Mc Mahon Example
To help you understand how the McMahon System works lets consider a small example. We have 8 players in a tournament where the McMahon bar is at 2d.
no. players name rank MMS 1 Danny Strongbow 5d 0 2 Daniel Burrly 4d 0 3 Danial Knee 2d 0 4 Cutey Pi 1k -2 5 Kyu Mcgrew 2k -3 6 Kyu Dibble 2k -3 7 Kyu Tibbs 2k -3 8 Kyu Bitz 4k -5
Ok so how do they pair up for the first round? Let's consider an example of 4 games with handicaps and results shown.
White Black handicap result Strongbow Burrly even 1-0 Knee Pi 2 stones 1-0 Mcgrew Tibbs even 0-1 Dibble Bitz no komi 1-0 
As handicaps are decided by McMahon Score (MMS) the 5d and 2d games is even.
no. players name rank MMS 1 Danny Strongbow 5d 1 2 Daniel Burrly 4d 0 3 Danial Knee 2d 1 4 Cutey Pi 1k -2 5 Kyu Mcgrew 2k -3 6 Kyu Dibble 2k -2 7 Kyu Tibbs 2k -2 8 Kyu Bitz 4k -5
For everyone who won a game their McMahon score increases by one point. In the case of a Draw, Jigo both players are awarded 1/2 point.
 Calvin: Why is this game no komi whereas the Knee-Pi game is 2 stones? Both have an initial MMS difference of 2.
Anonymous: You've got a point there, better change it :)
MrTenuki: One possibility is that Bitz entered the tournament at a higher rank, namely 3k...
I think this is a rather strange example. The idea of the McMahon system is to get the best player, by wiping out all uninteresting games. For example Strongbow - Bitz. This game is assumed to be won by Strongbow just by the ranking. This principle is translated into the McMahon points. If games are played with handicap, this does apply anymore. With handicap each player has roughly equal changes to win the game, so a McMahon score doesn't make sense. Sometimes a (reduced) handicap is used if the ranking difference is too big. This normally occurs in the lower rankings only. Also if one player is in the top McMahon group, there is never a handicap. So better change this example into non-handicap games.
IanDavis: Since handicap games can happen in a McMahon tournament, I included them in this example. That way a reader can understand what will happen when they occur. As the bar is at 2d the 5d player is treated as a 2d player, so he will experience reduced handicap. It may well be that the handicapping policy is something like MMS Difference - 1, so there is further handicap reduction. Overall, I don't think the example is that strange. It is just there to give an idea of how MMS scores are calculated during a tournament, and what effect the McMahon bar has.
willemien: This example is using the UK style of assigning initial McMahon scores. Continental Europe would use only positive scores, while under the AGA rules the initial McMahon scores would be something like below (it is not an exact science, it depends on bars and band seperations see http://www.usgo.org/standard-aga-tournament-protocols/ for the grity details
Initial McMahon score
no. players name rank UK MMS EU MMS AGA MMS 1 Danny Strongbow 5d 0 5 0 2 Daniel Burrly 4d 0 5 0 3 Danial Knee 2d 0 5 0 4 Cutey Pi 1k -2 3 0 5 Kyu Mcgrew 2k -3 2 -2 6 Kyu Dibble 2k -3 2 -2 7 Kyu Tibbs 2k -3 2 -2 8 Kyu Bitz 4k -5 0 -2
This is the reason why in Aga tournaments it is much more rarer to play against players from a different group.