Your idea that they can move you out of your seat to a better paying passenger make no sense. The computer decides how many seats (overbooking) will be for each flight based-on lots of different facts.
No, they don't move "you" (theoretical you) out of your seat to accomodate a better paying passenger. That's not what I meant, and this isn't about overbooking. The matrix (when there is one) kicks in when there is an equipment change with a different configuration or when two flights are combined. (And yes, I am simplifying, and there are add'l variables, but the two primary factors are usually price and status.)
Ex: Flight 001 is orig. scheduled to be on an MD-80 (14 FC, 128 coach). The flight isn't selling very well, so the equipment is changed to a CRJ-900 with 80 seats (10 FC, 70 coach). Let's say that at the time of the change, 50 seats have been sold, all of them in coach. The old plane had 73 empty seats left to distribute, but this one only has 20 empties. Exit rows can't be preassigned, so there went 4 -- now we're down to 16 empties. The MD-80 had 28 rows of coach seats, mostly 3/2, the CRJ had 14 rows, all 2-2. Obviously, even if the computer did it's dangdest to give people their same-location seat, a lot of those MD-80 locations simply don't exist on the CRJ. When this happens, ALL of the passengers can get tossed back in with no assignment, and the software starts to assign all over again, starting with those passengers who have the highest status and/or have paid the highest fare, and working from front/back with FF preferences factored in. Usually about 75% of the way through the reassignment process, the machine will have no sets of 3 left and very few pairs, so parties will begin to get separated. Normally the person with the best status or the most expensive ticket will get the open seat furthest forward (excluding single middles), and so on, until the program runs out of either empty seats or booked passengers. (Remember that some seats are always held open by the airline and not made eligible for advance booking. Also, someone always will end up in back because of weight distribution needs.)
The same process can also come into play when two flights are combined.
Ex. Flight 001 on airline X is at 3:50 pm, and Flight 002 is at 6 pm, same route. Flight 001 is 60% booked, 002 is only 20% booked. As it turns out, Airline Y really wants to schedule a flight at 6 pm., so it offers airline X a trade, that 6 pm slot for one at, say, 8 am and another at 10 am. OK, sold: Flight 002 is cancelled. Now we have to put those Flight 002 passengers on Flight 001. Obviously, some of them will have reserved a seat on Flight 002 that has already got an occupant on Flight 001. Back to the matrix: now all the passengers originally on Flight 002 are getting new assignments based on price/status. Or, perhaps, the time for Flight 001 changes to 3:51 and it becomes flight 003, and all of the passengers from both flights are redistributed via the matrix, because now it is a totally new flight with a totally new number.
