Stephen L. Carter / Bloomberg News

Polybius, in his “Histories,” tells the story of Antiochus IV, ruler of the Seleucid Empire, who invaded Egypt during the second century B.C. The Egyptians, led by Ptolemy, sent urgently to Rome for assistance. When the Roman ambassador arrived, he handed over a list of the Roman Senate’s demands, then used his staff to draw a line in the sand around the “astonished” Antiochus “and told him he must remain inside this circle until he gave his decision about the contents of the letter.”

This tale, if it really happened, represents one of the earliest uses of the term “line in the sand” in its current sense. Antiochus gave in because, as one historian has noted, he knew Rome by reputation: He understood the risks to both his kingdom and himself if he resisted.

The story comes to mind in light of the debate over the decision by President Barack Obama to back away from his own “red line” on the use of chemical weapons by the Syrian government in its civil war. In a speech at the National Defense University in December, Obama issued a warning to Syrian President Bashar Assad: “If you make the tragic mistake of using these weapons, there will be consequences and you will be held accountable.”

In his news conference this week, however, Obama insisted that no action would be appropriate in the absence of international consensus — that the United States didn’t want to “find ourselves in a position where we can’t mobilize the international community to support what we do.” In other words: The U.S. alone had no intention of holding Assad accountable.

This certainly sounds like the president is backing down, and he has been taking some hard shots for his change of mind. But what should fascinate the scholar about this episode is the way that it provides a real-world test of an intriguing academic debate with serious practical consequences: Which kind of regime, democratic or authoritarian, is more credible when it issues a threat?

The political scientist James Fearon, in an influential 1994 paper, argued that democracies were more likely to keep their commitments because of the “audience costs” — that is, political punishment from negative public reaction — were their leaders to back down. The idea, a common one in game theory, is that my commitment is more credible if I bear a cost for breaking it. The law of contracts, for example, makes promises more reliable by placing costs on the breacher.

Fearon’s insight was that authoritarian leaders worry less than democratic leaders about public response should they make and then break a commitment. The authoritarian leader, by hypothesis, has a significant degree of control over his public. By contrast, the need to satisfy his “stronger domestic audience” makes the leader of a democracy less likely to make threats he doesn’t intend to keep. Opponents in the international arena know this, and are therefore “more likely to shy away from contests and more likely to back down once in them.”

The model is an elegant one, even if later work has cast doubt on whether history bears it out. And we are testing it now. Obama is a shrewd politician; it is entirely possible that he calculated from the start that he and his party would suffer little domestic political cost should he back away from his implicit promise to intervene if Assad used chemical weapons. That is, Obama might have intuited that the “audience costs” theory is wrong.

On the other hand, the administration’s frantic leaks over the past few days that the president is “leaning toward” supplying weapons to the Syrian opposition might represent a recognition that the calculation was wrong — that the American public, as Fearon proposed, doesn’t want to see its leaders be the first to blink. If this is true, however, helping to arm an already well-armed opposition would not be, in Assad’s eyes, much of a consequence.

Interventionists are calling for a U.S.-enforced no-fly zone, but they called for one long before Obama made his initial threat. Opponents are insisting that the threat should never have been made. What’s useful to remember is the lesson of the story of Antiochus, who backed down not because of the reputation of any Roman leader but because of the reputation of Rome. Obama’s decision to back away from his line in the sand might not hurt him politically, but it surely damages the nation’s credibility.

A nation’s reputation for keeping its word is valuable; loss of that reputation has traditionally been understood as a cost a rational nation will not want to pay. Because once it’s lost, it’s hard to get back.