"Throw the bums out," the vernacular for incumbent fatigue, is the emotional response to the analytical dissatisfaction with the status quo.  Yet a bum can survive if a challenger can't promise a compelling vision of the new order.

Obama understands how this calculus of organization change applies to his re-election.  He knows that this election is a referendum on his record, his stewardship of the resources under his command, and how well he mitigated inherited messes.  Obama has been a failure on all three counts.  No, he has been spectacularly dreadful -- his record, stewardship, and mitigation -- leaving a legacy of despair and divisiveness. 

Thus, Obama loses the referendum.  And he knows it.

It is no surprise, then, that Obama's campaign has been devoted to framing Mitt Romney -- and Paul Ryan -- as unfit to lead the nation.  Nullification of Romney/Ryan legitimacy denies the challengers' standing to present a compelling vision of their new order.  Students of organizational behavior know that resistance against or invitation to change is a function of how well a compelling vision of the new order can be asserted and be convincing enough to outweigh the risks of dumping the status quo.

This simple mathematical formula -- (f) R = D+V (rough symbolism) -- is far from novel or profound.  Barack Obama beat John McCain because of Bush fatigue and Obama's compelling vision as the messiah.  Likewise, the 2010 Tea Party sweeps in the U.S. House and in state capitols reflected the deep unhappiness with the tax-and-spend, recklessly irresponsible fiscal policies of the Democrats.  And compelling new faces such as Marco Rubio and Scott Walker provided the vision for the safe bet in rejecting the status quo.

Of course, a few 2010 candidates failed miserably in presenting a compelling -- indeed, competent -- vision of the new order.  To wit: Christine O'Donnell in Maryland and Sharron Angle in Nevada.  Thus, resistance to change triumphed in some cases.

Sometimes, the compelling vision of the new order can be wrapped around charisma so powerful that even acquiescence with the status quo can be overwhelmed.  In 1960, Richard Nixon presented a continuation of the status quo -- "peace and prosperity" under Eisenhower -- despite a mild recession, which was largely acceptable to most voters.  But JFK was simply irresistible (aided by a few minor ballot box irregularities in Texas and Illinois).

In 1940, there was no compelling reason for the nation to re-elect FDR.  Despite FDR's soothing style and New Deal initiatives, the nation was still mired in a depression, with unemployment nearly 15%, albeit far better than when he was first inaugurated in 1933.  Some policies enacted by FDR during his second term, including higher taxes, actually made matters worse.  And he was running for an unprecedented third term.  However, voters still blamed the Republicans for the "status quo."  Wendell Willkie -- a national nobody, essentially the forfeiture candidate of the Republicans -- had no chance in competing with the dynamic persona of Roosevelt.

Ronald Reagan's landslide ouster of Jimmy Carter applied the calculus of change flawlessly.  The economy was in a shambles, the Iran hostage crisis was deeply embarrassing, and Carter projected malaise and despair.  Dissatisfaction -- check.  Reagan then painted a Hudson River School landscape portrait of America, displaying a personal style radiating trust, good humor, and boundless optimism.  Vision of the new order -- check. 

Mitt Romney and Paul Ryan need little help in convincing most Americans that the status quo can't survive.  Moreover, Paul Ryan brings high-voltage layman-friendly acumen in whipping dissatisfaction to a froth. 

But Mitt Romney now needs to assert with undeniable authority and clarity his vision about how he will fix what has caused the dissatisfaction.  Romney also needs to be convincing in that he can be trusted to be a reliable steward to defend and advance the values of the majority of Americans.

Romney has some 60 days to perfect the calculus of change.  I will guess that Romney's grades in differential equations were far better than any of Barack Obama's academic records in mathematics, higher or otherwise, judging by Obama's math skills as representative of his "57 states" remark and his omnibus illiteracy in economics. 

Yet Obama understands the calculus of electoral change, despite none of his understanding having been acquired in a classroom.  This week's Republican convention will prove whether Mitt Romney can take applied mathematics to the only level that matters.