Greed and avarice are part of human nature. For every Bill Gates who chooses to give away his fortune, there is an Al Gore ammassing private jets and mansions while telling us not to do so. Multi billion dollar scams like the Chicago Carbon Exchange or the recently defrauded Danish one (lost about $7 billion) run above board while organized crime rakes off billions below. Political fraud is rampant (check out the tens of millions of dollars of TARP and Stimulus funds going to non existent congressional districts, GM's accounting peek a boo to claim they "paid off" the US government loan, or closer to home the still missing millions from ADSCAM, or the more recent revelations of fraud and corruption in Quebec.)
The best way to close the wealth gap is to close off the avenues of approach for kleptocrats, most especially the ones in Government. Even changing to a flat or single tax system in Canada (eliminating tax exemptions and thus the ability to manipulate the tax code) is estimated to save about $3.5 billion in preparation costs alone, money that can stay in private hands to be used for savings, investment and consumption (and is the resources that can create about 70,000 full time jobs). That will go a long way to reducing the "wealth gap".