Thanks. Fixed.
badger
Karma: 2,482
Arrow’s theorem doesn’t apply to rating systems like approval or range voting. However, Gibbard-Satterthwaite still holds. It holds more intensely if anything since agents have more ways to lie. Now you have to worry about someone saying their favorite is ten times better than their second favorite rather than just three times better in addition to lying about the order.
Strategyproof Mechanisms: Impossibilities
See pg. 391-392 of The Role of Deliberate Practice in the Acquisition of Expert Performance.pdf), the paper that kicked off the field. A better summary is that 2-4 hours is the maximum sustainable amount of deliberate practice in a day.
I’m a PhD student working in this field and have TA’d multiple years for a graduate course covering this material.
Typo fixed now. Jill’s payment should be p_Jill = 300 - p_Jack.
The second-best direct mechanisms do bite the bullet and assume agents would optimally manipulate themselves if the mechanism didn’t do it for them. The “bid and split excess” mechanism I mention at the very end could be better if people are occasionally honest.
I’m now curious what’s possible if agents have some known probability of ignoring incentives and being unconditionally helpful. It’d be fairly easy to calculate the potential welfare gain by adding a flag to the agent’s type saying whether they are helpful or strategic and yet again applying the revelation principle. The trickier part would be finding an useful indirect mechanism to match that, since it’d be painfully obvious that you’d get a smaller payoff for saying you’re helpful under the direct mechanism.
I added some explanation right after the diagram to clarify. The idea is that if I can design a game where players have dominant strategies, then I can also design a game where they have a dominant strategy to honestly reveal their types to me and proceed on that basis.
Incentive compatibility and the Revelation Principle
That’s an indexed Cartesian product, analogous to sigma notation for indexed summation, so
is the set of all vectors of agent types.
Thanks for catching that!
I did introduce a lot here. Now that I’ve thrown all the pieces of the model out on the table, I’ll include refreshers as I go along so it can actually sink in.
Aside from academic economists and computer scientists? :D Auction design has been a big success story, enough so that microeconomic theorists like Hal Varian and Preston McAfee now work at Google full time. Microsoft and other tech companies also have research staff working specifically on mechanism design.
As far as people that should have some awareness (whether they do or not): anyone implementing an online reputation system, anyone allocating resources (like a university allocating courses to students or the US Army allocating ROTC graduates to its branches), or anyone designing government regulation.
Some exposure to game theory. Otherwise, tolerance of formulas and a little bit of calculus for optimization.
At least, I hope that’s the case. I’ve been teaching this to economics grad students for the past few years, so I know common points of misunderstanding, but can easily take some jargon for granted. Please call me out on anything that is unclear.
Mechanism Design: Constructing Algorithms for Strategic Agents
[Sequence announcement] Introduction to Mechanism Design
Alright, that makes more sense. Random music can randomize emotional state, just like random drugs can randomize physical state. Personally, I listen to a single artist at a time.
Music randomizes emotion and mindstate.
Wait, where did “randomizes” come from? The study you link and the standard view says that music can induce specific emotions. The point of the study is that emotions induced by music can carry over into other areas, which suggests we might optimize when we use specific types of music. The study you link about music and accidents also suggests specific music decreased risks.
All the papers I’m immediately seeing on Google Scholar suggest there is no association between background music and studying effectiveness, or if there is, it’s only negative for those that don’t usually study to music. If that’s accurate, either people are already fairly aware of whether music distracts them, they would adapt to it given time, or they don’t know what kinds of music are effective for them due to lack of experience.
Hmm… Atlas Shrugged does have (ostensible) paragons. Rand’s idea of Romanticism as portraying “the world as it should be” seems to match up: “What Romantic art offers is not moral rules, not an explicit didactic message, but the image of a moral person—i.e., the concretized abstraction of a moral ideal.” (source) Rand’s antagonists do tend to be all flaws and no virtues though.
One more hypothesis after reading other comments:
HPMoR is a new genre where every major character either has no character flaws or is capable of rapid growth. In other words, the diametric opposite of Hamlet, Anna Karenina, or The Corrections. Rather than “rationalist fiction”, a better term would be “paragon fiction”. Characters have rich and conflicting motives so life isn’t a walk in the park despite their strengths. Still everyone acts completely unrealistically relative to life-as-we-know-it by never doing something dumb or against their interests. Virtues aren’t merely labels and obstacles don’t automatically dissolve, so readers could learn to emulate these paragons through observation.
This actually does seem at odds with the western canon, and off-hand I can’t think of anything else that might be described in this way. Perhaps something like Hikaru No Go? Though I haven’t read them, maybe Walter Jon Williams’ Aristoi or Ian Banks’ Culture series?
I’m also somewhat confused by this. I love HPMoR and actively recommend it to friends, but to the extent Eliezer’s April Fools’ confession can be taken literally, characterizing it as “you-don’t-have-a-word genre” and coming from “an entirely different literary tradition” seems a stretch.
Some hypotheses:
Baseline expectations for Harry Potter fanfic are so low that when it turns out well, it seems much more stunning than it does relative to a broader reference class of fiction.
Didactic fiction is nothing new, but high quality didactic fiction is an incredibly impressive accomplishment.
The scientific content happens to align incredibly well with some readers’ interests, making it genre-breaking in the same way The Hunt for Red October was for technical details of submarines. If you are into that specific field, it feels world-shatteringly good. For puns about hydras and ordinals, HPMoR is the only game in town, but that’s ultimately a sparse audience.
There is a genuine gap in fiction that is both light-hearted and serious in places which Eliezer managed to fill. Pratchett is funny and can make great satirical points, but doesn’t have the same dramatic tension. Works that otherwise get the dramatic stakes right tend to steer clear of being light-hearted and inspirational. HPMoR is genre-breaking for roughly the same reasons Adventure Time gets the same accolades.
Since Arrow and GS are equivalent, it’s not surprising to see intermediate versions. Thanks for pointing that one out. I still stand by the statement for the common formulation of the theorem. We’re hitting the fuzzy lines between what counts as an alternate formulation of the same theorem, a corollary, or a distinct theorem.