Say, in a 10 team league, the 9th place team trades Albert Pujols away for two prospects on the 2nd place team. The managers that will be allowed to approve or deny the trade are the 7th, 6th, 5th and 4th place managers. Here's why:
Red and Bold are the two managers who have traded with each other. Count number of slots the 1st place team is from the 2nd and 9th place team. He is one slot away from the 2nd and eight slots away from the 9th. You can see, this and all of the other managers below:
1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
1 - 1 2 3 4 5 6 - 8
x 8 - 6 5 4 3 2 1 - 1
8 - 6 10 12 12 10 6 - 8
As you can see, when the number of slots away are multiplied together the 4th, 5th, 6th, and 7th managers have the highest numbers. Therefore, they are the managers who are allowed to approve or deny the trade. Take a different example:
1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
4 3 2 1 - - 2 3 4 5
x 5 4 3 2 - - 1 2 3 4
20 12 6 2 - - 2 6 12 20
In this example, the 1st, 2nd, 9th, and 10th managers are farthest away from the trade and therefore are allowed to approve or deny the trade. But both of these examples come up with four managers. There are some examples where there ends up being a tie for the highest products. For example:
1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
2 1 - 1 2 3 4 - 6 7
x 7 6 - 4 3 2 1 - 1 2
14 6 - 4 6 6 4 - 6 14
In this example, 1st place and 10th place are farthest away, but then 2nd, 5th, 6th, and 9th are all equally spaced away from the trade leaving six managers with approval rights. In this case or any case where more than four managers qualify, the managers that will count be will be ones that are lower in the standings. So, in this case, the four managers that would have approval or denial rights would be 1st, 10th, 9th, and 6th place.
Once exception to this rule is during the spring training of the first season. Since there are no standings of any kind, there is no way to figure out which managers will accept or deny using this method. Therefore, what will be done instead is that the waiver order that is created after the draft will determine a persons "slot" or rank. Therefore, the person with the first waiver priority will act the same way that the first place person would, etc, etc.