Besides the already mentioned issues, there are at least two very important ones.

First, one important thing that a university diploma signals is the ability to behave in proper ways that are demanded in professional situations, and to credibly maintain this appearance for several years. In particular, one of my pet hypotheses is that the notoriously high level of political correctness on campuses in fact serves a useful signaling role for employers. Even very productive and capable employees can end up as a net loss if they say or do something stupid that results in a harassment or discrimination lawsuit -- and people are much less likely to blunder in these ways if they have passed through several years of scrutiny by an institution that penalizes any indication of propensity for such excesses and relentlessly warns and propagandizes its students about how evil and dangerous they are.

Of course, another thing that universities are in the business of selling is the opportunity to mingle and make connections with high-status people, as well as the inherent increase in status that comes from the affiliation with a high-status institution. Status in human relations is often not reducible to a matter of signaling other traits, and the fact that universities currently possess high status and the power of bestowing it mean that they have control of an inherently scarce and fixed-sum resource, so they're impossible to undercut barring some very great social changes.

Have you read Bryan Caplan on this topic? The main problem he brings up is that such alternative schemes also signal weirdness, which many employers do not want.

the entire program would consist of spending sixteen hours a day solving by hand simple addition and subtraction problems.

I would suggest that they instead spend that time developing a programming language compiler or interpreter. Or creating a grass-roots political organization. Or a new marketing approach. Or writing a popular blog. Or gaining fame, power, or money in any of a thousand other creative ways.

My suggestion:

Instead of having them spend that month doing arithmetic, make them write something that's, say, 50,000 words long. As far as I can tell, the most important non-technical skill that someone is supposed to learn in college is how to write - and it's amazing how many people can't do it.

I think we all know that this would send negative signals, whatever the reason why.

How about this for a possible variant: Six months doing actual useful work. In my own field, this could consist of clearing some to-do list items for an open source software project. Perhaps experts in other intellectual domains could suggest similar tasks.

This would have the following advantages:

1. Much better general signaling properties. (Again, regardless of the reasons why, I think we all know that this would be the case.)

2. You'd learn something in the process. (College isn't only about signaling, after all.)

3. You'd get to demonstrate relevant skills as well as the ability to put in long hours; the quality of your work could be assessed.

4. And of course, actual useful work would get done.

In some professions, an employer will accept three years of experience in lieu of a college degree, and in some professions they won't. So, I would suggest that the most productive way to continue this conversation would be to provide one or more answers to the following two questions.

• In what profession is experience treated as being as good or better than a degree?
• How can you gain that experience and get paid doing it?

Three possible answers to the first question are journalist, restaurant chef, and computer programmer. Some corresponding answers to the second question should be obvious. A fourth answer to the first question would be political campaign operative. I don't know of a corresponding answer to the second question for that profession. (Maybe start out in paid interest-group fund-raising?)

Any other answer pairs?

It's also possible that colleges signal other things besides IQ and work ethic. At least some employers (in the sciences, maybe) are looking for traits like curiosity and the ability to think clearly. In which case, spending a month doing repetitive tasks would be a negative signal. Creative or intellectually curious people would be less likely than average to be psychologically able to "spend a huge amount of time doing extremely boring tasks with high accuracy."

Of course, for many jobs IQ and work ethic are by far the most important things. This program probaby would be a good signal for those jobs if it was well established enough not to trip employers' absurdity heuristic.

Doing very boring tasks whose only purpose is to have something to brag about is not very glamorous - it doesn't sound like the kind of thing either employers or employees would want to be associated to.

The idea could probably be tweaked though (replace the multiplications by something equally challenging but that at least looks kinda useful), but it seems that a tweaked version is pretty close to what a lot of people do: an unpaid internship at a prestigious company.

Also, you make no mention of social/leadership skills, and college extracurricular activities are important indicators of those, whereas your proposal very clearly isn't.

James_Miller:

An organization could have a one month program which only admits those who get a high score on the SATs or some other intelligence test.

This would indeed be profitable, but only for unsuccessful applicants and their lawyers. Search for "disparate impact" if you don't know what I'm talking about.

There is of course also the issue of signaling weirdness that another commenter has already raised.

Even assuming all your givens, why would this be a better alternative to college at signaling? College already works. And also sometimes teaches you stuff also. Prestigious schools are expensive because they have a high reputation, thus demand for their signaling is greater and they can afford to charge more. If you could simply inject signaling value into a program, you could just pick a random already-existing, cheaper college and do it with them, avoiding all the weirdness signaling that'd be going on here.