Agreement to attend arbitration without underlying contract

Factual Questions
1

Suppose two friends, Jon and Mike, have a dispute. Jon alleges that Mike defrauded him or ripped up his flower bed. Whatever. The point is that there is no contractual relationship between Jon and Mike. Jon sends Mike a letter asking him to attend arbitration in order to resolve the dispute. Mike replies by mail and agrees to attend arbitration.

Later, Mike reneges and refuses to attend arbitration. Can Jon compel Mike to attend arbitration? There was no underlying agreement to arbitrate so everything is going on Mike’s reply letter. Is the question a Contracts question? If yes, where can I find consideration?
DISCLAIMER: I am not asking legal advice. This is merely a hypothetical question.

2

I’m not a lawyer, but it seems to me that the consideration is that each party agrees to attend the arbitration and accept the result of it. That is, they are waiving their access to the normal court system in favour of the arbitration. That would seem to be valuable consideration.

3

Just spoke to a relative who is a lawyer and you hit the nail on the head! Congratulations and Thank you!