It's good this discussion has taken place because it's made m eresearch more and get a better understanding of things, and from a quick search for "Examples of Libertarian society" I was struggling to come up with anything very positive. The most recent example of anything close to libertarian ideas actually in place and working was in Chile
The following quotes are from here : http://www.spectacle.org/0403/loo.html
It is fair to examine the econometric analysis and historical record of the free-market capitalist ideas that would be in effect in a libertarian society. As the noted libertarian anarcho- capitalist David Friedman writes in his The Machinery of Freedom, "Some anarcho-capitalists do not [defend the historical record of capitalist societies]. They concede the justice of many of the usual attacks on 'capitalism,' but argue that everything would be different if we could get rid of government. That is a cop-out. Human beings and human societies are far too complicated for us to have confidence in a priori predictions about how institutions that have never been tried would work."(25) That is a fair statement, and so we will examine the econometrics of what would happen if the United States implemented libertarian economic policies.
If looking for real-world historical scenarios, Chile is a prime example of libertarian ideas at work. Though Chile did not get rid of restrictions on free markets, it is the closest example of such a state in modern history, and, by the standards of the David Friedman quote above, is certainly subject to examination. For this reason, I will be giving examples from Chilean history when discussing the impact of policies such as the repeal of the minimum wage. The economy of Chile from 1973 to 1990 was one in which a nearly unrestrained free market was turned loose with the full support of the government. The "Chicago Boys," a group of Chilean economists who received graduate training in the 1950s and 1960s at the University of Chicago under free- market advocates such as Milton Friedman and Arnold Harberger, were put in charge of reshaping the country's economic policies. Milton Friedman, Harberger, and Friedrich von Hayek all visited Santiago- Milton Friedman would even give a master lecture on television(26) as well as a one-hour course in economics to the dictator Auguste Pinochet(27). Joseph Collins, citing Shirley Christian, states "At least fifteen Chicago Boys would occupy top policy-making positions in the Pinochet military government."(28) Despite the authoritarian social policies of Auguste Pinochet, he gave free rein to the Chicago Boys to implement their economic ideas- possibly because he wanted to be remembered for "a historic act of national renewal, and he decided these bold technocrats held the key to a new, prosperous future that would forever distinguish his rule. In return, Pinochet was willing to guarantee protection from all political pressure."(29). This protection from political pressure would be necessary, as the economic measures proved unpopular enough that military intervention was needed to suppress the civil unrest the measures spawned(30). The Chicago Boys, working from libertarian economic ideals, promptly implemented policies which rolled back work laws, privatized health care, drastically reduced subsidized housing, and allowed wages to plunge. When we examine this historical example, we will find that the Chicago Boys' policies dramatically reduced the economic well- being and freedom of the poor.
And what happened?
During Pinochet's regime in Chile, the lack of an hourly minimum wage(54) led to expectations that employees work long hours of unpaid overtime. When an employee complains about unpaid overtime, he could simply be fired(55) since high unemployment ensures that there will be no shortage of volunteers to take his place. This effective degrading of the hourly minimum wage was an effect of the free market reaching a balance between employment and wages in the absence of regulation; a regular practice of Chile's construction projects was the weekly queuing up of workers to underbid each other for the week's work(56). Even when the Chilean economy recovered, wages remained low as profits simply went into the pockets of employers(57). Indeed, the rapid growth years of 1986-1989 resulted in no increases in real wages(58), despite a study that estimated that the minimum wage could be increased by 50 percent without increasing unemployment significantly(59). Not surprisingly, the poor remained poor, and the percentage of families in poverty increased. Real wages in 1989 were only 90.8% of what they had been in 1970(60). The real minimum wage dropped 40% from 1981 to 1988(61). As Lois Oppenheim writes, "Does freedom of choice really exist when only a small group has the resources to exercise choice?"(62). The utter lack of ability to exercise a choice is not functionally better than not having that choice at all- and the libertarian policy, rather than increasing the freedom of the poor, drastically reduced it. The historical record of Chile shows that the poor became further impoverished, impeding their upward mobility and reducing their liberty, thereby making the libertarian argument based on moral grounds a failure.
The repeal of funding for public housing would also have adverse effects on the poor. Many low-wage employees can only find affordable housing via public housing(63) Though free- market advocates expect that private contractors could do more to provide decent inexpensive housing than the government, Chile provides an alarming counterexample. From 1974 until the end of Pinochet's reign, the private sector not only failed to shrink the housing deficit which existed in 1974, it actually fell behind as population grew(64). The houses of the poblaciones, or shantytowns, often contained three to five families. As Collins writes, "The percentage of Chileans without adequate housing increased from 27 percent in 1972 to 40 percent in 1988, even though according to neo-liberal social dogma the private construction industry combined with supplemental vouchers for low-income households would solve the housing problem."(65). Imagine how much worse the problem would be if the limited government support of the vouchers did not exist.
So what happened in Chile as regulations and wage laws were repealed or loosened? Unemployment, which averaged around 6 percent in the 1960s(67) and dropped to around 5 percent in 1973 before Pinochet took over, averaged 20 percent from 1974 to 1987, peaked at 35 percent in 1982, and even when official unemployment numbers dropped, it was because working one day a week was enough to be considered not unemployed(68). It also spawned other problems for the now unemployed or underemployed, such as alcoholism and depression(69).
A common libertarian objection to charges that the repeal of welfare would hurt the poor is that the rich will donate more money to private charities, which in turn would be more efficient than the government. The combination of private charity, churches, communities, and family would be able to "bridge the gap" for those who do not earn enough to support themselves. Clearly, this did not happen in Chile as governmental spending on the poor dropped even as the rich got richer. Malnourishment increased(72), and the number of families which could not afford a basic "basket" of necessary goods doubled in the twenty years leading up to 1989. By that point, fewer than half the families in Santiago could afford that basic basket(73).
During the Pinochet regime, Chile sharply reduced state contributions to health services, greatly increased privatization in health care, and removed regulations. This led to less preventive care which in turn led to a greater increase in health emergencies, deterioration in the quality of hospital equipment, hospital overcrowding(81), and the danger of medical quackery(82).
When Chile largely privatized its Social Security, Chileans often operated from misinformation or outright lack of information(86). Inflation further degraded the benefits, and by 1987, Chilean labor economist Jaime Ruiz-Tagle estimated that only 22 percent of Chilean workers made a salary that might allow them to retire with more than minimum benefits(87).
I found examples listed of societies having similar traits as libertarian ideals, such as some stages of early Ireland and Iceland, or early US frontier situations, but the only other example coming anything close to it in more modern terms is the Amish, though I don't know that I should use the term modern necessarily.
So from what I can gather there have been a few examples of some societies adopting some principles a LONG time ago, but most were short lived and it would appear that it doesn't adapt well to modern society.