First of all, I apologise for my level of English. If it is too uncomprehensible, just delete it. 

Since he asked why we couldn't observe his results, I understand that he thought his model was realistic. 

On one side, modeling the earth as a rigid body with one person jumping on them is inacurate. We should take in count many other things. So, the acceleration of what you'd like to call strictly earth (not the earth+humans+animals+natural phenomena system) you would compute would be, averaged in a period of time, equal to 0 (I would think that mass (humans, animals, air, etc) above earth's surface is distributed homogenly).

I think that would answer to you question.

On the other hand, the center of mass of the system will have an acceleration due to external forces (gravitational forces exerced by the Sun, Moon and other planets). Internal forces such as gravitational interaction between humans and earth wouldn't change the systems center of mass. And, since the earth is considerably more massive than us and we can't be too far from the surface, the center of mass of the system would be the same as the earth's center of mass. (This is equivalent to the small acerleration argument).