Means-testing Social Security is a popular position among Republican presidential candidates this election cycle—if not among prospective voters. That means, essentially, turning the nation’s retirement system into a welfare program, targeted at those with real hardships. But how do you figure out who’s a “real” hardship case and who’s not? In fact, it’s well-nigh impossible.

When Alan Simpson and Erskine Bowles, the chairs of President Obama’s 2010 deficit commission, gave up on finding common ground with their colleagues and released their own set of deficit reduction proposal, they called for two big changes in Social Security: gradually raising the eligibility age for full benefits from 67 to 69 and upping the early-retirement age for reduced benefits from 62 to 64. They also directed the Social Security Administration to design a “hardship exemption for those who cannot work past 62 but who do not qualify for disability benefits.”

It all seemed eminently reasonable—so much so that most of our current class of Republican presidential candidates are calling for raising the retirement age and/or some form of means-testing benefits. Jeb Bush, Rand Paul, Marco Rubio, Ted Cruz, Chris Christie, John Kasich, Lindsey Graham, Rick Santorum, and Scott Walker (since withdrawn from the race) all agree on this point.

If they get their way, not only will Social Security benefits be slashed for millions, but something fundamental will have changed: our national retirement system will be transformed from a social insurance program to a welfare program. That’s in keeping with Republican ideology, which has never accepted that Social Security is anything but a disguised form of welfare: a tax transfer from affluent working people to low income retirees.

Getting there would be a lot harder than our intrepid entitlement reformers may think, however. If we take Bowles-Simpson as our case in point, then the idea, again, is to raise the Full Retirement Age (FRA) for full benefits and the Early Entitlement Age (EEA) for reduced benefits, exempting those who aren’t physically able to work from any benefits reduction. After all, that’s only fair. But how do you—or, rather, how does the Social Security Administration—decide who’s eligible for a “hardship exemption” and who can just as well go on working?

There’s the rub, according to Hilary Waldron, who works in the SSA’s Office of Retirement and Disability Policy  and recently released a report with the long-winded title, “A Multidisciplinary Review of Research on the Distributional Effects of Raising Social Security’s Early Entitlement Age.” If it takes a while to get through that thicket, Waldron’s conclusion is clear as a bell: “the U.S. population has never been easily separable into a group at risk of hardship and everyone else.” More specifically, “it does not appear that the Social Security–covered worker population can be easily separated into two groups—an unaffected (or low-risk group) and an adversely affected (or high-risk group).”

That means that if a future Republican president and Republican Congress wanted to raise the retirement age without harming at-risk individuals, they’d have a devil of a time figuring out how to do it. Proposals to raise the EEA have been circulating for decades, and numerous studies have been conducted as to the impact. In her paper, Waldron reviewed these, and found that no two experts agreed on how to define hardship, a physically demanding job, or ability to work. Studies Waldron cites come down with estimates of the at-risk population if the EEA was raised that vary wildly: from 3% to 52% in one report, depending on the definition used, to 10% to 33% in another, and from 1.3% to 37.4% in still another.

Raising the EEA seems to affect workers in the top income brackets the least, so some form of hardship exemption would be needed for those lower down. But until you get to the absolute top percentiles, “men claiming at age 62 in the top earnings quartile die sooner than men in lower quartiles claiming later,” which suggests that “even among men of high socioeconomic status, there is substantial variation in risk.”

Incidentally, Waldron notes, this was something the 1935 Committee on Economic Security, the presidential panel that drew up the initial blueprint for Social Security, expected would be the case:

A key conclusion that arose out of the designers’ examination of various approaches to the problem of economic insecurity and their experience in state government was that all workers were at risk, rather than just an unfortunate minority.

Within almost every subgroup you can think of, it turns out, there are variations in risk: workers who spend their careers in physically demanding jobs would seem to be more at risk of not being able to work after age 62 than those in desk jobs, but many of the latter have poor health as well and have to quit. Figuring out how near-retirees’ health status factors into at-risk projections is difficult as well, because individuals’ self-evaluations vary all over the place, making many studies unreliable. Waldron cites

an Australian national health survey in which a self-reported health question was asked of a random subsample of respondents both before and after an additional set of health questions. The authors found that 28 percent of respondents changed their self-reported health status when asked about it twice in the same interview, and that the distribution of self-reported health status was different between respondents who were twice interviewed and those who were once interviewed. The tendency to revise responses varied by age, occupation, and income.

The same goes for mortality: It’s hard to use life expectancy as a factor in setting a cut-off for eligibility for a hardship exemption, because studies haven’t found any such bright line; instead, it follows a gradient. In other words, life expectancy doesn’t drop off dramatically at any one point on the income spectrum; it declines gradually as one moves from the highest to the lowest incomes percentiles. Any attempt to draw a bright line would be arbitrary and would risk leaving many individuals who need it without the option of retiring early. The same goes for education, another study found.

Studies that attempt to identify a group of workers “at risk” of not being able to work past 62, for instance, find themselves contemplating an extremely heterogeneous group that would be very hard for Washington to target with a hardship exemption. One study that divided the population into deciles according to health and longevity risk found so little difference between some of these subgroups that “a proposal designed to apply to the bottom 20 percent of the male lifetime-earnings distribution could be off by 20 percentage points and actually apply to the bottom 40 percent.”

This is one very important reason Social Security was conceived by Roosevelt and his advisors as a social insurance system: because  old-age income isn’t just a concern for the have-nots; otherwise, up and down the income curve, disastrous reversals of fortune would be a very real threat. As Waldron notes, “The less this target population [of have-nots] can be readily identified, the less confident we can be that the welfare framework [for Social Security] has empirical support.”

Of course, it’s always possible to cobble together some kind of standard, given the will and the resources. But then there’s the problem of applying it. The SSA is already underfunded and understaffed. Applying convoluted, in all probability illogical “hardship tests” to each of the 75 million baby boomers now wending their way into retirement will only make matters worse. Because nowhere in the Bowles-Simpson plan, for example, was any money allocated to help the agency staff up to meet the new administrative task.

All is not lost, however. For those determined to keep more workers working past age 62, Waldron’s paper notes some hopeful facts and figures. In one 1986 study, “controlling for occupation and education, the author found that individuals with discretion over activities and the pace of the job were almost twice as likely to be working as those with low levels of discretion.” The same study found that “being a member of a labor union was also positively correlated with the likelihood of working.”

So there’s a goal for our entitlement-reforming presidential hopefuls: mandating kinder, gentler workplace rules, and promoting union membership. Let’s see if they take the hint.