I largely agree with Mr. Yee.
An order compelling arbitration can be reviewed by the Court of Appeal by way of a proceeding called a Petition for Writ of Mandate. These are difficult but not impossible to win.
One key question is whether you informed the judge at the hearing that you were nor served with the motion. If that issue was not raised, you may have to file the Motion to Vacate pursuant to Civ. Pro. section 473, because the Court of Appeal generally requires that all issues be first raised at the Superior Court level.
If you are serious about challenging this ruling, you should consult with an attorney familiar with arbitration and appellate law. See, e.g., http://www.sanjoseappeals.com/Arbitration%20Appeals.html.
Best of luck.
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Why were you not served with the motion to compel arbitration? I think you mean "vacate" rather than "vacant." Motion to quash is not an appropriate motion. A motion for reconsideration is a theoretical possibility but it is strongly advised that you not file such a motion as it is an over-used motion, particularly by those who are pro pers. Such a motion is appropriate only on the basis of "new or different facts, circumstances, or law" that were not shown at the original motion hearing. The fact that you did not receive the motion for some reason does not constitute "new or different facts, circumstances or law" in my opinion. Another possibility is a CCP 473 motion based on "mistake, inadvertence, surprise, or excusable neglect" on your part. To be successful, you will need a memorandum of points and authorities and a strong declaration demonstrating the mistake, inadvertence, surprise or excusable neglect. These are terms of art and there are cases which discuss the meaning of these terms. If you are serious about pursuing this, I think you need to speak to a lawyer. It is unlikely you will be successful on your own trying to have the court vacate its ruling. Good luck.
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The other attorneys have given good advice. To add to it, it might not be worth your time and effort to try and get the order overturned. Depending on the type of case, arbitration might be a better way to go. Talk to an attorney who can evaluate the matter and give you the pros and cons of arbitration as it applies to your specific situation.