Libertarian Anarchism gets rid of government in the sense of legislatures, executives, courts, and bureaucracy yet it preserves governance through free associations.
Exactly.
However coercion would become an issue when people decide they no longer agree with or will submit to rules they previously helped negotiate. Other people will cheat. That's human nature.
I may have lost you. Any system of governance is based on rules, and some people may try to violate those rules for their own benefit. In a libertarian anarchy, people who violate private property-related rules (ie. those who initiate force against other people's property, etc.) would be considered criminals (just as people who violate legislated law are considered criminals today).
Those against whose property those criminals initiated force will be entitled to use force (probably through professional intermediaries) to restore their property rights. They would have a stronger personal interest in prosecuting those criminals (compared with government prosecutors whose incentive to prosecute varies greatly), and the freedom to choose the most effective (legal) means to restore their property.
Through competition between organisations dedicated to the various stages of the property-protection service (passive protection, active deterrence, victim insurance, identification of criminals, prosecution of criminals, extraction of restitution from convicted criminals, sharing information regarding criminality risk, etc.) will cause the quality of services to continue to increase, and their price to decline.
Thus over time we would expect the effectiveness of institutions dedicated to property right protection (i.e. to preservation of enforceable rules of a libertarian anarchy) to continue to increase.
Crime will never go away, but we can expect it to me less and less material.
Furthermore how could the Free Association be timely and effective if its not based on majority rule.
There are other mechanisms for ensuring effective service. For example, many of the services currently provided by government could be provided by insurance companies collecting premiums. Competition between such companies will cause the quality of their service to go up. Those who provide poor service will quickly go out of business.
The association still makes rules and enforces them so why get rid of representative democratic government in order to protect individual liberty ?
Because representative democracy isn't voluntary. It uses force to subject even those who oppose it, feel it doesn't service their interests, and wishing to find alternatives.
Free men are not equal and equal men are not free.
Government is not the solution. Government is the problem.