Discussing an unpublished approach of a former team member I started my research as a PhD student a few years ago. I was assigned to researcher X's team and had to assist him in finding a solution as the project got stuck. However, X was not able to implement his approach properly and, after some time, I doubted that the solution's concept would work out at all. Nevertheless, X demanded that we continue following his approach.

After a few months, there was still no progress and people started getting disappointed. X got into severe and dirty conflicts (on a personal level) with his other team members. Conflicts escalated and finally X (and another guy) were removed from the project and forced to quit.

I continued working on X's approach for several more weeks. Since my work was not controlled by X, I was looking at the proposed solution more critically. I came across severe conceptual errors and also some implementation errors. I had to discard the current solution and started working on a completely new approach (not related to X's approach). After several more weeks, I finished the implementation and it was working quite well.

Now I am outlining my PhD thesis. One of the topics is my approach to solving the aforementioned problem. However, my approach is not that straightforward, compared to X's approach. It is more complex and expensive. Therefore I need to justify in my thesis, why I decided to use MY approach and NOT X's approach. I can show this his approach does not work. Therefore, I have to describe his approach, show the implementation and present some of the results. Unfortunately, nothing has been published by him. I would be the first to present his approach - this feels uncomfortable. In the department there is a huge fear of retaliation (e.g., accusations of scientific misconduct), since X was forced to quit. We know that he monitors our publications. I need to handle this at low risk without reducing the quality of my thesis.

My options are:


Leaving out X's approach in the thesis completely. I do not like this, since I invested a lot of work/time and, what is even more, my thesis appears to be not comprehensive without it. It's especially interesting for the reader to know, why X's approach (the most obvious one) does not work. Leaving it out reduces the quality of the thesis and creates open questions which remain unanswered (e.g., why I am using such a complex approach, could I not simply do X's method). However, this solution has no risk.
Describing X's approach without mentioning X. One argued that I had done enough work on it so I should just leave his name out. I do not like this at all as this is ethically not correct.
Describing X's approach and clearly attributing it to X (altogether on 2 or 3 pages). I would include an explanation of conceptual issues, leaving out implementation errors (=no personal blaming). That would be my preferred method, however, I am still publishing and discussing his (unpublished) approach. Is this acceptable or does it expose me to some risk?


I would like to use the third option. Is this acceptable or do other/better solutions for such a situation exist?
I need to justify...why I decided to use MY approach and NOT X's approach. 


I don't think you need any such justification: "[X's approach] does not work....nothing has been published by him." Thus, the literature contains nothing about X's work and you need not compare your results to his unpublished work. Nonetheless, if you feel that some reference to his work is necessary, then you could mention that X is working on the topic or that some of your ideas followed from discussions with X or ...


  It's...interesting...to know...why X's approach...does not work.


Many approaches don't work. You cannot possibly mention them all. It is perfectly reasonable to omit discussion of X's approach. That said, in some cases -- e.g., when the obvious solution seems feasible -- you might like to very briefly mention why the obvious solution doesn't work. For instance, you could mention: This problem can be intuitively solved by ABC, however, ... (You could also mention that X pursued some of these ideas, or that you pursued some of these ideas with X.)