The sad answer is there is no way to know what Mr. Romney really believes. His unguarded expression of contempt for 47 percent of the population seems as sincere as anything else we’ve heard, but that’s only conjecture. At times he has advocated a muscular, John McCain-style foreign policy, but in the final presidential debate he positioned himself as a dove. Before he passionately supported a fetus’s right to life, he supported a woman’s right to abortion. His swings have been dramatic on gay rights, gun rights, health care, climate change and immigration. His ugly embrace of “self-deportation” during the Republican primary campaign, and his demolition of a primary opponent, Texas Gov. Rick Perry, for having left open a door of opportunity for illegal-immigrant children, bespeaks a willingness to say just about anything to win. Every politician changes his mind sometimes; you’d worry if not. But rarely has a politician gotten so far with only one evident immutable belief: his conviction in his own fitness for higher office.

So voters are left with the centerpiece of Mr. Romney’s campaign: promised tax cuts that would blow a much bigger hole in the federal budget while worsening economic inequality. His claims that he could avoid those negative effects, which defy math and which he refuses to back up with actual proposals, are more insulting than reassuring.

By contrast, the president understands the urgency of the problems as well as anyone in the country and is committed to solving them in a balanced way. In a second term, working with an opposition that we hope would be chastened by the failure of its scorched-earth campaign against him, he is far more likely than his opponent to succeed. That makes Mr. Obama by far the superior choice.