Here is Scalia's: "the Due Process clause provides no substantive protections against 'excessive' or 'unreasonable' awards of punitive damages."
I have read that after every case(Gore vs. Bush being the exception) heard before SCOTUS all nine justices have lunch and basically discuss the case and vote there. A Justice is then decided to write the majority opinion and a Justice is decided to write the dissenting opinion.
Scalia and Thomas's dissent can placate the absolutist word "Constitutionalist" Libertarians, while Ginsburg dissent placates the activist left.
And all in all, SCOTUS strikes down the economic damage done to this country by trial lawyers.
That's more or less right. After the initial vote is taken, The Chief, assuming he is in the majority, assigns the opinion to a certain Justice, who proceeds to write it. Dissenting opinions are usually not assigned; the Justices decide on their own whether to write one or not.
Regardless, once the opinions are drafted, they are circulated amongst the Justices who comment on the substance or whatnot. The other Justices decide if they want to join or concur and it also gives the opposing sides and opportunity to critique the other side's opinion--which produces the occasional (and often entertaining) "Battling Footnotes."