For the past few years, Elena Kagan, former dean of Harvard Law School, and Harold Hongju Koh, former dean of Yale Law School, have led parallel lives.

Appointed to lead two top law schools only a year apart, they both left academia last year to take prominent posts in President Barack Obama’s administration — Kagan as solicitor general, Koh as legal adviser to the State Department.

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Now, just a few weeks after Supreme Court Justice John Paul Stevens announced he will retire this summer, Kagan’s name has quickly ascended to the top of media shortlists to succeed him. Koh’s name, meanwhile, has appeared on fewer shortlists — even though, in the past, Koh was often regarded as a likely pick for the Supreme Court and has been called one of the “most brilliant” legal minds of our era.

Kagan’s advantages as a nominee for the position seem to line up with what critics have identified as Koh’s problems. Richard Ford, a professor at Stanford Law School who got his law degree at Harvard and served as a fellow there before working at Stanford, said Kagan is widely perceived as a uniting figure who created consensus during her time as dean at Harvard. Her views, though liberal, do not seem to draw the ire of conservatives, Ford said.

But Koh has taken flack from conservatives for his liberal stances on a wide array of issues. Most controversially, Koh has espoused a judicial philosophy that would allow international law to inform decisions made in American courts. Conservatives fear that such a philosophy will “soil” American constitutional values and eliminate “American exceptionalism,” said Richard Albert ’00 LAW ’03, assistant professor of law at Boston College Law School and a contributor to Politico, an online political newspaper. Kagan has not taken a stance on this philosophy, also known as “transnationalism.”

“It’s like waving a red flag at a bull, to take the position [Koh has] taken,” said Brian Leiter, a professor at the University of Chicago Law School and a prominent legal blogger. “Elena Kagan has the great advantage of having very few discernible positions. Koh is the more distinguished scholar, but that’s obviously only a very minor consideration.”

Kagan declined to comment through a spokeswoman, and Koh did not respond to a request for comment.

Indeed, Kagan’s lack of a clear left slant has made her far more palatable to conservatives, and one of her major pieces of scholarship about executive power falls in line with the opinion of George W. Bush ’68, Albert said. Kagan’s views on the unitary executive theory, enumerated in a 2001 article in the Harvard Law Review titled “Presidential Administration,” pushed for stronger presidential control of the executive agencies.

While Albert said Kagan does line up with liberal activists on “bread and butter” issues — including opposition to “Don’t Ask, Don’t Tell” — she is far more of a centrist than Koh, Albert said.

“He would be the paradigmatic liberal lion that liberal activists are looking for, and she probably would not,” Albert said.

As Obama attempts to move forward for his domestic agenda, it is possible that he will not nominate a “liberal lion” like Koh for fear of the fight that might ensue, said Anupam Chander, a former visiting professor at Yale Law School and the University of Chicago Law School who now works at the University of California, Davis School of Law. But while it is one thing, Chander said, to nominate a jurist with a clear record of centrist positions, it is another thing entirely to nominate someone like Kagan, whose positions remain unclear.

Chander said he worries Obama, in considering Kagan to be a nominee, is in danger of making the same mistake George H. W. Bush ’48 made in nominating David Souter to the Court. Though Bush had become convinced that Souter, despite his light record of legal scholarship, held the views of a moderate conservative, once Souter reached the Court, he did not make the decisions conservatives expected, Chander said.

“Here’s the question: Does the president say, ‘Oh, I know this person well enough that I believe she’ll be a solid progressive for the next two generations of people who come after me?’ ” Chander said. “I think it would be remarkable hubris of the president to feel that he had, through personal conversation, gained enough insight into how a person might rule over the next 40 years, and I hope he doesn’t have that hubris.”

But according to Harvard Law professor Mark Tushnet LAW ’71, the Souter example does not apply to Kagan’s situation because Souter never claimed to be a solid conservative. Instead, Souter was known to be a moderate Northeastern Republican, Tushnet said.

Regardless, Tushnet said, Kagan is more clearly liberal than Souter was conservative.

“If you look at what Elena Kagan has said and done, she’s a standard, centrist liberal Democrat,” Tushnet said. “I don’t think she’s actually a conservative in liberal’s clothing.”

Further bolstering Kagan’s candidacy may be her gender — both Chander and Albert said Obama is likely to nominate a female justice now, not only because several of the most viable candidates are female, but also to correct what Chander called a “grave imbalance” on the Court and to prevent himself from being compelled to nominate a female upon the retirement of Ruth Bader Ginsburg. When Stevens retires, Ginsburg, 77, will be the oldest justice on the Court and will likely be the next to retire, Albert said.

All this speculation aside, none of those interviewed said they expect Kagan or Koh to be Obama’s nominee. Chander said he thinks Diane Wood of the Seventh Circuit Court of Appeals will get the nod; Albert, too, said he considers Wood a viable candidate, and also listed Leah Ward Sears, the former chief justice of Georgia’s Supreme Court, as a contender. For his part, Leiter said he thinks current Secretary for Homeland Security Janet Napolitano will be the nominee.

Current news reports indicate that Obama will nominate Stevens’ replacement sometime in May.