The definition of hegemony is the leadership or predominant influence exercised by one nation over others. 

I lost a debate because the judge didn’t know what hegemony meant, and I didn’t spend enough time explaining it.  

The basis of the argument was that the BRIC nations were not threatening United States Hegemony.  Unfortunately the judge didn’t know the definition and assumed that hegemony had something to do with trade deficits.  

Lesson learned - when using a 4 syllable word in debate, make sure that the definition is extremely clear.