The disagreement on fractional-reserve banking is twofold. Is it fraud? Is it economically prudent? Only the first question is a libertarian one.
Libertarianism can be loosely defined as the political and social philosophy based on the right of every person to the peaceful use his own body and property. Stated in a ‘negative’ manner: libertarianism opposes force and fraud; the latter is a form of theft because it is the wrongful assumption of a property title.
Thus, if fractional-reserve banking is fraud, then it falls squarely within the realm of libertarian theory, and it would be outlawed by a free-market system. But if it is not fraud and merely imprudent, then it falls outside of libertarian analysis however interesting or useful an economic issue it may be. In other words, if fractional-reserve banking is voluntary and non-fraudulent, then a libertarian society would not outlaw the practice even if it proved to be a foolish one.
As long as both parties accept the logic of the exchange, it is not the business of an .. 3rd party to intervene and invalidate the contract. Just as the free market and libertarianism do not outlaw stupidity, neither do they prohibit a breach of logic. And a 3rd party has no business substituting his logic for that of the contracting parties.
The question has become “Which is the best banking system: fractional or 100% reserve?” My answer: let the free market decide. Let individuals choose for themselves.