There is a strange rule of thumb that bookings on a given route are not proportional to the number of flights (or number of seats) available on each airline. The airline with the most flights will get a disproportionately higher % of the bookings. For example, if UA has 3 flights/day on a given route and AA has 1, UA will get significantly more than 75% of the bookings and AA will get less than 25%.

In the case of Hawaii, because UA has so many more flights than AA, the UA flights will actually fill up more quickly than the AA flights. It sounds contradictory but it is nevertheless true.