So Washington University has its consolation prize — after four election cycles of hosting presidential debates, the school will next year instead hold a battle of No. 2 hopefuls.

But who will be the vice presidential nominees duking it out on the Danforth Campus? This could be a fun parlor game, especially as political news slows down in the run-up to Thanksgiving.

For the sake of brevity, let’s assume for now that one of the two front-runners in each party get the nod: That would be Rudolph Giuliani and Mitt Romney for the Republicans, and Hillary Clinton and Barack Obama for the Democrats. (With apologies to Mike Huckabee and John Edwards.)

Here’s my best guesses for who each of those candidates would pick for the bottom of their ticket.

• Clinton: Should the New York senator get the nod, it’s hard to imagine her picking anyone other than New Mexcio Gov. Bill Richardson. The former envoy to the United Nations has foreign policy credentials, and, as the only Latino running for president, credibility on immigration. Another potential Clinton running mate is Indiana Sen. Evan Bayh. The former Hoosier State governor could be framed as a Midwestern moderate, a sturdy counterbalance to the potentially polarizing “Clinton factor.”
• Obama. This is a tough one, because there has never been a candidate quite like Obama before: An African-American whose charisma and poise on the stump catapulted him from state legislator to White House hopeful in barely three years. The only name that comes immediately to mind is Joe Biden. The senior senator from Delaware has a bit of brash personality — which caused him trouble early on with Obama — but he has the foreign policy experience that Obama lacks. Biden’s popularity in the dense Northeast corridor may also be helpful.    
• Giuliani. Three words: I heart Huckabee. Selecting the former governor of Arkansas would bolster Giuliani’s appeal with social conservatives, and signal that he is willing to work with other Republicans who don’t necessarily share all of his beliefs.
• Romney. Another difficult choice, in part because Romney already has conservative appeal, and name-recognition in the Northeast. Here’s a wildcard: California congressman Duncan Hunter, a Vietnam veteran and former chair of the House Armed Services Committee. He has a son in Iraq, and lives near the Mexico border, meaning he can speak personally about two key topics — the war and immigation.

Those are my thoughts — check back in eight or so months to see how far off I was. Until then, feel free to put your own guesses in the comments below.