The system of weights and measures described in Alma 11:5–19 was instituted by King Mosiah (11:4) as part of the legal reforms he instituted (11:1) to serve the needs of the justice system that began with the new reign of the judges. Why was this economic reform necessary?
Previously, the king administered the justice system and appointed judges. To be a judge was a position of honor, and the elders would take their turns serving. It was the responsibility of all adult men to participate in the legal process. The virtue of judging righteously was expected to be a universal virtue in the Old Testament. The men were supposed to know the law and judge according to the proper values and conventions of the Law of Moses. But the names of their "different pieces" of gold or silver varied from town to town, and "in every generation" (11:4). They did not "reckon" (count) according to the old Jewish manner of accounting used in Jerusalem, and they did not use the old Jewish measurements, or names for their weights and measures (11:4).
For the Nephites, all this changed with the reign of the judges. They had a professional, nationwide judiciary now. The judges would have to award damages and their judgments would need to be clear. In addition, they would have to be paid themselves. The governors needed to know how much to pay them. This is likely why the creation of this new legal system and the standardized Nephite monetary system came into being, hand-in-hand. Previously the Nephites "altered their reckoning and their measure, according to the minds and the circumstances of the people, in every generation, until the reign of the judges, they having been established by king Mosiah" (11:4).
This monetary system had no coins as such. They only had weights of standard sizes that could be then equated with certain measures of grain or other commodities. Mosiah’s basic silver system had six binary weights: a leah, shiblum, shiblon, senum, amnor, and ezrom, with the onti being the sum of them all (Figure 1). They would have known how to use these in the marketplace, allowing them to convert from silver, or gold, into "barley, and also for a measure of every kind of grain" (11:7), and from there into the various other commodities. Nephites would have had weights for each of these sizes that they could use in weighing produce on balance scales to determine whether they had the right amount of barley, oil, or any other commodity. For efficiency, an antion (equal to 1/12; measure) was added, which actually maximizes the number of amounts that could be weighed with the fewest number of weights.
Figure 1 John W. Welch and Greg Welch, "King Mosiah’s Monetary System," in Charting the Book of Mormon, chart 110
John W. Welch, "Weighing and Measuring in the Worlds of the Book of Mormon,"Journal of Book of Mormon Studies 8, no. 2 (1999): 36–45, 86: "This sidelight in the book of Alma contains enough facts to support meaningful parallels between King Mosiah’s weights and measures and those used in other ancient cultures. For many reasons, these monetary details found in the large plates are weighty matters indeed. The attempted bribery, the overreaching of the lawyers, the royal standardization and official codification of these measures, their mathematical relationships, and the unusual names involved in Alma 11 have long intrigued readers."