Second option (warning: not for people who can't stand horror movies or violence):
Let's hope, nobody uses my answer to use it in real life in a game show ;)
I claim that, under a stricter interpretation of the problem, the solution is
Although the question is tagged lateral-thinking I'm going to treat it as an information-theory problem, which means ignoring everything except the messages passed between rooms. I'll assume that the participants, either the two honest parties or the single malicious party, have ...
I have another quite simple one:
Prepare two identical looking boxes with red buttons on it
The first one will hurt (tazer, tear gas, whatever) the person when pressing the button, the second one will simply open and contains a sheet of paper with a message.
Send the first person the box. Tell this person: "Don't press the red button: It will hurt you ...
Ask them to type on the keyboard some complex poem one letter at a time (the left room should type odd letters, the right room even letters).
You just need to measure the time it takes.
If there is one person in each room, it'll be reasonnably fast.
You would get something like:
Words: Two households both equal in dignity
Time : 0--------------------------...
Here is another possible solution
First, a simple one, then one that could deal with a more suspicious person.
What we need:
This is our plan (simple version):
If we are dealing with a more suspicious individual:
Some side notes:
Since I can't yet comment ("reputation" issues) I'm posting this as an answer, and would just like to point out that all "Ask the two rooms to perform a one-shot action on the same time" solutions (and by "one-shot" I mean it's not continuous work, you click a button, for example, and are done, as opposed, say, to typing in the entire text of "Hamlet" in one ...
I think the best way to come up with an answer to this question is to look at this backwards - instead of thinking of ways to reveal if there is one person or two, think of how you would try to keep your secret if you were the one in the rooms.
To start with, I would make sure that all my interactions were carefully recorded so that I wouldn't ...
Question (even better if not facing the people in the room while asking, but turn around to see potential answer): Can you see?
Mute will do nothing, able-bodied person will raise right hand, blind person will raise left.
Many of the answers seem to violate the question of not being able to mention any disability in the question, or ignore the fact that the three people don't know of each other and aren't in the same room.
Updated to hopefully eliminate the irreal spotted by @JanusBahsJacquet