Integrity of the review site
Some review sites have a very low bar for reviewers to jump over before they can post an entry. Others are more discerning. For example, TripAdvisor allows anyone to post reviews, requiring no proof that the reviewer actually stayed at the hotel in question or even is who they say they are.
By contrast, Booking.com only permits reviews from guests who have used their booking service to reserve rooms in the first place. Because of this additional level of consideration, ratings from Booking.com are weighted more heavily in the GEI calculation than those from TripAdvisor.