Excess Signaling Example

To understand my argument against admirable activities, it helps to understand the concept of inefficient signaling.  Here is a simple example. 

Imagine there are two equal sized groups of employees: good and bad.   Good employees produce twenty units of value for an employer, while bad employees produce ten units of value.   The problem is, it is not easy to tell which employees are which.   With many competing employers, each employee will be paid what he appears to be worth on average.  A good employee will be paid twenty, a bad one will be paid ten, and an employee of random unknown type will be paid fifteen.

Imagine that employees can go to school before they look for a job, but that they would learn nothing useful at school.   They might go to school anyway though, to signal their ability.   Imagine it costs good employees six units of value to complete school, while it costs bad employees twelve units.  In this scenario, we can have an equilibrium where good employees complete school, and bad employees do not.   Employers would pay twenty to graduates, and ten to non-graduates.   

Good employees get a net of fourteen from going to school, which is better than the ten they would get from skipping school.   Bad employees would only get a net of eight from going to school, and so they are better off skipping school.  Notice, however, that both types of employees would be better off if school were not possible, as they would each then get fifteen. 

This example illustrates the concept of inefficient signaling: the effort to make yourself look better than others comes in part at the expense of those others, which means that all else equal we do too much signaling. 

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  • Zhong Lu

    Robin, I read your link and I disagree with it from the first paragraph. We do “admirable” activities because they make our lives and the lives of the people around us better- hence these activities are “admired.” If people admire me more than X, than that means I’m a better person than X.

    A person who shines brightly will make the people around him look dim. But people with caliber, when surrounded by people better than them, use that as an incentive to work harder and shine bright themselves.

    Success begetting success is how the world should be.

  • Stuart Armstrong

    Thanks for that example Robin. It clarifies things.

    Though it does seem to rely on the admirable activity being only worth it as a signal, and not actually providing an improvement. Let’s see, if the school provides the student with an additional one unit of value, then good employees still finish school and the bad don’t, and the good employees are paid 21 (so back up to their previous total). But the bad ones are still stuck at ten (total result -5).

    Now let the school provides three units of value. Then if Gs = good go to school, Bs = Bad go, Gd = Good don’t go, Bd = Bad don’t go.
    The returns are then (Gs,Bd) = (17,10); (Gs,Bs) = (12,6); (Gd,Bd) = (15,15); (Gd, Bs) = (10,11) (or (20,1)). So the bad will continue to not go to school, and the good will go: (17,10): a gain for the good, but a loss for the bad, overall a loss.

    As the value of school increases to six, then the good will always go to school. (Gs,Bd) = (20,10), (Gs, Bs) = (15,9). So the bad won’t go, and the situation is ideal and fair (20,10).

    But if the school value is eight, then (Gs,Bd) = (22,10), (Gs, Bs) = (18, 12). Then both will go and the situation is (17,11), a loss.

    So if we want the signalling to be both accurate and beneficial, the admirable activity should provide positive or neutral improvement to those who are good at it, and a large penalty to those who are bad.

    So just the mere presence of signalling is not enough to rule that there must be wasted effort. Again, back to the debate as to the value of art, sport, jokes, etc… and people’s biases around them.

  • Stuart, a single example is not a theorem – the idea was just to illustrate the problem.

    Zhoug, you have been posting a lot of comments, all of which suggest that you do not understand what we are talking about. You might be happier at some other blog.

  • ChrisA

    I agree with you Robin, too often we are engaged in signalling rather than actually doing an activity for the sake of it, this is especially true of education, as I have found by experience. But, in terms of recognising that this is a bias of society as a whole, what can we do about it? In your example if I said to myself I am going to skip school as it is a waste of time I will be four units worse off. Individually I can’t overcome the bias. This would also be true in other areas, such a sexual competition, I could easily find myself efficiently without a mate!

  • Chris, what I hope for is that when we comment on the global situation we lament admirable activity, as we do war and global pollution, instead of praising it. We might admit that we are personally better off going to war and polluting, but at least we usually don’t claim they are good for the world.

  • dbullock

    Signaling is rent-seeking!

  • Robin, I know this is just an example, but I still think you’re not covering all the bases appropriately.

    Your example is privately inefficient but not neccesarily socially inefficient, since you have ignored the benefit to employers of sorting the good employees from the bad. I’m sure you know that it is socially efficient if the marginal benefit is greater than the marginal cost, which here equals either 12 or 6. Looking at real world numbers, let’s assume all of the costs of attending grad school are opportunity costs. So it’s one year’s salary, say $50,000. I think it’s plausible that employers would value this employee quality information at more than $50,000, since the employee’s career is likely 20+ years. Further, it’s plausible that the costs of education would be shared between employees and employers.

    The only clear reason I see for inefficient signaling in this real world example is that grad school is subsidized by the government. Mere social approbation and disapprobation I do not see as neccesarily producing socially inefficient levels of signaling. Please explain how that might be.

  • Will, yes of course there can be sorting benefits. In my example, if the value of an unsorted employee was only 11, as opposed to the 15 I assumed, then the signaling equilibrium is better. But note that is a very large sorting benefit.

  • I’m trying to make sense of your example which seems to obviate the usefulness of ‘school’ while still asserting that it costs less for the ‘good’ employees.

    Perhaps if you would adapt your example to a problem my company has, I’d understand it better.

    Our situation is that we are a rapidly growing company with no middle management. The principals have made a (bad) habit of hiring ‘only the best’. We have a great number of highly talented people who have all kinds of other employment options.

    Because of the lack of middle management, we have issues with communications the end result being a lot of employee turnover. However the few managers at the top who are clueless to the larger problem have only been effective at responding to those few employees that signal their frustration. The result is that they become part of a kind of informal inner circle.

    There are benefits to being in this inner circle but they do not address the problem.

    What is the ideal path with silence versus signal and staying vs quitting?

  • Cobb, the example isn’t intended to relate to any real company problems out there.

  • Nic “RedWord” Smith

    I just happened to stumble across a email whitelisting service, and can’t help but think that it might make a less “loaded” example, as even people who want to overcome bias have bias. Suppose there are two classes of people who send email – spammers and opt-in list admins (I’ll use the term “marketer”). Suppose spammers earn $0.10 per email sent, marketers earn $1.00, the cost to maintain the list is $0.50 per email, the cost per email received is $0.11, and the cost per email filtered is $0.05. If all marketers signal that they are marketers and not spammers, they earn $0.50 per email, spammers make nothing, and (assuming an equal proportion of spam and legitimate messages) the owners of the email boxes pay an average of $0.08 per email. The presence of a signal in this situation dramatically reduces the earnings of the marketer while bringing a much smaller benefit to those who receive email (-$0.50 vs +0.03) so the signal is a net bad.

    Please note that the numbers presented have been selected completely arbitrarily and are a poor reflectional of the actual email situation. One odd little thing that you might have noticed is that I assume that spammers keep sending spam after they are no longer received by anyone. If they were rational and in control of their actions, they would stop, and the benefit to email receivers would be greater. However, in this scenario, spammers who meet this criteria wouldn’t be spammers in the first place, but marketers; in other words, spaminess and spam frequency are taken as innate.

  • Zhong Lu

    Ok. I agree. I really don’t understand what you’re talking about.

  • Paul Gowder

    But given that there’s a massive and probably insoluble collective action problem in getting from the inefficient signaling equlibrium to the nobody-goes-to-school equilibrium, why bother? I can’t help but feel like exhorting people to give up inefficient signaling is in itself a form of the same.

    (Also, if we’re wired to like an inefficient level of admirable activity, we have to count that pleasure into our general utility function somehow, and I’m not sure how that would work — maybe the individual over-expenditures on admirable activity create enough positive externality to outweigh the waste?)

  • Paul, if school is in fact an inefficient signal, the first step is to talk about it that way. We pollute and go to war for our local benefits, but at least we usually do not claim that such things are good for the world.

  • That depends upon whether one can say with any certainty that today’s world is good since it obviously lies at the very end of all previous wars.

  • Stuart Armstrong

    a single example is not a theorem

    I am most aware of that – my point was to extend the example to see if there was extra insight to be gained (the theorem version of what I said would be “If there is no penalty for good people to signal and a high enough penalty for others that a bad person does not improve his income by signaling, even if he is the only bad person to do so, then the signaling is accurate and at least socially neutral.”)

    But your example has convinced me that unless there is a substantial gain from the activity, then signaling will mean that effort will be wasted.

    However, if the gains are large, then the signaling will not be a problem (if the gain is large across the board, then the signaling is inaccurate, but the social benefit is positive). There’s also the issue of a free-market economy, deriving common good from (to a large extent) individual desire to signal.

    The original question was simply: would it be better for the world if globally we reduced these admirable activities? And is there a bias towards them? The presence of signaling in these activities is a sign that some of them could be done more efficiently (the ones that suffer from their signaling). But the activities are too varied, and their benefits and costs are also too varied to generalize about admirable activities.

    To analyze the results of a global reduction or increase in art or education would be very difficult. I don’t see that we can short-circuit that analysis simply because they are admirable activities.

  • Stuart, if you let the complexity of the world discourage you from ever drawing any conclusions about whether there is too much or too little of anything, you may never be in a position to make any recommendations. Deciding that there is too much of something of course does not imply that any particular regime of regulation or social pressure would not be worse.

  • Stuart Armstrong

    I just think that estimating these admirable activities is a lot less like deciding on the existence of free energy machines (can be decided on basic principles) and more like deciding on the existence of global warming (needs lots of careful studies and an awareness of lots of factors that could throw the data).

    I’m calling for prudence, not impotence 🙂

  • Richard Sharpe

    It would seem then that those of low ability should have an interest in preventing those of high ability from signaling … and that defectors from those of high ability might do very well by organizing those of low ability …

  • Dan

    “…an employee of a random unknown type get paid fifteen.”

    Producing twice as much as the next guy but getting paid the same? Sounds like communism.

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