Why do we say certain things three times (e.g., "Mayday, Mayday, Mayday"), rather than two or four? Repetition is a key characteristic of communication in the control tower, cockpit, and control room.  Some phrases, like "Mayday" get repeated. The speaker says the same thing three times. We know this is for redundancy. 

Why exactly three times? 

Why not twice or four times? Is there research suggesting three is the most effective number, or is there a historical reason for the convention?
Yep, the critical commands are repeated 3 times.  This ensures there is ABSOLUTELY zero doubt in anyone's mind (especially on a big crew airplane) of what needs to be done in a critical situation.  It also standardizes these criticalities across different aircraft and aircrew cultures.  "Bail out, bail out, bail out"  "Eject, eject, eject"  "Abort abort abort" "Pan-pan, pan-pan, pan-pan."  I was 27 years a USAF pilot, and this is how the training has worked for over 50 years.  I only saw these terms used 2-3 times, but it certainly gets your attention and amps up the sense of urgency.  A little history:  back in the day of very poor radio communications, it was necessary to repeat to "get someone's attention" or in the event a single "mayday" didn't come across when the transmit button was pressed.