If Michael Bloomberg makes an Independent White House bid, Vice President Cheney and Sen. Joe Lieberman (ID-Conn.) could end up choosing the next president of the United States.

That’s just one of numerous bizarre scenarios, thanks to quirks in the Constitution, that could occur if New York’s billionaire mayor throws his hat into the ring.

If the newly Independent Bloomberg with his deep pockets and bipartisan appeal can manage to win a purple state or two, like Florida, he could prevent both the Democratic and Republican nominees from garnering 270 votes in the Electoral College, which would initially throw the decision to the House of Representatives.

Under the 12th Amendment, the House would vote by state delegation, not by individual Member, and at least 26 states must vote for the winner. They must choose one of the top three vote-getters in the Electoral College tally.

On paper, Democrats would hold an advantage, because they control 26 of 50 state delegations, versus 21 for the Republicans, but it is such a slim advantage that a sudden death or a single defection could create a deadlock. Before the 2000 White House election was settled, for example, then-Rep. Connie Morella (R-Md.) angered her GOP colleagues when she mused that she could wind up siding with Democratic nominee Al Gore over Republican George W. Bush in a House vote because her district had supported Gore so heavily.

That’s where the Senate comes in. In the case of an electoral stalemate, the Senate would choose the vice president from among the top two veep candidates, and if the House remains deadlocked on its presidential vote, the vice president-elect would become president.

So if Lieberman or a single Democrat were to cross party lines and vote for the Republican vice presidential nominee, or if a Democratic Senator were to die and be replaced by a Republican, the Senate could deadlock 50-50. And Cheney would cast the tie-breaking vote and choose the next president.

Democratic Congressional Campaign Committee Chairman Chris Van Hollen (D-Md.) laughed about the scenario.

“I think that Bloomberg should weigh that very carefully,” he said. “Does he really want Dick Cheney choosing the next president?”

There also could be an election along the lines of 1824, when Andrew Jackson won a plurality of the popular vote and the Electoral College, only to have the presidency snatched from his grasp in the House of Representatives in a deal he dubbed a “corrupt bargain.”

George Washington University law professor Jonathan Turley said the prospects of an undemocratic and messy electoral scrum show the need to ditch the Electoral College, which he called an “absurd, archaic institution,” and go to a popular vote system.

“These scenarios have always been spun out as something of a parlor game for law professors,” Turley said. “But it is a game that is not without legitimate concern. It could happen because of the dysfunctional role of the Electoral College.

“You have this bizarre system where we spend hundreds of millions of dollars trying to convince citizens to elect a candidate and hundreds of millions more trying to count the vote only to have that dead end in a system that is almost arbitrary and capricious,” Turley said.

Democrats in conservative or purple states won by the Republican nominee or Bloomberg would face the dilemma of voting for their party or for the choice of their state. And vice versa for Republicans.

And all three of the top presidential candidates could be wheeling and dealing — offering cabinet posts and the like — to try to sway votes.

All of that assumes, of course, that Bloomberg can win a state, something that has been very hard for unaligned candidates to do.

“That kind of speculation is silly,” said Rep. Barney Frank (D-Mass.). Frank said Bloomberg would have problems winning votes because of his ties to the Bush administration and his history as an opportunistic party-switcher who flipped from Democrat to Republican to get on the mayoral ballot in 2001 and is now ditching the Republican label to potentially run for president.

“He was out there campaigning for George Bush in 2004,” Frank said, adding that Bloomberg deserves some of the blame for the problems he is now railing against. “He was a strong Republican. … I don’t think he’s going to be this very plausible above-the-battle guy.”