Once upon a time there was a rooster named Tom who suffered from Multiple Personality Syndrome Disorder, or Multiple Personality Disorder Syndrome, as the case may be. Either way, it didn't make much difference to Tom because he had a very limited vocabulary and his vocabulary included none of those words. Nor did it include any of the words in the Diagnostic and Statistical Manual of Mental Disorders of the American Psychiatric Association. When it came to words and diseases such as MPDS or MPSD, as the case may be, Tom was blissfully ignorant.
Tom's blissful state of ignorance extended to his own mental state and his own multiple personalities, of which Tom had 3 in total. A catalog of Tom's various personalities went as such: 1) there was Tom the rooster who enjoyed the barn and crowing at the crack of dawn. 2) There was Midge the barn swallow who enjoyed nesting in and near barns, which was fortuitous because it gave Tom even more reason to love barns. And the third was a wrought iron weather vane who had no name as weather vanes have no need of names, but nonetheless enjoyed his perch atop the roof of buildings, especially Farmer Brown's barn, indicating the direction of the wind. Which was also fortuitous because Tom always knew which way face when the sun began to rise.
One day, Tom's personalities got together and built a nest on top of Farmer Brown's barn as it was a point of agreement between the three, even though they had never met nor had they any inkling of the existence of the other two. One day, Tom, as Midge, laid an egg on top of the barn who's two sides faced East and West. As the wind was out of the East the day, the egg would have rolled down the West side of the barn but Midge build a strong nest and the wrought iron weather vane personality of Tom's provided a small amount of protection from the wind.
So, in answer to the question "If a rooster laid an egg on a roof with one side facing East and the other side facing West, which way would the egg roll?" The answer to that is "It depends on the rooster and the competency of his multiple personalities."