Preponderance can be interpreted in any number of ways, but here's a thought for you: What if the globalization game was biased to produce results favouring certain nations time and again? That would indeed be a form of (malign) influence insofar as someone sets the rules of the game a certain way. If it's tails they win, and if it's heads they win again.
Here's a sporting analogy for you. Think of modern US influence this way: Like "undefeated" Timothy Bradley, the United States would not win a straight fight with many of its contemporary challengers. (As an aside, the US is a lawyer-infested society precisely to keep such ill decisions valid. Pace its never-ending quest to make the world economy a microcosm of legalistic American culture.) Fortunately, with the WTO established in 1995, it long ago set the rules that raise the likelihood that it will get its way. Why, for instance, should Las Vegas host so many marquee boxing contests when China's special administrative region Macau surpassed it as the world's top gambling destination long ago?
Even if the sentiment of a far larger majority and the facts line up against you--CompuBox stats say "Manny outlanded Bradley 253-159 in total punches and had a 190-108 edge in power shots landed. Manny outlanded Bradley in 10 of 12 rounds," it is very easy to flip others off. In the trade realm, consider the US just ignoring Antigua's claims against America for blatantly violating its services trade commitments by banning offshore online gambling and decimating Antigua's economy in the process.
Globalization as represented by trade is thus seen as rigged not only by Antigua but by so many others. Just as online betting concerns in Europe refuse to honour this farce, witness the never-ending quest to complete the Doha Round of negotiations. If most of the others thought it was a good idea to sign on, then it would have been completed a long time ago. Message to America: did you ever consider that it is not only in boxing where you are unfair but in so many other things? Like for Manny Pacquiao in boxing or Antigua in gambling for that matter, why bother to even wake up when the White Man's Burden in the 21st century is simply to screw you over?
Simply put, some have a habit of not fighting fair whether in sports or in economic matters. And that's all she wrote for the "American" ideal of fair play.
UPDATE: This sort of horseplay is not confined to boxing. Consider the even less cerebral, er, sport of hotdog eating. You'd think the world's hotdog eating champion would be American given how incredibly fat they are, but no. Still, they have frozen out the great (and actually quite lean) Takeru Kobayashi from competing freely in America.