Which these arguments is most likely to have influence the dissent of the supreme court decision that the students had the right to wear the armbands to school

You didn't provide the arguments, however, the dissent opinion in Tinker v. Des Moines dissenting opinion was that although people have free speech that does not mean that they're allowed to hold speeches wherever and whenever they want. In addition, the justice established that the school is state supported and that there should be no opposition to state policies from schools that are federally funded.

The answer is installation.