He starts by investigating the source of constitutional legitimacy. After all, why bother trying to interpret a constitution if it’s illegitimate? If the only reason people obey government officials is fear of punishment — if its constitution is not in some way morally relevant — then it really doesn’t matter what it says.

Consider the traditional basis of constitutional legitimacy: the consent of the governed. Our own Declaration of Independence famously declares that to secure these rights, Governments are instituted among Men, deriving their just Powers from the Consent of the Governed. Yet everyone concedes that the constitution lacks unanimous, explicit consent. (Did you consent? Personally, I don’t remember doing so.) So if explicit consent is out, perhaps some form of indirect or implicit consent will work. Barnett takes Chapter 1 to debunk various forms of implicit or indirect consent, e.g. consent via representation, "by voting, you consent," "by not leaving the country, you consent," "by receiving the benefits of government, you consent" etc., etc.

Lysander Spooner believed [t]here [to be] no alternative but to say, either that the separate, individual consent of every man, who is required to aid, in any way, in supporting the government, is necessary, or that the consent of no one is necessary. (No Treason, emphasis mine.) Barnett takes this cue from Spooner and stops trying to ground constitutional legitimacy in consent. But if the source of the constitution’s legitimacy isn’t consent, what is it? How can a government legitimately govern the non-consenting?

Assuming you agree that respecting the rights of others is morally binding, here’s how you might go about establishing the legitimacy of laws (pp. 44–45, emphasis his):

… A law is just, and therefore binding in conscience, if its restrictions are (1) necessary to protect the rights of others and (2) proper insofar as they do not violate the preexisting rights of the persons on whom they are imposed.

The second of these requirements dispenses with the need to obtain the consent of the person on whom a law is imposed. After all, if a law has not violated a person’s rights (whatever these rights may be), then that person need not consent to it. The first requirement supplies the element of obligation. If a law is necessary to protect the rights of others (again, whatever these rights may be), then it is as obligatory for the person on whom it is imposed as protecting that person’s rights is obligatory on the legal system itself. Persons have an obligation to obey such a law just as they have an obligation to respect the rights of others…

OK, so this gets us part-way. He’s established that laws may sometimes be legitimate. But just because a government acts legitimately in some particular case, why should anyone trust that it will continue to act legitimately in other cases? This is where some kind of Benevolent-Dictator-for-Life scenario breaks down: there’s no reason to believe the BDFL will continue to be benevolent, and every reason to believe (cue Lord Acton) that he’d quickly become a malevolent dictator.

Barnett believes that what’s lacking in the BDFL case is some kind of procedural assurance that his actions can be presumed legitimate: In the absence of actual consent, a legitimate lawmaking process is one that provides adequate assurances that the laws it validates are just in this respect. (p. 45, emphasis his)

We’d like it if we could give the government’s activities the benefit of the doubt. If its processes are designed so that we can be reasonably sure that the output (laws and government actions) are just, then we can give it the benefit of the doubt — we can presume that the government is acting justly until shown otherwise. Here’s a different wording, from p. 3:

… Even in the absence of [unanimous] consent, however, laws can still bind in conscience if the constitution that governs their making, application, and enforcement contains adequate procedures to assure that restrictions imposed on nonconsenting persons are just. Such a constitutional order can be legitimate even if it was not consented to by everyone; and a constitution that lacks adequate procedures to ensure the justice of valid laws is illegitimate even if it was consented to by a majority.

What I love about this is the emphasis on method. We give the results of new scientific research the benefit of the doubt precisely because we trust the scientific method. Just so, we could give the benefit of the doubt to the output of a government with a sufficiently trustworthy process. Whether or not our current government's processes meet this standard is left as an exercise for the reader.