To say that a 'fair share' is the taxes prescribed by the current laws is ridiculously circular. Of course it's the _intention_ of laws to be fair, but no one can claim with a straight face that the current loopholes are actually fair. It's quite obviously unfair because larger companies with more money get away with paying less.
The problem with these loopholes is an international one; countries screw each other over with it, and it's difficult to pressure them into closing them.
My claim is that the definition of 'fair share' is codified by the laws on taxation. If the people don't agree with that code they should change it. An example that was local to me was California changing their laws on taxation such that citizens buying from Amazon would not be able to avoid paying local sales tax. Amazon did however threaten to not sell to anyone in California (which is kind of a hollow threat since California is huge market). Californians now pay sales tax on their Amazon purchases.
The problem with these loopholes is an international one; countries screw each other over with it, and it's difficult to pressure them into closing them.