Gray argues against the liberal tradition of Locke, Kant and Rawls that believes there is a "best way of life" where "the ideals of life" are "fused into one all-encompassing human good" that can be reached by rational consensus. Gray says that perspective doesn't work in a pluralistic world where there are conflicting freedoms and interests. He supports the alternative liberal tradition of Hobbes and Hume that argues that the best that can be hoped for is a peaceful co-existence among competing values, and Gray believes it is possible to "grade" various governing norms and regimes regarding their ability to manage such conflict.
This argument is clear enough, but it gets fuzzier when he weaves his way through these two traditions. He states that "Justice does not speak always with one voice," which suggests that there is more or less some notion of what justice is. He writes that there are "universal human goods and evils" and that, "too affirm that humans thrive in many different ways is not to deny that there are universal human values. Nor is it to reject the claim that there should be universal human rights." But, he adds, "It is to deny that universal values can only be fully realized in a universal regime." This suggests that, while there are universal values, there are many ways to achieve them. But the distinctions he makes between values, interests, good, evil, justice, and a universal "best way of life" quickly gets confusing, particularly when one of his four chapters is about "plural values," which makes the reader wonder what are universal values and what are plural values and, thus, what tradition Gray actually favors.
Gray does a good job on the pluralistic side of things, noting how seemingly universal values like freedom get expressed in incompatible ways (conflicting freedoms). But he perhaps goes too far when he writes that "in ethics there are no a priori truths." As products of an evolutionary heritage, we are self-seeking beings. Is that not only the biological (a part of our internal and universal species heritage) basis for freedom (from restriction), but also isn't this the essence of what we ought to be? Of course, this leads to the conflicting freedom problem that is the basis for Gray's plural values argument and his modus vivendi approach (what's practical, feasible) to resolve conflicts. Logically, it then follows, and this is something that Gray says that J.S. Mill and Hobbes attempted to do, that one's freedom to seek should not conflict with the freedom of others to seek their own ends if the freedom of each is to be expressed. Some form of the golden rule ("justice" as balance) is necessary within group life: Individuals don't deceive, manipulate or impose; they don't rob, rape or murder; and governments don't restrict unless it's necesary to maintain order and promote balance between self and other. Also, it follows logically that equality is required to obtain and maintain the balance between conflicting freedoms. In other words, freedom is a priori in the sense that it is embedded in our biology; justice and equality are a priori in the sense that both are necessary conditions for our essential (as in essence) freedom.
Seen this way, perhaps Kant and Rawls were onto something after all. But even within this overarching, universal and a priori framework, there is a need for norms and governing systems to reconcile the conflicting freedoms. Other than respecting the freedom of each, there might not be such things as "human rights" - although the "freedom of each" concept encompasses a lot - and how conflicting individual interests and values get resolved is a matter of convention and negotiation. As Gray writes, some cultures and governing systems are better (fairer, or more conducive to order) than others. While Hobbesian theory about how best to protect the freedom of each might be vigorously debated, there still might not be the inherent conflict with Kant and Rawls that Gray outlines in this book about the universal value of freedom for that too was Hobbes' goal. Humankind desires freedom, and equality and justice (as balance) goes along with that freedom. Once those overarching values are clearly understood for both traditions, the next question is how to best achieve those ends and, understandably, there will be the divergence of opinion for the reasons Gray notes.