
Traditionally, one would say Breyer, Souter, Ginsburg, and Stevens are liberals, Roberts, Alito, Souter, and Thomas are conservatives, and Kennedy is usually conservative but often votes liberal. (Or, if you’re really conservative yourself, you think Kennedy usually votes liberal but sometimes votes conservative.) But the breakdown of the Justices and the way they look at things is much more complex and nuanced than “liberal-conservative” and this simplistic way of looking at the law at its highest level is dangerously inaccurate.
This case is an example of that. The question: the scope of a punitive damage award against the big tobacco companies for contributing to a man’s death from lung cancer. The breakdown: Stephen Breyer wrote the majority opinion, joined by Chief Justice Roberts, Anthony Kennedy, David Souter, and Samuel Alito. Dissenting were Ruth Bader Ginsburg, and joined by John Paul Stevens, Antonin Scalia, and Clarence Thomas; the primary dissent was written by Justice Ginsburg and Justices Scalia and Thomas joined her opinion. The entire slip opinion is reasonably short, and I will probably be using it in my future classes because it’s much shorter than the State Farm v. Campbell case I have been for the purpose of describing the modern method of determining punitive damages.