Even when the economy is terrible, when the incumbent Democratic president has not been able to demonstrate success on job creation or growth, and even when the standard of living for Americans is declining on his watch, the country will choose a Democrat “who cares about the problems of people like me” over the Republican. That alone is enough to make Republican heads spin for some time.

Many established beliefs about presidential politics have been proved false by Obama’s re-election: The idea that, when unemployment is above 7 percent, incumbents fail; The notion that incumbent presidents who are re-elected always increase their percentage of the vote over their first race; The idea that late deciders break for the challenger; The belief that if majorities say the country is on the “wrong track,” the incumbent will be defeated. All wrong.

The problem with all of these so-called laws of politics is that they are based on a tiny sample. There have only been 20 presidential contests between 1936 (the year these “laws” are usually dated from) and today. That’s too small a data set from which to glean reliable trends, far less iron laws of politics.

Romney made his share of mistakes. It’s possible that if he hadn’t alienated Hispanic voters during the primaries by his harsh anti-immigration stance, if he hadn’t committed the “47 percent” blunder, and if he had more effectively rebutted the Obama smear campaign against him as a rapacious capitalist who was willing to inflict unemployment on thousands to increase his own and his shareholders’ profits, he might have pulled out a victory.

But it’s also true that Romney had many strengths, and Obama had many weaknesses. One lesson for Republicans in this defeat (beyond the issue, addressed by this column before, of immigration) is a familiar one that we must examine anew: The Republican message of free enterprise, self-reliance and individual initiative is a harder sell than the Democratic message of “Let the government take care of you.”

This is particularly true among single women. Romney won male voters 52 to 45 percent, but he lost women 55 to 44 percent. While Romney prevailed among married women by 53 to 46 percent, Obama’s margin among single women was a crushing 68 to 30 percent. Adding to the gloom for Republicans, fewer than half of American households now feature a married couple. The illegitimacy rate is 40 percent. And the women’s vote has been increasing as a share of the total for the past several election cycles. In 1980, women were 50 percent of the electorate. This year, they were 54 percent of voters.

The decline of marriage is far more than just a political problem for Republicans. Unless reversed, it may represent the unraveling of our civilization. But it is also a political problem. The Democrats’ message to single women is simple: We will give you free stuff. Free birth control. Free medical care. Welfare payments for your children if you are poor. Food stamps. The whole welfare state package. Women want security above all. You don’t have to be a political wizard to sell that message. If it’s not Santa Claus, it’s certainly Mr. Rogers. Ironically, the worse the economy gets under Democratic governance, the more single women cling to Democrats to protect them from the consequences of that failure.

A Republican has the much more demanding challenge — to convince voters that smaller government and more free enterprise will improve their lives, their incomes and therefore their security. A good paying job is far superior to even the most lavish welfare benefits. That message has the advantage of being true, but it just may require a bit of political genius to sell it effectively.

That’s not to say it cannot be done. If Republicans can find a candidate who conveys the requisite concern for the struggles of the ordinary person, whose personal story is not one of privilege, who conveys a Kempian enthusiasm for the glories of free markets and free peoples and who is pro-immigrant, that person could win. It may be Marco Rubio. There are other possible contenders: Scott Walker, Bobby Jindal, Nikki Haley, Ted Cruz and Susanna Martinez all spring to mind.

To be a successful Republican requires more brains and imagination than to be a successful Democrat. Fortunately for the party and the country, we have a deep bench.