The idea that you can find the strongest M&M in the pack by comparing one until it breaks, then using the leftover one to compare in a serial fashion, is simply wrong.
As I see it, you are applying stress to the surface coating of an M&M each time you compress it. Following the method outlined above, you would end up comparing an M&M with the stress fatigue of up to (bag total - 2 pieces) compressions against the final M&M in the pack, which would have not been stressed previously. This cannot be, by any stretch of the imagination, a balanced test.
To do this right, I suggest a system of "playoff" rounds: Take pairs of M&Ms from the bag and test them, placing the "winners" aside. If you have an odd number in the bag, take the final piece and place it with the winners, as a random seed. Then pour all the winners back in the bag and repeat the process until you end up with one final M&M. This is much more likely to be the strongest M&M in the bag.
(You can then repeat the process per bag, then play the bag winners off each other, but if you have that much time, get a job!)
(note: as far as I know, this is how most sports championships are decided nowadays.)