From a psephological perspective, there are two different ways of looking at Tuesday’s presidential election results. Psephology, of course, is the science–or at least wannabe science–of analyzing elections.

The first way is not so bad for Mitt Romney. It reminds us that it’s hard to beat an elected incumbent running for re-election. From 1900 to 2004, a total of 14 elected incumbents have sought an additional term, and 10 of them won. And now, of course, counting 2012, it’s 11 successful re-elections out of 15 attempts. It’s simply not often that a president loses a re-election bid; a partisan change in the White House usually comes when there’s no incumbent running.

Moreover, since 1896, only once has a president, and his party, been turned out of office after only four years. That was Jimmy Carter, who lost his re-election bid in 1980, thus returning Republicans to the White House after only a four-year exile. The other incumbents running for re-election who lost–William Howard Taft, Herbert Hoover, and George H.W. Bush–were all part of a string of incumbents for their party. In their cases, the public had grown tired of the incumbent party, as well as the incumbent himself. Only Carter was a single-termer both for himself and for his party–that’s Carter’s own claim to electoral ignominy.

So by that reckoning, we can ask: was Barack Obama, in 2012, as weak of an incumbent as Jimmy Carter in 1980? And the answer, simply, is “no.” Obama’s personal approval ratings were 10 points higher than Carter’s, and the “right-track/wrong direction” poll question–which once showed a 2:1 “wrong direction”–had crept up to a manageable single-digit minus.

And interestingly, Obama is the first president since Woodrow Wilson in 1916 to win a second term by a narrower margin than in his first term.

Okay, so that’s not so bad.

The second way is harsher on Romney. The economy is the Number One issue for Americans, and Romney was supposed to be Mr. Fix-the-Economy, yet the voters didn’t buy it. No president has won re-election with unemployment so high since Roosevelt in 1940, and FDR could at least claim to have lowered it substantially since he first took office. Yet Obama won anyway. Maybe running the Bain guy wasn’t the best way to capitalize on the voters’ economic discontent.

Moreover, as many analysts have noted, if today’s unemployment is measured by the labor-force participation rate–that is, the ratio of adults over 16 in the workplace–the unemployment picture looks far bleaker, in the double digits. So it would have been a worthwhile project for the GOP to elaborate more on the true dimensions of unemployment. But that’s the sort of education effort that had to begin, party-wide, years ago–during the campaign was too late.

In addition, Republicans need to think more about better approaches on other bread-and-butter issues, including Medicare. And not just “reforms” in Medicare that most seniors regarded as budget cuts, but reforms that could mean actual improvements in senior health, and public health. After all, healthier people cost less than unhealthy people.

Indeed, the healthcare equation has two halves: the healthcare-finance half and the healthcare-science half. Yet in Washington policy circles over the past few decades, the focus has been almost entirely on the first half, finance. But we might ask ourselves: when we’re sitting in a doctor’s office, what are we most worried about? The cost of the care? Or whether that care–or cure–is even available? That is, do we come away from the medical office with our bills covered? Or a clean bill of health? Which would you rather have?

As I have written here before, Romney would have been good a choice to put a national focus on, say, Alzheimer’s Disease–which is presently incurable. Of all Romney’s strengths and weaknesses, even his critics agree that he is inordinately effective at getting people and resources into play to solve a problem. And yet he chose not to display that strength by seizing the Alzheimer’s issue, or any other tangible health issue, such as, say, using new advances to fully rehabilitate Wounded Warriors.

So sure, there will be a lot of time spent analyzing all of Romney’s missed opportunities. And note to future GOP presidential candidates: It’s always better to be for something–something tangible and positive and life-affirming.

Indeed, Republicans need to reflect on the fact that they have now lost four of the last six presidential elections. And if we measure the popular vote only, the GOP has lost five of the last six. This losing trend is not unprecedented–Republicans lost five in a row in the ’30s and ’40s–but it’s surely a flashing warning light for today.

Over the first 13 decades of its history, from 1860 to 1988, the GOP won 21 of 33 presidential elections. The general sense that Republicans were the natural occupants of the White House gave rise to Chris Matthews’ formulation that the Republicans of those days were the “daddy party,” the party of executive-branch governance, while the Democrats were the natural “mommy party,” the party of legislative-branch access and voice.

But now, not so much, as the election results show. Over the last six elections, the GOP has averaged approximately 43.5 percent of the popular vote. So what does that say about Republicans on the national stage?

To put it mildly, considerable discussion on these points will come–from all quarters.

As for other elections yesterday, the Republicans, who had hoped to win back the US Senate in 2012, now find themselves having lost seats. More considerable discussion is to come about that, too, specifically, how the party recruits and nominates candidates.

The Republicans had a better night in the House, of course, and so now Speaker John Boehner continues his reign as the only Republican with real power on the national stage. Boehner thus has his own no-tax-increase mandate to take with him into the “fiscal cliff” negotiations.

A few other points:

The engine of social liberalism–or, if one prefers, libertarianism–keeps chugging along. Proponents of gay marriage won popular referendum victories in Maine, Maryland, and Washington State. And marijuana legalizers won similar victories in Colorado and in the same Washington State.

Oh, and about New Jersey governor Chris Christie. In a close election, any observer with a point to make–or a bone to pick–can fairly say that any one particular factor was decisive. And so it is with Christie, who gave Obama a hand–a big hand–in the last week of the campaign in regard to Hurricane Sandy recovery. So is Christie now going to be regarded as a sterling exemplar of bipartisanship? Or a blackened example of party disloyalty? It depends on who you ask, of course, yet the overall answer from the country will help set the tone of national politics in the coming years.

Indeed, since bipartisanship works both ways–Christie’s help for Obama is Obama’s help for Christie–it’s a safer bet now that Christie will be re-elected next year. And so Christie will continue to be a big figure on the national stage, of both admiration and obloquy.

Finally, Pinkerton’s Principle of Political Regression tells us that while it’s never as good you hope, it’s also never as bad as you fear. And so conservatives, fearful of a second Obama presidency, can be cheered at the thought of Republicans holding the House. As they say in D.C., “The President proposes, and the Congress disposes.”

So while Boehner will be under enormous pressure to “grow in office”–that is, cave in to Beltway pressures–the Speaker and his legion should remember that the American people seem to like divided government and all that such a dispensation entails.

In the 67 years since the end of World War Two, one party has controlled the White House and both chambers of Congress for just 28 years; in the other 39 years, power was divided. And now, for at least another two years, it will divided again. So maybe the public thinks that gridlock is bad, but unchecked power for anybody, Americans believe, is worse. So once again, yesterday at the polls, the American people got what they wanted.

The re-elected 44th President has a perfect right to feel good about things this morning, and his mind is no doubt filled with potential legacy-builders. Yet history shows that second-termers have a way of hubristically over-reaching. If so, the political system–and the Constitutional system–is ready for that challenge.

James P. Pinkerton is a contributor to the Fox News Channel and a TAC contributing editor. Follow him on Twitter.