[wanorris]

You're right, and overfitting cannot be an explanation for this phenomenon -- when there are many equally valid alternative outcomes to a problem, which is what's being described, the solution is underdetermined by definition.

In the (ML) terms I'm used to, it is as an error surface with many local minima. That is, if you start out with a guess for the parameters and try to progressively optimize the cost function to reach a point where the error is lowest (i.e. the tangent of the error is 0), where you end if is extremely dependent on where you start out. When you find a local minimum, you have found a point where there is no nearby point that is better, but there may be some other point (or many) somewhere else in the model that is better. The very best one is the global minimum.

This is a well known problem in ML for non-convex error functions, and there are various methods for trying to avoid local minima and reach a global minimum.

But this case is actually worse than that -- it is an error surface with many global minima. Each is effectively a perfect fit for the data to date, but give different predictions about future data. Since each function is a perfect fit, it is literally impossible to predict the proper parameters. Which is what underspecification is.