The elite evaluator story discussed in my last post is this: evaluators vary in the perceived average quality of the applicants they endorse. So applicants seek the highest ranked evaluator willing to endorse them. To keep their reputation, evaluators can’t consistently lie about the quality of those they evaluate. But evaluators can charge a price for their evaluations, and higher ranked evaluators can charge more. So evaluators who, for whatever reason, end up with a better pool of applicants can sustain that advantage and extract continued rents from it.
Thanks. Andreessen and Horowitz went to Mike Ovitz for advice, and they conceive of their VC firm as resembling a Hollywood talent agency. Ovitz and four other agents left the William Morris Agency in 1975 and started CAA, so that's a famous example of a successful entry into an Elite Evaluator business.
My vague impression is that movie talent agencies tend to have a lot of nominal stability in terms of the William Morris Agency and CAA being a big deal decade after decade, but there is also much tumult behind the scenes at agencies with coups and desertions and the like. The movie trade papers follow the ups and downs within agencies closely, but I don't follow them.
Well the spirit of the model says it is surprising that a new VC firm could be ranked so highly. He needed to bring in some strong status markers to make that work.
The existing Hollywood Stock Exchange, which plays without real money, is useful because it encourages insider trading.
What does your model predict for Mark Andreessen's six-year-old venture capital start-up?
I like the direction you're taking here, making it a repeated game, but it seems unnatural to assume that applicants know xi, but the observer doesn't. And that assumption seems to be doing a lot of work here, because without it, an evaluator would be much more tempted to compete with higher ranking evaluators by raising its xi, since the observer would update on that and raise its estimates of that evaluator's applicants for the current round.
(Another problem: why doesn't evaluator N raise its price from 1/2 to 5/8? At pN=1/2, its applicants are going to get a profit of 1/4. With pN=5/8, that profit drops to 1/8, which is still no worse than the next best choice of going to evaluator N-1.)
What if we change your setup so that applicants don't know xi either, and have to infer based on past data? Intuitively, no evaluator would want to reduce xi, since it can't attract any additional applicants that way. Raising xi is costly in the current round, so it won't be done as long as discount rate is high enough... But no, that depends too much on each applicant being able to apply to only one evaluator, which is not realistic...
I posted it as a top-level comment. I'm not an economist, and it could probably be cleaner, but it does reproduce the following facts:-If evaluators do not change their quality, applicants and observers have the equilibrium we're postulating.-Evaluators who lower their quality will make money in the short term but pay for it later.-Evaluators can only increase their quality by taking losses in the short term--either lowering their prices below short-term profit-maximizing level, or raising their quality without any immediate price raise.
I thought the second point was a bug, but it might actually be a feature--I suspect that a university in real life actually could eventually raise its prestige given enough money and patience. So the conditions for self-sustaining prestige might actually have to do with time horizon/capital constraints.
The point of the model isn't crystal clear to me. ['Economists love formal models' isn't elucidating.] But I gather that the part "economists" would question in the absence of a formal model is "evaluators who, for whatever reason, end up with a better pool of applicants can sustain that advantage and extract continued rents." (Emphasis added.)
Does it take much restrictiveness to show that it's possible for prestige to be self-sustaining? That seems all he's aiming for. You seem to expect a model that helps establish the argument by yielding illuminating (unexpected) results.
Here's my attempt at an alternate model:
In addition to applicants and evaluators, introduce a third agent, the observer (corresponding to the 'later observers' in OP who determine the applicants' reward; this is a single agent for simplicity). The observer plays after the endorsement phase, and tries to accurately assess the quality of each applicant. I don't think the exact incentive structure will matter too much, so just say the observer pays a cost equal to the squared difference between their assessment and the actual quality. The observer's only information about this round's applicants is what evaluator endorsed them. They also have accurate historical info on the quality applicants endorsed by each evaluator in prior rounds. They do not know what quality the evaluator is claiming to enforce this round.
Applicants' reward is now the difference between the observer's assessment of them and the price of their evaluator, and they know the assessments of applicants from prior rounds. Evaluators must determine their price and quality simultaneously with one another, and they have no exogenous constraints on what quality they will choose. Students will choose randomly if their expected reward is tied. Otherwise the game is as above.
Now, as an ansatz in our search for equilibrium, suppose that observers assess each candidate as having the average quality of last round's applicants from the same evaluator, each evaluator has chosen quality xi=2^(i-N-1) and charges a price pi=xi, and each applicant with quality x chooses the evaluator with the greatest xi s.t. xi < x.
This implies that the candidates endorsed by evaluator i will have qualities uniformly distributed in the range (xi, x(i+1)), so the observer will have no incentive to spontaneously deviate. This implies that the assessment for applicants endorsed by evaluator i will be (x(i+1)-xi)/2, so applicants have no incentive to spontaneously deviate.
That leaves the evaluators, which is the hard part. I'm out of time right now, but some general thoughts.-It seems like a combination of price cutting and quality raising could lift an evaluator's long-term earnings, possibly at short-term cost--so this is not a stable equilibrium.-We might correct this by changing the incentives of the evaluators; perhaps future rounds' earnings are time discounted.-But this could lead to the counterintuitive result that high-ranking evaluators will slash their quality for a one-round profit at the expense of the future--maybe we want some kind of loss aversion relative to current income?-We could also try giving the observer a noisy history to give them an incentive to look at the average of many prior rounds, making rank climbing slower.
I wanted to make sure I understood Robin's model before evaluating it, but I agree that if movement order is doing all the work, that does not seem like a good explanation of real-world "elite evaluator rents". Would be interested to see your model when you finish it.
So without further ado, let me present such a model.
My guess is that most readers would have been grateful for further ado. Between an intuitive description of the general problem and a formal example, it would be most helpful to have an intuitive description of the strategy to be used in constructing the formal example. [Philosophers are good at doing this; mathematician and economists not.] (See "Overzealous concision: Density" — http://disputedissues.blogs... )
If this means that your model implicitly assumes that evaluators are equally skilled, shouldn't you make that explicit?
it remains to be seen whether they can charge such high fees that they can subsidize the bettors AND extract a hefty amount of rent.
If they have sufficient market power (which RH has shown includes prestige), they will do what monopolies do: restrict "production," meaning only taking elite clients who are willing to pay high fees.
Again, think Harvard. There will also be prediction markets like podunk community colleges.
Orgs that hire elite prediction markets will be looking for prestigious decisions, to quell rival factions (as RH has much discussed and you mention).
[I don't see that the expensiveness of the service is a negative factor in the determination of the size of the rents obtained.]
I agree that transparency would reduce the "surplus prestige" of the company," but I doubt that subsidy would be the sole factor. I'd think the prediction companies would offer clients considerable assistance in formulating their betting propositions.
This doesn't seem like the right dynamic; movement order is doing all the work. The answer to "What Does Harvard Do Right?" probably isn't 'move last'.
In particular, I think the model should depend on state--it shouldn't leap into the expected pattern in the first round.
I tried to capture this by building a model where applicants' rewards come from agents trying to guess their value based on their evaluators and results of previous rounds. It got complicated, but it looked like evaluators would have incentive to increase their standards and/or cut their price, incurring a one-term loss (until observers noticed their increased quality) in exchange for a recurring gain.
Isn't the prediction quality on a given question a fairly transparent function of the subsidy level of that question (at least in a thick market)?
Well, in the case of VC it's not really expensive to maintain a better clientele. For universities there are expenses (they have to be somewhat demonstratively better, offer better facilities, etc...) but the (potential) clientele has long accepted payment of enormous fees for those marginally better results, plus merely being exclusive enhances value as well. Both present prime rent extraction opportunities.
Public prediction markets would really have to spend a lot more to get significantly more accurate predictions. They can then surely charge higher fees but it remains to be seen whether they can charge such high fees that they can subsidize the bettors AND extract a hefty amount of rent. This might be possible if they go the way of consultancy (being used to provide status to already decided policy choices).