The SegWit discount of 4x is arbitrary though.

Pre-SegWit nodes see SegWit transactions as anyone-can-spend "unsigned" transactions, so they don't know of signatures and the weight thereof. They do count the bytes of OP_RETURN though as it's not segregated. 

 It's not arbitrary, it was picked because it makes spending inputs cheaper than creating new outputs. 

 The "4x" is arbitrary. The discount in general not.

With "arbitrary" I mean there is no scientific reason why exactly this number is the correct one. 

 It isn't arbitrary, it's the smallest whole number where we cross that threshold of making inputs cheaper 

 Sounds arbitrary to me. Why not use a decimal number ;)

Ok, TIL. Will read up on the details ... 

 You don't want to use floats for money