What is a Paradoxically Rejected Block?
When a block is paradoxically rejected it is rejected even though at the given market prices it should have been accepted. It is not possible to include the block into the solution without modifying the prices to such an extent that the block is rejected at the new prices. This is the definition of a paradoxically rejected block (PRB).
To ensure that it is not possible to insert the paradoxically rejected block into the given solution the PRBs are tried reinserted in the PRB Reinsertion Module. The PRBs are ranked by how deep they are into the money the market session is recalculated by inserting a single block into the solution. There is a time restriction on the total calculation time therefore the module is not always able to test every PRB in the solution.
Under special circumstances such as numerical difficulties in the algorithm the algorithm may not be able to find more than one solution. In these cases it is a bigger chance that the PRB Reinsertion module is not able to cover all PRBs.
When it comes to reducing the risk of this happening, smaller blocks in volume and length can be a helpful factor in certain situations, but it does not a guarantee that it will not happen again.
Example of how Paradoxically Rejected block looks like in the system: