You give no reasoning why it is rational to choose the majority. Actually, you're trying to prove that that is the rational thing, which makes this whole thing a circular reasoning.
It's the rational or rather the determined response because it requires a majority to fulfill. Thus it makes it the most likely one to be correct. If you're wrong, the poll will be a mess in the end thus showing there is no consistent human behaviour in this test.
If your axioma is: "Humans have consistent behaviour." Then that would be an okay reasoning. Also, your axioma would be horribly wrong.
Patterns can be found especially in the visual and logic realm. My axioma would not be horribly wrong especially in the study of human behaviour.