Democratic government tend to give the greatest political influence to the majority.
Hence why us Libertarians are for democratically elected officals and not unelected bureaucrats... which something Democrats support.
A capitalist economy gives the greatest individual economic influence to the wealthy.
No, it gives the greatest economic influence to the best and brightest entrepreneurs. The best are determined by whether the free market that is driven by the consumer wants the product being offered and as a result entrepreneurs become wealthy while the costumer gets what they want.
The wealthy tends to be a small group.
Depends on what you consider to be "wealthy". But just because there is one group with a lot of wealth does not mean that the middle class is not well off.
The majority tends to be poorer.
Actually, capitalism has allowed for mass production of goods and wealth. People are better off now because of it.
Political influence is economic influence.
Which is why we need to keep government from controlling too much of the economy.
The invisible hand is the net effect of all individuals economic influence minus the economic influence done though political influence.
Huh? The invisible hand is how companies survive or don't based on how vauled they are to the people who they do business with. If the product or service is in high demand the company will survive, but if the product or service is not in demand then the company will be faded out.
All is well with the invisible hand as long as every body has roughly equal economic influence, however once a group begins to gain more then the others this group will begin to exploit the others for their benefit, the smaller this group(of a particular economic influence) the less representative it is of society.
If by "exploit" you mean expand their services and invest more in their business as well as others then yes... they "exploit" other. As for the "less" representation bit, a person recieves a vote in a Libertarian society regardless of their economic status.
The only way for the more populous and more representative group(s) to gain enough economic influence to counter their exploitation is though political influence. This Economic influence will manifest itself as Regulations, minimum wage laws and other such things.
It's hard to consider it "exploitation" when both parties are better off. Sure, some regulations are needed, Libertarians tend to follow the Austrian School of Economics which is against fraud and even Adam Smith admitted that some services(road making) are better off left to the government. However, too much regulation will lead to companies leaving the country and businesses suffering. As for minimum wage, all that does is causes high unemployment and ships jobs over seas.