President Bush experienced something of the same phenomenon: his choice of Justice David H. Souter, thought to be a conservative, unintentionally placed on the court a solid member of the most liberal bloc.
The National Legal Center also says that, even if a judge does turn out to be conservative, the chances are that the very idea of being a conservative means that the judge will not lightly overturn past rulings, even if uncomfortable with them.
Finally, that organization says, the present court is "not as precipitously balanced as some might expect."
There was a great deal of consensus, it suggests, even in the contentious term of the court that ended in June with such sharply divided rulings as those on abortion, school prayer, homosexuals and aid to parochial schools.
Much of the speculation about the next president's opportunity to fill Supreme Court vacancies centers on three justices: Chief Justice Rehnquist, who turns 76 on Oct. 1, and Justices Sandra Day O'Connor, 70, and John Paul Stevens, 80.
The fact that none of them has given even a hint of choosing to retire has done nothing to end the speculation. So far as is known, neither Bush nor Gore has focused on lists of potential justices. But speculation is rife about what they might do.
It is commonly assumed, by outside observers of the court, that if O'Connor were to retire, the next president would have no realistic option politically but to name another woman; otherwise, the court would be left with a single female justice, Ruth Bader Ginsburg.
If Bush is elected, it is assumed that he would turn to the most ideologically conservative appeals court - the 4th U.S. Circuit Court that sits in Richmond - for future justices. One of its conservatives is Judge Karen J. Williams, 49, who was put on that court in 1992 by candidate Bush's father.
If Gore is elected, he is likely to consider an experienced female judge from his home state of Tennessee, Martha Craig Daugherty, 58, named by Clinton to the 6th U.S. Circuit Court of Appeals in Cincinnati after serving on the Tennessee Supreme Court.
Also mentioned as a possible Gore nominee is Judith W. Rogers, 61, put on the U.S. Circuit Court of Appeals in Washington, D.C., by Clinton after she had served as chief judge on the District of Columbia's highest local court.
Those speculating about other nominees by Bush or Gore believe that each would seek to become the first president to name a Hispanic justice - if that nominee won't replace a female justice.
Bush could elevate Alberto R. Gonzales, a former member of Bush's Cabinet, who he placed on the Texas Supreme Court. Gonzales, 45, has been a judge for less than a year, and that could diminish his chances of an early appointment.
For Gore, the usual speculation is that he would turn to Jose A. Cabranes, 60, now on the 2nd U.S. Circuit Court of Appeals in New York City; Clinton named him to that position.
Gore, some observers have suggested, also would consider a court nominee achieving another "first": a disabled person.David S. Tatel, 58, named by Clinton to the federal appeals court in Washington, D.C., is a widely respected judge who is blind.
There are more names circulating about potential Bush nominees than likely Gore selections.
Among others who have made it onto lists of possible Bush choices are three conservative judges in the 4th Circuit Court - Chief Judge J. Harvie Wilkinson III, 55, a Reagan appointee, and two George Bush appointees, J. Michael Luttig, 46, and a Baltimorean, Paul V. Niemeyer, 59.
Outside the 4th Circuit Court, another potential Bush nominee is a friend, Jerry E. Smith, 53, a former Houston lawyer and now a conservative judge on the 5th U.S. Circuit Court of Appeals.