I paid for a trip to Jamaica. Person invited agreed to come and did not show up. Can I sue them?
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For what? Was there an agreement that the invited person would pay for half the trip? Did they put down any kind of deposit to show this if there was no written agreement? Unless you can show some duty to pay then I don't see that you are entitled to recover anything but then I don't have all of the facts.
Does the other person live in GA? If not, then I would not sue them in GA but where they live. If they are in GA then sue them in the county where they live.
GA small claims is up to $12,000 (I assume that your claim is well below that). Here is a link to the forms: http://www.georgiacourts.org/councils/magistrate/forms.html
Before you sue, you might try asking for reimbursement in a written letter, either sent by you or an attorney. Send via certified mail or UPS/FedEx with signature confirmation to prove that the letter was sent and that the person got it. In the letter, if there was an agreement, try to reiterate that or get the other person to admit the obligation. Then you can sue if the other person does not pay. Also, the benefit of a letter is (a) getting to see whether the other party is going to present anything which can help/hurt you and (b) some magistrates like to see that an attempt was made to work this out before going to court.