Slowly, carefully, Mr. Woodruff builds a case for Odysseus. But this does not mean, the author argues, that justice was well served by the king. Agamemnon failed by not creating mutual respect between himself and his soldiers and not honoring the unique contributions of those like Ajax. Instead, the king ruled with a heavy, at times almost tyrannical hand, breeding suspicion and seething anger among his men. When Ajax is denied the armor — in a contest he sees as favoring the eloquent Odysseus — the loyal soldier’s rage explodes, and tragedy results.

Mr. Woodruff uses this part of the story to point out that justice is much broader than a legal function and much messier than a set of rules or large principles. Whether in the boardroom, Congressional chamber or family kitchen, justice “must resolve a conflict in a way that leaves the community whole.” And that does not happen here.

He says that by deciding against Ajax, the jurors — with the king’s assent — effectively destroy not only Ajax’s motivation, but also the morale and engagement of the other troops, virtually all of whom see themselves as loyal.

It’s a short hop from Ajax to today’s workplace: “When Ajax stops or slows,” Mr. Woodruff writes, “important work stops or slows with him, especially if he is the lead workhorse on the team.”

The book thus toggles between the ancient story and modern realities. Then and now, the author says, we are prone to placing too much importance on knowledge to the exclusion of wisdom, which he defines as “the ability to make good decisions in demanding circumstances.”

“We all know highly learned people who are fools,” he writes. “Experts often use their knowledge or skill to do dreadful things.” He also stresses the role of compassion in making just choices. “If justice is going to help us get along,” he says, “it has to affect our feelings,” which implies that it must consider what others have at stake emotionally. One reason Agamemnon fails so badly here, Mr. Woodruff argues, is that he displays little or no compassion for the shame and dishonor Ajax feels in not winning the armor.