I'm a plaintiff's lawyer, so my answer comes from that perspective. I would not hesitate to use a mediator who had a background as a defense lawyer or who is a friend/former partner with the defense lawyer in the case to be discussed. In fact, I think it can be a great benefit.
When I look to select a mediator, I really want someone I trust and who will have credibility with my client. But one important factor is the relationship/respect the mediator can develop with the folks in the defense rooms.
I want someone who the defense will listen to and respect. I would think that the potential mediator, especially since he's being suggested by the defense lawyer -- fits that bill.
I would do some independent due diligence into the mediator to see if he is a good choice, regardless of his relationship with the defense counsel. If so, I would explain to my client why he makes a good choice....of course, the hurdle may be convincing your client to agree to the mediator.
But if he has a good record and reputation, the fact that he has a history with the defense lawyer is a positive not a negative.
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I can understand your concern. However, your attorney would be in the best position to determine whether the mediator's past relationship with the defense firm would either hinder or enhance the chance of a fair settlement. If you are not represented then you might want to pass on this mediator for your own peace of mind.
In the past I have intentionally selected a mediator who had some prior relationship with either the defense counsel or the insurance adjuster. In those cases I felt the mediator's prior relationship might help persuade the other side to be more objective in evaluating the weakness in their position.
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I'm going to cut the middle here. If your qualified lawyer is comfortable then you probably should be too. If you do not have an attorney I would not recomment this situation at all. One possible caveat, mediation in New York is non-binding. Good luck.
If you are unrepresented, this is probably not a good idea. If, however, you have a lawyer, I would recommend listening to your lawyers advice. There are many reasons (as stated by my other colleagues) that this situation may be of great benefit to you. Assuming your lawyer has some knowledge of the mediator, they should be able to determine if this is a good idea or not.
The answers provided by me in this forum are not to be construed as "legal advice" and in no way should the asker assume that any attorney-client relationship is created by virtue of the answers provided. This is a public forum, therefore, no confidentiality exists.