WASHINGTON Why did the Supreme Court agree in December to hear a major same-sex marriage case and then seem to think it had made a terrible mistake Tuesday when it came time for arguments?
The answer lies in the gap between two numbers. It takes four votes to hear a case and five to decide one.
If nothing else, this week's arguments provided a glimpse into the process through which the court selects its docket, one shrouded in secrecy. The arguments also cleared up most of the mystery of whose idea it had been to hear the case, a challenge to Proposition 8, California's ban on same-sex marriage.
As it turns out, it would seem that the conservative members of the court, making a calculation that their chances of winning would not improve with time, were behind the decision to take up the volatile subject.
The aha moment came Tuesday.
After Justice Anthony M. Kennedy suggested that the court should dismiss the case, Justice Antonin Scalia tipped his hand.
"It's too late for that now, isn't it?" he said, a note of glee in his voice. "We have crossed that river."
That was a signal that it was a conservative grant.
To see why, it will help to review the bidding. When the justices gathered for their private conference on Dec. 7, they had many choices.
For starters, it was virtually certain that they would agree to hear one of several challenges to the federal Defense of Marriage Act of 1996. Two federal appeals courts had struck it down, and the court almost always reviews decisions from lower courts invalidating federal laws.
The question there, moreover, was the relatively modest one of whether the federal government must provide benefits to same-sex couples married in states that allow such unions. The case did not directly concern whether there is a right to same-sex marriage in other states.
So the justices chose one case on the 1996 law, United States v. Windsor, No. 12-307.
They then confronted a second, more ambitious case, Hollingsworth v. Perry, No. 12-144, concerning whether the Constitution guarantees a right to same-sex marriage. Most observers thought the court would hold the case while it worked through one on the 1996 law, and some thought it might deny review, letting stand an appeals court decision that had struck down Proposition 8.
Instead, the court granted review in the case. That was a surprise and a puzzle. Who had voted to hear it?
One school of thought was that the court's four liberals were ready to try to capture Kennedy's decisive vote to establish a right to same-sex marriage around the nation.
That theory was demolished in the courtroom as one liberal justice after another sought to find a way to avoid providing an answer to the central question in the case. The decision to hear the case, it turned out, had come from the other side.
Scalia, almost certainly joined by Justices Clarence Thomas and Samuel Alito Jr., apparently made a twofold calculation: that their odds of winning would not improve as same-sex marriage grows more popular and more commonplace, and that Kennedy, who is likely to write the decision in the case concerning the 1996 law, would lock himself into logic that would compel him to vote for a constitutional right to same-sex marriage in a later case.
That leaves the question of the fourth vote. The most likely answer is that it was that of Chief Justice John G. Roberts Jr., though he did not sound at all pleased Tuesday to have the case before him.
There is also a chance that the fourth vote came from Kennedy himself, and his very questioning provides support for that theory.
"I just wonder," he said, sounding a little plaintive and a little angry, "if the case was properly granted."
According to "Supreme Court Practice," the leading manual on Supreme Court procedure, it is bad form for a justice who voted to deny a petition to thwart a decision on the merits.
There may, of course, have been more than four votes to grant review. Tallies are never published by the court, but they do emerge years later in the justices' papers.
The decisions are made on most Friday mornings during the Supreme Court term, when the nine justices meet in a private conference to vote on which cases to hear.
Margaret M. Cordray, a law professor at Capital University in Columbus, Ohio, who has studied the process, said it lacks most of the qualities of traditional judicial work, including deliberation, accountability and majority rule.
In examining the papers of Justices Harry A. Blackmun, William J. Brennan Jr. and Thurgood Marshall, though, Cordray said she did find "pretty strong evidence that the justices act more strategically in high-profile cases."