Sotah as a Separating Equalibrium

Separating Equilibrium:
An economic trick to create incentives to help a guilty party unwittingly reveal their guilt through their behavior

Inudicium Dei (Judgements of God) as Separating Equilibrium
Medieval citizens' belief in iudicium Dei created a separating equilibrium. guilty defendants expected ordeals to convict them. Innocent defendants expected the reverse. Thus, only innocent defendants were willing to undergo ordeals. Conditional on observing a defendant's willingness to do so, the administering priest knew he or she was innocent and manipulated the ordeal to find this. . . .
An ordeal register from Varad, Hungary (modern-day Oradea, Romania), under the reign of King Andrew II, which Zajtay and van Caenegem was analyzed. The Regestrum records hot-iron ordeals that Hungarian clerics administered in the basilica of Nagyva´rad between 1208 and 1235. These records include outcomes for 308 cases involving ordeals. In 100 of these cases, the ordeal was aborted before it produced a final result, typically because the parties settled. My theory suggests that defendants in these cases were guilty, but of course there is no way to know whether this was so. Examining the outcomes of the 208 cases in which defendants underwent ordeals is more instructive. The data are telling: probands failed their ordeals in only 78 cases, or 37.5 percent of the time. Probands passed their ordeals in 130 cases, or 62.5 percent of the time.33 Unless nearly two-thirds of ordeal-officiating priests did not understand how to heat iron, these data suggest priestly rigging intended to exculpate probands. Ordeals exonerated the overwhelming majority of probands tried in the basilica of Nagyva´rad.
Peter T. Leeson, The Journal of Law & Economics , Vol. 55, No. 3 (August 2012), pp. 691-714

Van Halen and the Separating Equilibrium of Brown M&Ms
By the early 1980s, Van Halen had become one of the biggest rock-and-roll bands in history. They were known to party particularly hard while on tour. “[N]o matter where Van Halen alights,” Rolling Stone reported, “a boisterous, full-blown saturnalia is bound to follow.” The band’s touring contract carried a fifty-three-page rider that laid out technical and security specs as well as food and beverage requirements. On even calendar days, the band was to be served roast beef, fried chicken, or lasagna, with sides of Brussels sprouts, broccoli, or spinach. Odd days meant steak or Chinese food with green beans, peas, or carrots. Under no circumstances was dinner to be served on plastic or paper plates, or with plastic flatware. On page 40 of the exhaustive Van Halen rider was the “Munchies” section. It demanded potato chips, nuts, pretzels, and “M&M’s (WARNING: ABSOLUTELY NO BROWN ONES).”* What was up with that? The nut and chip requests weren’t nearly so nitpicky. Nor the dinner menu. So why the hang-up with brown M&M’s? Had someone in the band had a bad experience with them? Did Van Halen have a sadistic streak and take pleasure in making some poor caterer hand-sort the M&M’s? When the M&M clause was leaked to the press, it was seen as a classic case of rock-star excess, of the band “being abusive of others simply because we could,” Roth said years later. But, he explained, “the reality is quite different.” Van Halen’s live show was an extravaganza, with a colossal stage set, booming audio, and spectacular lighting effects. All this equipment required a great deal of structural support, electrical power, and the like. But many of the arenas they played were outdated. “[T]hey didn’t have even the doorways or the loading docks to accommodate a super-forward-thinking, gigantor, epic-sized Van Halen production,” Roth recalled. Thus the need for a fifty-three-page rider. “Most rock-and-roll bands had a contract rider that was like a pamphlet,” Roth says. “We had one that was like the Chinese phone book.” It gave point-by-point instructions to ensure that the promoter at each arena provided enough physical space, load-bearing capacity, and electrical power. Van Halen wanted to make sure no one got killed by a collapsing stage or a short-circuiting light tower. But every time the band pulled into a new city, how could they be sure the local promoter had read the rider and followed all the safety procedures? Cue the brown M&M’s. When Roth arrived at the arena, he’d immediately go backstage to check out the bowl of M&M’s. If he saw brown ones, he knew the promoter hadn’t read the rider carefully—and that “we had to do a serious line check” to make sure the important equipment had been properly set up. He also made sure to trash the dressing room if there were brown M&M’s. This would be construed as nothing more than rock-star folly, thereby keeping his trap safe from detection. But we suspect he enjoyed it all the same.
Levitt, Steven D.; Dubner, Stephen J.. Think Like a Freak (pp. 140-142). William Morrow. Kindle Edition.