The Supreme Court is the highest Federal court of this land, and the decisions that they reach, have national repercussions, yet, the way that this court is currently structured, the justices through as little as a bare majority of one vote, make new law with national implications which may indeed overturn or overrule legislative law, for this court's power reaches far beyond their mere interpretation of legislative laws through its take of our Constitution, they do indeed by their decisions and their opinions: set new nationwide law. The fact that a simple majority of justices can overturn, even long standing law, or essentially nullify the legislative actions of our congressional representatives, gives these justices an enormous amount of power, of which, decisions reached by such a court, can and do come down to factions within the Supreme Court, so that the majority of the court, can be in actual fit and form, merely representing their own personal and political viewpoints, rather than adhering to the Constitution, itself.
There are numerous examples of the Supreme Court making simple majority decisions that have had and still have profound implications for citizens of this country, such as Miranda v. Arizona, which set forth certain procedures for the police in their interaction with suspects and their rights, including specifically having to informed such that they had the right to counsel as well as to silence. So too, in the District of Columbia v. Heller, the majority of five Supreme Court justices decided that the Second Amendment did indeed apply to individuals, which enables such to keep and bear firearms. In the Citizens United v. Federal Election Commission a simple majority of the Supreme Court ruled that corporations are now permitted to spend unrestricted amounts of money to influence politics. Finally, In Bush v Gore, the Supreme Court declared that the recount ordered by the Florida Supreme Court was invalid; thereby certifying that Bush would become the next President of the United States.
If, on the other hand, a supermajority had been required on each of these foregoing Supreme Court decisions, than either there would have had to have been another justice that would have had to have been persuaded to vote with the majority, or because of this being a mere simple majority, the lack of such a supermajority would have essentially upheld the ruling of the lower court.
In point of fact, the legislative branch requires a 2/3 supermajority in order to override a Presidential veto. In addition, in order for the legislative branch to successfully amend the Constitution this requires a 2/3 supermajority vote, and to ratify an Amendment to the Constitution requires the approval of 3/4 of the State legislatures. This clearly indicates, that there are specific situations that call for a supermajority, and decisions made by the Supreme Court, should require such a Court, to overcome the same sort of supermajority hurdle, rather than to have a court, vote strictly along partisan lines or similar, which arguably is what they exactly did on Bush v Gore.
The justices that make up the Supreme Court are in theory, the wisest and most esteemed justices in this nation, but the selection of these justices, in which they are first nominated by the President of the United States, then subjected to a Senate hearing, and then confirmed or not by the Senate, indicates, that partisan politics most definitely plays a significant part as to who actually becomes a Supreme Court Justice, so that, it is absolutely no stretch of the imagination to recognize, that judicial decisions are, in fact, rendered by the partisan leanings of such justices, and therefore indicates that decisions reached by a simple majority of justices that are the final interpreter of federal law should not now, or ever, be so certified by a simple majority of such justices.