Steve, It's going to seem like I'm just arguing with you today, and that is not my intent. But I do think some clarification is needed here. In many varieties, especially the mandarins and their hybrids, the presence or absence of cross-pollination may have a large effect on seed number. But that's generally not the case in sweet oranges. I suppose there may be some small effect (6 seeds vs. 4 in a 'Valencia' for example), but really the seediness level of an orange is genetically determined, so such things as Navels, 'Hamlin', 'Valencia', etc., inherently have small seed counts, while things such as 'Pineapple' and 'Parson Brown' have inherently high seed counts.
Indoors, lack of even self-pollination could have an effect here, but in an outdoor-grown tree, I'm assuming that there are enough bees and other insects to rule that out.
Malcolm