Thank you all! I will go back through the bylaws to see if they mention anything. Honestly, this is an organization that hasn't been very, well....organized in the past few years. Their procedures and customs seem to mostly stem from RONR, but a lot were made up by student leaders and have been adopted as "the way we do it." This is a university student government.
The problem I'm dealing with is the election result. We had 3 choices, and no clear majority winner. We didn't state anything prior to note that this was a vote by plurality. I'll have to go back and see if we actually do say anything about how a winner is determined. My guess is no, b/c the students wouldn't have ever thought we needed it spelled out.
So, according to what I can find online, balloting must continue until there is a clear majority. It sounds like, based on the answers here, that I can say we are bound by common parliamentary law, which means I *CAN* use RONR when determining the next steps in this election.
For context, 2174 people voted. The top two choices had 768 and 790 votes. The third choice had about 600.