Why does POS Blockchain trimming algorithm require 2/3 of miners to sign checkpoints?

I'm analyzing this algorithm:

I'm thinking that maybe there is a reason for the 2/3 number and that basically it involves miners being able to include signatures of fake miners, basically you remove miners that aren't real accounts signing off on a checkpoint and for first checkpoint you can remove 1/3 of the real miner signatures and substitute your own fake signatures, for the second checkpoint you now can use your 1/3 fake signatures from last block, plus 1/3 more real signatures, now you have 66% of the signatures and can direct the blockchain how ever you want. Which makes sense if the algorithm is simply two thirds of the miners of the last block must sign off on this block.. but given that a checkpoint contains a merkle root.. maybe that isn't the case because those signers wouldn't be counted.

So, anyone know the reason for this? Arbitrary number?



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