How to move your field away from a widely accepted practice that has a catastrophic error?

Two quotes immediately came to mind:

A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it. - Max Planck

I'm trying to free your mind, Neo. But I can only show you the door. You're the one that has to walk through it. - Morpheus from The Matrix

To elicit a change of the magnitude you indicate, four aspects must be communicated clearly and unequivocally:

1. The existence of the error (i.e., demonstrate that the prior approach is incorrect). Other academics in the field may not recognize that there is an issue.
2. The history of the error (i.e., why the prior approach was used and how it has persisted for 50 years). Given its age and prevalence, other academics may understandably presume that the prior approach has been validated before and may dismiss your claims on that basis.
3. The implications of the error (i.e., what negative impact the prior approach has). The effect of the prior approach may not be clear or other academics may perceive it as negligible relative to the effort necessary to adopt a new approach.
4. The change itself (i.e., the course of action to rectify the error - the new approach). Other academics may not know what should replace the prior approach.

You should first make sure that these have been satisfied in your previous publications. Assuming this has been achieved, there is really only so much you can do (see the quotes). You obviously can't force people to change their ways. In addition to being patient, you can (where appropriate):

• Continue referencing it in future papers and conference presentations.
• Highlight it in peer review.
• If you teach, incorporate into your courses.
• Write a review article of the error in your field (one way to address #2 above).
• Communicate (1-4) in relatively plain language on your academic blog (assuming you have one).
• Send your paper(s) to the authors of the undergraduate textbooks with a letter explaining (1-4) and why the change should be included in the next edition.
• Write your own textbook.

Improper use of statistics is a widespread problem in many experimental sciences. I worked for some years in discrete optimization and got more and more frustrated that the "numerical experiments" were usually done without any reference to a statistical method, so that many good results where just random noise or calibrating of an algorithm to a very small data set.

I read horrible things about abuse of statistics in psychology and medicine (resulting in very low reproducibility). And I guess the same thing happens in many experimental fields.

My (pessimistic) view is that in a "publish or perish" culture, people tend to bend methods until they break, and this is especially easy with statistics: It is mathematical and often hard to grasp for the non-expert, and errors often do not lead to hard logical contradictions but to a weakened result.

Establishing questionable statistical methods in a research area often results in much more "positive" results that people can publish. And actually, this is what everybody wants. Most results are never reproduced, so non-reproducible results are likely to stay "true" very long.

Start by convincing people like me.

I have read your articles and posts on these supposed errors. While you have convinced me that there are shortcomings in Modern Portfolio Theory (and all its offspring), I think most practitioners and academics operate under the assumption that all models are wrong, but that some are just useful. I.e., I think most of us already know the difference between models and reality.

I don't think you'll convince anyone that your solution to the portfolio problem is any less of a model than the one that your are critiquing. As a result, I would recommend that you shift your focus away from the technical arguments regarding the shortcomings of others and instead focus on the high-level benefits of the paradigm shift.

I'd also like to emphasize the "high-level" aspect. The argument, although technical, should be written clearly and concisely. It should be readily accessible to practitioners. If MBA students don't understand the benefits of switching, stodgy academics will see no reason to stop defending the status quo.

I recommend you start by convincing people like me because, ultimately, you need to convince practitioners that the benefits are worth mental and tangible switching costs.