It looks and feels like a presidential contest, but at times it sounds like a national experiment in mind reading — a great guessing game about the country’s future.

The two campaigns insist that voters are about to make a momentous decision between sharply divergent visions for American life. But the candidates have largely failed to provide specifics about those visions, leaving voters to guess about the consequences of their choice. Almost half the voters say they want to know more about President Obama’s plans for a second term, and almost two-thirds want to hear more about what Mitt Romney would do differently.

Romney has declined to reveal some crucial details about his tax plan. If he did, Romney’s campaign has said, it would be harder to get Congress to go along with them later. “We want to get it done,” said his running mate, Rep. Paul Ryan (R-Wis.).

Obama is equally vague about his second-term plans. Obama sometimes sketches his agenda as a list of questions, which hestill needs to answer. “How [can] we continue to build an economy that works for middle-class families?” he said last week in Tampa, reeling off five questions for himself.

It is still possible to make a few educated guesses about how Romney or Obama might change everyday life in the next four years. But only a few. In recent polls, 49 percent of voters said they wanted more details from Obama, and 63 percent wanted the same from Romney.

In an interview broadcast Sunday night on “60 Minutes,” Romney faced questions from CBS’s Scott Pelley about his refusal to divulge more details of his tax plan.

“The devil’s in the details. The angel is in the policy, which is creating more jobs,” Romney said.

“You have heard the criticism, I’m sure, that your campaign can be vague about some things. And I wonder if this isn’t precisely one of those things?” Pelley said.

Romney said, in essence, that vagueness is necessary sometimes. “You don’t hand [lawmakers] a complete document and say, ‘Here, take this or leave it.’ Look, leadership is not a take-it-or-leave-it thing,” he said.

The vagueness at the heart of this campaign seems a reaction to its overall gloomy circumstances. The economy is lagging, the capital is gridlocked, and the country is grappling with a growing debt. All the proposed long-term solutions — cutting spending, increasing tax revenue — are likely to make a huge block of people mad.

The campaigns may have calculated that it’s better to let people wonder about their intentions rather than release details and confirm those worries.

“In a sense, they’re afraid to come up with solutions. Because any solutions will anger voters,” said Robert N. Roberts, a professor at James Madison University who has written an encyclopedia of presidential slogans and promises.

“The campaigns really have no choice,” Roberts said, but to say, “ ‘You may not like me, but the other guy is worse.’ ”

For anyone trying to forecast the impact of November’s election, the best place to start is health care. That’s because there’s already a law on the books — the 2010 health-care overhaul — that will bring noticeable changes in the next term.

Now, to make these changes happen, all Obama has to do is win.

In 2014, for instance, most Americans will be bound by the mandate to purchase health insurance or pay a fee. At the same time, insurance companies will be banned from denying coverage for pre­existing conditions. And insurers will be prohibited from imposing annual dollar limits on benefits.

If Romney is elected, by contrast, he has promised to seek the law’s repeal and allow individual states to craft their own health-care plans.

It’s not a sure bet that he would succeed. Romney would probably need help from Republican majorities in both houses of Congress. If he were to succeed, the much-maligned mandate would vanish.

But so would more well-liked pieces of the law, one of which allows children to remain on their parents’ health-care plans until age 26 (and which Romney has indicated he might want to restore in a future health-care bill). Another bans insurance companies from imposing “lifetime caps” on coverage.

“There are many people in the country who might be happy to see the Affordable Care Act go away as an ideological” symbol, said Drew Altman, president of the Kaiser Family Foundation, using the law’s official name. “But there are going to be very few people in the country who would be happy to see its popular benefits go away.”

Another potential impact of the election: If Obama survives for a second term, so too will the 2010 Dodd-Frank financial regulation law.

Next year, the government is scheduled to implement parts of that law that will require mortgage lenders to make sure borrowers can afford the loans they’re taking. Another piece will protect from foreclosure borrowers who are trying a loan modification.

Romney wants to repeal the broader law and replace it with more “streamlined” regulations. Bankers say that would help consumers by freeing banks from overly burdensome regulations and paperwork. It would mean those new mortgage laws would disappear, along with the Consumer Financial Protection Bureau set up to enforce them.

In Congress, however, getting rid of Dodd-Frank might prove even harder than repealing the health-care law.

Beyond the subjects of health care and financial regulation — the two areas in which a law is already on the books — it gets even harder to forecast the impact of November’s choice.

For Obama, that’s because many of his ideas for the next term have already been proposed, and shot down, during his first term.

His “Buffett rule,” which would mean tax increases for some people earning more than $1 million, fizzled in Congress. As did the Paycheck Fairness Act, which would give a company’s employees more power to sue for punitive damages for wage discrimination between men and women. As did the American Jobs Act, a $447 billion bill to invest in infrastructure and hire teachers and firefighters.

For those ideas to work in a second term, Obama would probably need Democrats to hold the Senate and take the House. At this point, that looks unlikely.

In his own “60 Minutes” interview Sunday, Obama said Republicans might show a new “spirit of cooperation” if they do not defeat him in November.

Romney, by contrast, has proposed a slew of broad ideas. But, in many cases, he has declined to fill in key specifics about how those ideas would work.

Romney wants, for instance, to cut $20 billion from federal spending on “Day One” in office. Romney says he would exempt the military from those cuts. But he hasn’t said exactly what programs would be hit, or how hard.

On tax reform, Romney has laid out some pieces of an ambitious plan. He wants to eliminate the “death tax,” end capital gains taxes for people making less than $200,000 and cut everybody’s marginal tax rate by one-fifth across the board.

But here’s the missing piece: Romney also wants to slash tax loopholes and special breaks so that there isn’t an overall drop in the amount of tax money coming in. That would be a difficult task, because each loophole usually has a strong lobbying group ready to defend it.

And, for now, Romney and Ryan won’t say which ones they would go after.

“We don’t really know what Romney would do, because we only know half of his plan,” said Roberton Williams of the nonpartisan Tax Policy Center. The center estimated that Romney’s plan would raise taxes for 95 percent of Americans.

Romney said that was wrong. But he told ABC’s George Stephanopoulos this month that he wouldn’t say what was right. As governor in Massachusetts, Romney said, he’d learned it was bad politics to say, “Here, this is my bill. This is the way I want it.” Instead, Romney said, “You lay out your principles.”