[malgorithms]

Perhaps an even simpler analogy is a light switch. Each person decides randomly either to flip the light switch or leave it where it is. This is basically what random XOR'ing is.

If you're one of 10 people doing this to the light switch, then as long as you choose randomly, it doesn't matter what the other 9 people do. It has a 50% chance of ending up on and a 50% chance of ending up off. Even if the other 9 people are cheating together.

Of course this has the problem that whoever goes last wins, which is why the commitment ceremony is necessary.