The Stanford prison experiment shows that if you give average people power over others, an alarmingly high percentage will abuse that power. The Milgram experiment shows that if average people are commanded by a perceived authority to commit atrocities, an alarmingly high percentage will obey.
On a cheerier note, Axelrods data show that average people, without any central authority to coerce them into cooperation, will nonetheless tend to cooperate to mutual benefit.
For libertarians, the principal moral of these findings is clear: the prevailing ideology has grossly underestimated the dangers of, and grossly overestimated the need for, government. If people tend to play badly with others when coercive authority is present (be that power their own à la Stanford or someone elses à la Milgram), but tend to play well with others when coercive authority is absent, its clear what the problem is.
But theres a further left-libertarian moral, because its not merely coercive authority that is shown to be problematic by the Stanford and Milgram experiments. The jailors in the Stanford experiment had no power to force their prisoners to stay; and the authorities in the Milgram experiment had no tool of compulsion more imposing than a lab coat. Neither had the backing of any legal sanctions. Nor did they have so much as the power to fire anyone from a job. Yet such authority as existed was still abused, and still obeyed.
The moral is clear: even absent coercive enforcement, there is a tendency for people both to abuse authority when they have it, and to acquiesce, indeed become complicit, in its abuse by others. Hence the assumption, common among some right-libertarians, that authority and hierarchy are fine and dandy so long as they dont involve literal forcible compulsion, seems dubious.
[Hopefully unnecessary clarification: No, I am not saying that non-forcible forms of authority are rights-violations, nor that they should be combated by forcible means appropriate to such violations, nor again that those who wield non-forcible authority should be hurled into the Pit of Azathoth, there to boil and burn for all eternity in His howling, bubbling chaos. The solution to noncoercive authority is not coercive authority, any more than the cure for flu is pneumonia.]
If people have a harmful tendency that manifests itself in certain circumstances, then the appropriate response is obviously to try to a) reduce the strength of the tendency, and b) reduce the frequency of the triggering circumstances.
The tendency to abuse and/or obey authority may be too ingrained in human nature (or, more accurately: in the human situation) to be completely eliminated, but cultural factors can certainly reduce or exacerbate it. In our own culture, despite lip service (and, admittedly, often more than lip service) to anti-authoritarian values, the legitimacy of authority is constantly reinforced via everything from political propaganda and tv cop shows to the structure of school and workplace. This is one reason that left-libertarians often stress the need to promote anti-authoritarian moral attitudes that go beyond mere opposition to rights-violations. In the case of the Milgram experiments, part of the motivation for those who went along with the orders seems to have been the fear of embarrassment at the prospect of being the only one not to conform to what was expected and treated by others as normal; the inculcation of individualist ethical values would be a useful corrective here. (For a related point, see Christine Silks Randian take on Why Did Kitty Genovese Die?)
The other prong of the left-libertarian response is to decrease the frequency of those situations in which tendencies to abuse and/or obey authority is manifested, by working to reduce the prevalence of authority. Even if the elimination of all noncoercive hierarchy is not possible (and perhaps not even desirable), we could certainly do with quite a bit less of it. This is one reason that left-libertarians care, to right-libertarians bafflement, about combating such things as the hierarchical structure of the workplace.
Left-libertarians also think that such hierarchical structures are made more likely by various form of state intervention that socialise diseconomies of scale and render the labour market oligopsonistic; but thats a separate point. Actually there are at least three linkages between statism and workplace hierarchies. On the one hand, statism promotes workplace hierarchies (so the two are linked via consequence thickness). On the other hand, workplace hierarchies, by reinforcing the culture of hierarchy and authority, promote statism (so the two are linked via strategic thickness). Hence statism and workplace hierarchies are part of an interlocking, mutually reinforcing system that needs to be combated as a whole. But on the, um, third hand, even apart from causal connections the two are linked by grounds thickness i.e., workplace hierarchies are wrong for (some of) the same reasons that government-enforced power is wrong. The fact that government power tends to get abused is not the only reason for opposing it (not for us natural-rights types, anyway), but its certainly one reason to oppose it; and the Stanford and Milgram experiments show us (if the daily workplace experience of millions of people somehow, mysteriously, wasnt convincing enough already) that this reason for opposing government power applies to private, non-forcible hierarchies as well. (And ditto of course for other disorders of hierarchy such as male supremacy, white supremacy, and hetero-supremacy, even when these are not propped up directly by force both governmental and freelance.)