If certain statistical properties are ensured about the appearance of elements in the tuples, then the number of times an element is chosen as most positive minus the number of times it is chosen as most negative can be used as a sentiment score.
we experienced that if the BWS annotation is performed by directly sampling from the lexicon (or from a general corpus, for that matter), most 4-tuples would not contain any items with a clear non-neutral polarity, let alone one most positive and one most negative item.