Marginally Zero-Sum Efforts

Bostrom recently noted the problem of the commons in labeling efforts "important"; each managerial player has an incentive to label their project world-shakingly important, even though this devalues the priority label as used at other times or other projects, creating positive feedback in inflated labels.

This reminds me of how my grandfather, a pioneer in quantitative genetics, regularly bemoans the need to write more and more grant proposals to maintain a constant level of funding.  It's not that the funding is drying up in his field.  But suppose there's money for 20 grants, and 21 scientists in need of grants - or one scientist who'd like to run two projects, or receive more funding for one project...  One scientist doesn't get his first grant proposal funded, so he writes another one.  His second grant proposal does get funded, which uses up a grant that could have gone to another scientist, who now also has his first grant proposal denied, and has to write and send off a second grant proposal too...

The problem here is that, while some initial level of effort is beneficial, all effort beyond that is marginally zero-sum; there's a marginal return to the individual on additional efforts, but no marginal return to the group.  If there are 20 grants, then ultimately only 20 grant proposals are going to be funded.  No matter how many grant proposals anyone writes, the total funding available remains the same.  Everyone would be better off if everyone agreed to write only one grant proposal.  But in this case, there wouldn't be much competition for any given grant, and the rewards for writing another two or three grant proposals would be huge... until everyone else started doing the same thing.

There's no obvious limit to this process; the 21 scientists could write 1,000 grant proposals apiece, and still get only 20 grants between them.  They'd all be better off if they only wrote one grant proposal apiece; but anyone who cuts back unilaterally will be snowed under.

In a way, this is even worse than the classic problem of the commons.  A common grazing field eventually gets eaten down to bedrock and the farmers find something else to do with their herds.  When professional efforts are marginally zero-sum, but yield positive returns to the individual, the resulting cycle of busy-work can expand to the limits of individual endurance.

I've often suspected that a similar effect governs bureaucracies (both government and corporate); the longer you stay at your desk each day, the more you are perceived as a hard worker and get promoted.  But there's only a limited number of promotions to go around... and only a limited amount of genuinely important work to do.

Social approbation is the usual method for dealing with non-positive-sum actions.  Theft has positive returns to the individual, but not positive returns to society, so we put thieves in jail.  But in this case, the social dilemma is that neither writing grant proposals, nor showing up at your office desk, is inherently an evil deed.  Some grant proposals do need to get written.  It's not inherently a zero-sum activity.  It's just marginally zero-sum beyond a certain point.

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I once suggested to the EU (whose research funding application process is exceptionally laborious) that when evaluating the effectiveness of their grants scheme, they should take into account not only the internal costs of administering the scheme, but also the costs of applying. More specifically, they should estimate the salary cost of the time the applicants put into learning about the program and applying (unsuccessful applicants included) and view this as an administrative cost of the program. I think it would be an eye-opener. Of course, the chances that they would actually start doing this as a result of my suggestion are indistinguishably close to zero.

I am currently a taxi driver in a small town in northern Sweden. Its a very competitive job: At an given time, there are maybe 100 or so cabs out from a number of different brands, but only 50 or so customers. The number of customers does of course change sporadically, but its hard to predict in any detail. When someone calls the taxi-number (911 911 in our case :)), they come to the telephone-exchange, who sends out a message to a small computer terminal in the cab that happens to be closest. This encourages drivers with no customer to position themselves strategically; which is good, both for the customer and the company. But; when a customer calls ahead of time, that customers address and preferred departure time is shown on the terminal: this so that drivers can know ahead of time if there is a rush anytime soon, and if you drop of a customer some distance out of town, you can check to see if there happens to be some job for you out here if you just stick around for a while, so you don't drive halfway and then have to turn back. One consequence of this however (and here is the point) is that on calm days with few customers, if there pops up a job in the terminal 30 kilometers out of town, a whole bunch of drivers are going to race out there in order to be closest when it's released. This is bad for the company (drivers angry at each other, extra fuel costs, etc), and bad for the customer (s/he would have had a cab sent from downtown with time to spare anyway, and all this only drives the prices up), not to mention stressful and dangerous for the drivers, and all for no net benefit; it does not generate more customers, it only distributes the ones that already called. And here the same pattern appears: If I think that is silly, stupid, and un-eco-friendly, and decide to not engage in that sort of thing, I won't get as many customers; so I'm forced to compete. This of course stems from there being to many cars out to begin with, but here the same problem arises: If my boss didn't send out as many cars when he new there weren't a lot of customers, he wouldn't get ANY of them.

OT: This is my first post here, have read a lot of posts over the last year or so, and have finally decided to read all posts in chronological order. I'd also like to note that English is not my first language.

Hi all! waves hand

I believe economists call this type of zero sum competition an 'arms race'. It occurs in many situation where there is a scarcity of positional goods (e.g., living in the centre of town, being top of the class, getting the top job, having the biggest yacht, being the most famous celebrity). In some cases (educational attainment) the externalities are positive (everyone gets smarter). In others (acquiring status or accumulating wealth), the effect can be very wasteful. Social and psychological norms such as feelings of envy, or a distate for people who show off or "over-achieve" evolves to control for the effect, but that's often a very imperfect mechanism.

Job applications are another example of this effect.

For funding agencies that are all under the control of (e.g.) the US government, rationing the total number of applications any researcher (or group) can put in could be a solution.

Byrne, that would involve very rapidly diminishing social returns, since if the fitness of grant proposals is normally distributed the required population size goes as the exponential of the square of the number of standard deviations required for the cream of the crop.

Zubon, Caplan's example of collusion in the classroom is a good illustration of the phenomena I intended to single out by their absence, as it were. Grading on a curve only makes competition zero-sum if you care nothing except grades, just as playing Go is zero-sum only if you care about nothing except winning. But, as a matter of real life, if the students all study harder, they all know more economics. A farmer who farms twice as hard may drive prices down for other farmers, but in the end there's twice as much food. There is competition, but not socially zero-sum competition. On the other hand, when corporate bureaucrats work twice as hard to impress their bosses, their corporation doesn't get double the income. It may even get less. This is the distinction I was trying to point out.

The dollar auction is the most famous version I know of this. In grant proposals, every bidder must pay, not just the top two bidders, which increases the problem dramatically. You see similar effects in lobbying, or really anywhere you can bid for control of a finite pool of resources. The greater the benefits for collusion, the gerater the incentive to defect.

Bryan Caplan makes a similar point about collusion in the classroom.

One answer is that grant-writing is an evil deed. I don't tend to that belief, or the more plausible one that offering grants is an evil deed, but I think they're worth mentioning.

Not grant-writing per se, but grant-writing in excess of one's fair share (where "fair" is whatever you deserve - this would be a significant judgment point). The situation is complicated if everyone else is already grant inflating. It seems like a similar dilemma to that of preemptive violence: the line between self-defense and offense can be fuzzy.

Marginally zero-sum: kind of like publish-or perish?

This is a very general problem. If the government decides to give away $X to someone, people are willing to spend up to $X to get it. If people intensively compete for the money then you would expect people to collectively spend $X trying to get the $X.

If we assume that the time wasted writing multiple grants outweighs the benefits of stiffer competition (stimulating creativity or harder work?), there are several ways success rates could be increased: more total funding, smaller grants, limiting grants/researcher, or fewer researchers. One reason we have so many researchers is that overhead payments to universities exceed the marginal cost of doing more research. So they keep hiring more researchers, independent of teaching needs.

Nick Bostrom's point is important: We should regard the induced competition as a negative externality of the process that induces the competition -- grant writing, consideration for promotion, etc. The "correct" solution as Bostrom points out is to internalize the cost.

I think good companies do this quite carefully with the inducements they build into their culture -- they are looking to only generate competition that will produce net benefits to the company (not always the individuals).

Conversely, there are well known shop floor self-management processes (workers punishing each other for competing to win management favor) that form to prevent exactly this kind of zero-sum competition (zero sum from the worker's point of view since they don't get a share of the increased profits).

I would bet that in at least some granting processes, informal regulation like this arises to control the costs to applicants. It would be especially easy in the context of peer review.

This is a reasonable interpretation of behavior that produces "old boys clubs" -- the members of the club have formed a coalition to reduce their costs of marginal zero-sum behavior. Of course it imposes other costs...

the social dilemma is that neither writing grant proposals, nor showing up at your office desk, is inherently an evil deed.

One answer is that grant-writing is an evil deed. I don't tend to that belief, or the more plausible one that offering grants is an evil deed, but I think they're worth mentioning.

Promotion based on hours at the office, or working at a company that does that do seem to me like evil deeds, but human bias means that practically all companies have this effect, to some extent.

This is a useful example of competition at a particular level of organization creating pressure for increased cooperation at a higher level of organization.

You're ignoring the information effects. Your point is valid if every applicant applies only for the best possible grant, but if there are 20 applicants and 20 funders, the odds of that are low -- and the more applications per researcher, the higher those odds get.