Ethos

You'd think that Supreme Court Justices don't have to use rhetoric in writing their decision. After all, they're not writing to persuade anyone; the decision's already signed, sealed, and delivered.

You'd especially think the justices didn't have to use ethos as a rhetorical technique. They're the Supremes—they've already established their credibility and expertise. But they do it anyway, citing court cases to show the extent of their (or their clerks') knowledge and to lend credibility to their decisions.

The Miranda v. Arizona text is all about rights and how people should be treated. The text also uses ethos to persuade because both the majority opinion (written by Earl Warren) and the dissents (by Harlan and White) include appeals to what is right and wrong. Both sides believe that they've got the moral high ground, that they're on the side of truth, justice, and the American way.

Pathos

At the same time, the text does include appeals to emotions. For example, there's Warren's warning about how allowing police misconduct would be "contagious"; Harlan's use of the grandiose Temple imagery and his "astonishment" at the court's decision; White's statement that "In some unknown number of cases, the Court's rule will return a killer, a rapist or other criminal to the streets and to the environment which produced him, to repeat his crime whenever it pleases him" (WhiteDissent.IV.9). These guys are pretty passionate about their opinions.

It's All About the Logos

Ultimately, the Opinion and Dissents appeal to logic and reason to convince. This is presumably what the justices have been doing during their deliberations: reviewing older cases to look for precedent; pointing out logical fallacies in each other's arguments; suggesting what a rational person might do or believe in a certain situation.

Here's an example from White's dissent:

In view of the statistics on recidivism in this country, and of the number of instances in which apprehension occurs only after repeated offenses, no one can sensibly claim that this aspect of the criminal law [taking criminals off the streets] does not prevent crime or contribute significantly to the personal security of the ordinary citizen.

Secondly, the swift and sure apprehension of those who refuse to respect the personal security and dignity of their neighbor unquestionably has its impact on others who might be similarly tempted. That the criminal law is wholly or partly ineffective with a segment of the population or with many of those who have been apprehended and convicted is a very faulty basis for concluding that it is not effective with respect to the great bulk of our citizens, or for thinking that, without the criminal laws, or in the absence of their enforcement, there would be no increase in crime. Arguments of this nature are not borne out by any kind of reliable evidence that I have seen to this date. (WhiteDissent.IV.5)

White seems to be saying, "Seriously guys, look at the evidence. Use your common sense."

We all hope that appeals to reason are the primary way these folks present their arguments to the world in the written decision. We don't want to think that our emotions are being manipulated or that we have to accept an Opinion just because the writer is the Chief Justice or a smarty-pants. But we've seen how two justices can look at the same fact and come to wildly different conclusions, so there must be more to it than just rationality.