Your question is unclear. Are you in arbitration or mediation? If this is important enough for you to post a question that only a lawyer can answer, perhaps you invest in an hour or two of a lawyer's time.
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Your question is indeed unclear. If you're in arbitration, and the witness is non-responsive, the arbitrator will likely compel a response (on their own or on your request), if the question is not objectionable.
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If you are in an arbitration hearing and the witness doesn't answer, there are various devices you might use, but you may not have to do anything. Obviously the arbitrator is right there, too, and can see what is happening. This gives you the opportunity to argue in your closing statement and closing brief that the witness' failure to answer should be interpreted to mean that if the witness had answered, the witness' response would have supported your position.
Usually, the best thing to do is immediately ask the arbitrator to order that the witness answer ("Mr. or Madam Arbitrator, I move that you order the witness to answer the question.")
Other options would vary depending on the situation, who the witness is, what you know the witness would say, and more.
Ask the witness if the reason he or she is not answering is because he or was told not to do so by an employer (or whomever is relevant).
Ask if the witness is not answering because the answer supports your case.
Ask why the witness is not answering.
Ask why witness what you have to do to get him or her to answer.
Remind the witness he or she is under oath and that a failure to answer may be considered contempt (depending on if this is court-ordered arbitration).
All that said, I agree absolutely that your best bet is to retain an attorney to train you for a few hours in the rules of evidence, witness examination and cross examination. For this type of assistance, you can expect to pay hourly. Plaintiffs employment attorneys in California charge anywhere from $250 to $750 an hour depending on many factors including experience, area of law, geographic location, work load, interest in the case, difficulty of the case and more. You should expect to need at least three hours for this kind of consultation.
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Refresh their recollection with the previous answer, assuming the previous answer is helpful to your position. And/or ask the arbitrator to order the witness to answer.
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