How to resolve the tie?

[Virginiá]

To me, it appears that first the candidates can come to an agreement to share the term, and if they can't agree, then it goes to the House. I am basing this on the order in which these options appear, as they are numbered after all.

I really think it would be best if they did share terms though. It's like you said, throwing it to the House inevitably results in partisan decisions and one side will be bitter (though it already seems like that is the case!)