Imagine you are the referee of a giant, invisible game played in the world of business and schools. In this game, players (like companies trying to be green or students trying to get into college) take hidden actions to improve their performance. A referee (like a rating agency or a test scorer) sees a noisy clue about how hard the player tried, but the real audience (investors or universities) only sees the referee's final score. The tricky part is that the players are smart; they know the referee's rules and might try to "game the system" by faking their effort or focusing only on what gets them a high score, rather than doing the actually good work. This is the world of information design and moral hazard. "Moral hazard" is just a fancy way of saying "people might slack off or cheat if they think they won't get caught," while "information design" is the art of deciding exactly how much truth to reveal to keep everyone playing fair. The big question is: Should the referee show every single detail of the player's performance, or should they hide some parts to keep the players motivated?

This paper, titled "Optimal Rating Design under Moral Hazard," dives deep into that question. The authors, Maryam Saeedi and Ali Shourideh, act like master game designers trying to figure out the perfect rulebook for rating systems. They discover that there is no one-size-fits-all answer. Sometimes, showing everything is best. But often, the smartest move is to censor the information—meaning, to deliberately blur the lines between certain outcomes. They find that the best way to censor depends entirely on how the player's effort changes the odds of success. If trying harder makes a "home run" more likely but also makes a "strikeout" more likely, the best rating system should hide the bad outcomes (lower censorship) to encourage risk-taking. Conversely, if trying harder just makes results more consistent and less risky, the best system should hide the amazing outcomes (upper censorship) to discourage inaction. They even show that in complex situations where players can fake their way to a good score without actually doing the work (called "window dressing"), the referee should sometimes hide the middle scores entirely to stop the fakers.

The Game of Hidden Effort and Noisy Clues

To understand the paper, let's set the stage with a simple story. Imagine a baker who wants to sell the best bread in town. The baker can choose to work hard (using premium flour and kneading for hours) or take a shortcut (using cheap flour and a machine). The town's customers (the market) want great bread, but they can't see the baker's hands; they can only taste the final loaf. A rating agency (the intermediary) watches the baker and sees a "clue"—maybe the smell of the kitchen or the color of the crust. This clue is noisy; a good smell doesn't guarantee great bread, and a bad smell doesn't guarantee bad bread.

The rating agency has a choice: tell the customers exactly what the clue says, or give them a vague summary like "Good," "Okay," or "Bad." The baker knows the agency's rules. If the agency is too harsh, the baker might give up. If the agency is too easy, the baker might stop trying hard and just try to look good. The agency wants to design a rating system that gets the baker to work as hard as possible, or perhaps to help the poor bakers survive, or to stop bakers from faking their way to a "Good" rating.

The paper's main trick is realizing that the rating system doesn't just give a score; it creates a price for the baker's effort. If the rating is "Good," the baker gets a high price for their bread. If it's "Bad," they get a low price. The baker decides how hard to work based on how much extra money they expect to make if they try harder. The authors introduce a clever concept called interim prices. Think of this as the baker's "second-guessing" belief. Before the final rating comes out, the baker thinks, "If I see a good smell, what will the customers eventually think?" The paper proves that if the rating system is fair (meaning higher smells always lead to higher expected prices), then the set of possible rating systems is limited to those that "smooth out" the extreme ups and downs of the raw clues. You can't create a rating system that makes the price jump more wildly than the raw clues do; you can only average them out.

The Magic of Hiding the Truth

The most exciting part of the paper is how it answers the question: "When should we hide the truth?" The authors find that the answer depends on how the baker's effort changes the shape of the possible outcomes. They identify three main scenarios, which they call MLRP, ELRP, and CLRP.

1. The Standard Case (MLRP): Show Everything!
In the classic textbook world, if the baker works harder, the bread just gets better across the board. A hard-working baker is always more likely to have a great loaf and less likely to have a bad one, no matter where you look. The paper confirms that in this boring, predictable world, the best rating system is full disclosure. You should tell the customers everything. Why? Because if you hide the bad bread, you might accidentally hide the fact that the baker is actually trying hard. If you hide the good bread, you take away the reward for their effort. So, in this standard case, transparency is king.

2. The Risky Innovator (ELRP): Hide the Disasters!
Now, imagine the baker is an innovator. They are trying a crazy new recipe. If they work hard, they might create a legendary, world-famous bread (a huge win), but they might also burn the whole batch (a huge disaster). If they don't try, they just get a mediocre loaf. Here, working harder expands the tails: it makes the best outcomes and the worst outcomes more likely. This is the Expanding Likelihood Ratio Property (ELRP).

The paper suggests that in this case, the best rating system is lower censorship. This means the agency should hide the really bad outcomes. If the baker burns the bread, the agency should just say, "Well, it's not great," but not reveal the specific disaster. Why? Because if the baker knows that a total failure will be publicly shamed, they might be too scared to try the risky new recipe. By pooling the bad outcomes together and giving them a "safe" average rating, the agency gives the baker insurance against the downside. This encourages the baker to take the risk and work hard, hoping for the legendary bread. It's like a parent telling a kid, "If you try to build this rocket and it explodes, we'll just say it was a learning experience," so the kid isn't too scared to light the fuse.

3. The Careful Maintainer (CLRP): Hide the Miracles!
On the flip side, imagine a baker who just wants to make sure the bread is consistent. If they work hard, they stop making mistakes. They don't get more legendary loaves, but they stop making burnt ones. Working hard compresses the distribution toward the middle. This is the Compressing Likelihood Ratio Property (CLRP).

Here, the paper argues for upper censorship. The agency should hide the really good outcomes. If the baker accidentally makes a perfect loaf, the agency should just say, "It's good," without revealing it was a miracle. Why? Because if the baker knows that a perfect loaf will be rewarded handsomely, they might be tempted to take shortcuts and hope for luck. But if the agency hides the top prizes, the baker realizes that the only way to get a "Good" rating is to be consistent and avoid the "Bad" ratings. By hiding the high scores, the agency discourages the baker for being inaction or inconsistent, because if they are inaction, they might accidentally produce a bad loaf, and that bad loaf will be revealed and punished. It's like a teacher who hides the "A+"s but shows the "F"s, forcing students to focus on not failing rather than hoping for a lucky break.

The Window Dressing Trap

The paper also tackles a sneaky problem: window dressing. This happens when a player can do something that looks good on the rating but doesn't actually help the market. For example, a company might spend money on a flashy ad campaign (window dressing) to make their ESG score look great, while ignoring actual environmental damage. Or a student might memorize test answers without learning the material.

The authors find that even if the rating system is perfect at measuring effort, it can still go wrong if the player can "fake" the signal. They introduce a rule called Monotone Relative Informativeness (MRIP). This is a fancy way of saying: "Does a high score mean the player did the real work, or just the fake work?"

If high scores are always more likely to come from the fake work, the best rating system is upper censorship (hide the high scores). This stops the faker from getting a huge reward for their trick. If high scores are always more likely to come from the real work, the best system is lower censorship (hide the low scores) to encourage the real worker. The key insight here is that you don't need to change the whole system; you just need to censor the specific part of the score that the fakers are good at. It's like a teacher realizing that a student is good at guessing multiple-choice answers but bad at essays. The teacher might decide to hide the multiple-choice scores and only show the essay scores to get a true picture of the student's knowledge.

The Middle Ground: Redistributive Tests

Finally, the paper looks at a different goal: redistribution. Imagine a school system that wants to help disadvantaged students. The school knows that some students have it harder (maybe they don't have a quiet place to study), so they have to work twice as hard to get the same score. The school wants to design a test that encourages everyone to try, but also gives a boost to the struggling students.

The authors find that in this case, the optimal test might use mid-censorship. This is a weird middle ground where the test hides the middle scores but reveals the very high and very low ones. Why? Because if you hide the middle, you prevent the struggling students from being discouraged by a "mediocre" score that doesn't reflect their hard work. At the same time, you keep the high scores visible to reward the top performers and the low scores visible to keep everyone motivated. It's a balancing act: you pool the "okay" results to be kind, but you keep the extremes sharp to maintain the incentive to do your best.

The Big Picture

The paper concludes that there is no single "best" rating system. The perfect design depends entirely on the nature of the work being rated.

• If the work is routine and predictable, show everything.
• If the work is risky and innovative, hide the failures to encourage boldness.
• If the work is about consistency and safety, hide the miracles to discourage inaction.
• If the work involves faking, hide the scores that the fakers can manipulate.
• If the goal is fairness, hide the middle ground to protect the vulnerable.

The authors prove these results mathematically, showing that these "censorship" strategies are not just guesses but the optimal solutions derived from complex equations. They show that the best rating systems are often simple, deterministic rules: "If the score is below X, say 'Bad'; if it's between X and Y, say 'Average'; if it's above Y, say 'Good'." But the magic is in where you draw those lines. By understanding how effort changes the odds of success, we can design rating systems that don't just measure performance, but actually create better performance.

In a world full of ratings—from Amazon reviews to college admissions to ESG scores—this paper offers a toolkit for regulators and designers. It suggests that when we see a rating system that seems to hide the truth, it might not be a mistake or a conspiracy. It might be the smartest possibl