In Australia, it is compulsory to have a bell or horn on a bike to warn other road users. This seems strange, because when cycling, hands are in use, but the mouth is not. So it would make sense to use the mouth to produce sounds, leaving the hands for steering. Perhaps a better law would require cyclists to be able to produce the bell or horn sound, giving them the choice of whether to use their mouth or a device for this.
Currently in all species I know of, each generation raises its children, who in turn raise their children, etc. This can be described as an overlapping generations model where each generation lives 2 periods, receives resources from the old of the previous generation in its youth and transfers resources to the young of the next generation when old. There is another equilibrium: each generation raises its grandchildren, has its children raised by its parents, and the children in turn raise their grandchildren. Instead of transferring resources to the next generation and receiving them from the previous, transfer resources two generations forward and receive them from two generations back. There are an infinite number of such equilibria: for each n, transfer resources n generations forward and receive them from n generations back. There are of course practical problems with large n, because the organisms do not live long enough to meet their level-n offspring.
There are complaints in developed countries that childbirth is postponed in life to acquire education and start a career. A possible solution is transitioning to an equilibrium of taking care of grandchildren, together with having children at a young age so that the grandparents are still alive to see the teenage years of their grandchildren. However, the equilibrium transition from taking care of children to taking care of grandchildren means that one generation must raise both children and grandchildren. The equilibrium transition in the other direction is easy – one generation does not raise its children or grandchildren, because its children are raised by its parents and its grandchildren by its children. Any other equilibrium is less stable than the raising-children one, because it is difficult to transition to it and easy to transition away.
The equilibrium stability comparision is similar to the social security equilibria in overlapping generations. In one equilibrium, everyone saves for their own retirement and consumes their savings when old. In another, every generation when young pays the social security costs of the previous generation who is old at the same time. The transition from the saving equilibrium to the equilibrium of paying the previous generation is easy, because one generation gets its savings and the contribution from the young, while the young do not save and receive the contribution of the next generation. The reverse transition is difficult, because one generation does not get a contribution from the young in its old age, but has to finance the retirement of the previous generation when young.
The ranking of universities is very stable over time (http://m.chronicle.com/article/Rank-Delusions/189919) regardless of the difference in resources, scandals and other factors affecting popularity and quality. There are several positive feedback mechanisms keeping the rankings constant. These come from the multiple coordination games when choosing a university.
1) Smart and hardworking students want to be together with other smart and hard workers. If for some reason the best are in one location, then in the future all the best people have a motive to go to the same place. So the best arrive at that location and help attract other best people in the future. Similarly, party animals want to go to a university famous for its parties, and if many party animals come to a university, then it becomes famous for its parties.
Why would smart people want to be together with other intelligent folks? Just for interesting conversation, for useful contacts, collaboration. For these reasons, even the stupid may want to be together with the smart. Then an assortative matching results, as Gary Becker predicted for the marriage market (http://public.econ.duke.edu/~vjh3/e195S/readings/Becker_Assort_Mating.pdf).
2) Students want to go to a school with the best teaching staff, and the best professors want to teach the best students. I have yet to hear anyone wish for stupider students or teachers for themselves. Again the preference is the same among smarter and stupider students and professors, so assortative matching is a reasonable prediction.
3) The best professors want to be with other similar ones. Where there are such people, more will arrive.
4) Smarter graduates are likely to earn more and can donate more to the university. Then the university can hire better teaching staff, which in turn attracts better students, who donate more… The more talented also accumulate more power after graduating, in government institutions for example, which they can use (legally or not) to benefit their alma mater. Predicting this, again many people want to go there, and in the stiff competition the best get in.
5) If the employers believe that from some place, more intelligent people come than from elsewhere, then they are ready to make better offers to those coming from there. This makes the place attractive to all future employee candidates. Due to competition, the best get in, which justifies the belief of the employers.
6) Smarter people can be taught faster, at a pace that the stupider cannot keep. This mechanism gives everyone a motive to go to a school corresponding to their level.
7) Faster teaching means more knowledge during a standard length higher education, which the employers should value. The graduates of a school giving more knowledge are favoured, which makes the place attractive to everyone and leads to only the best getting in. The ability of the average student remains high, which enables faster teaching.
Theory research requires figuring out the result and how to prove it, and then writing these down. Empirical research requires the same, plus running the experiment or analyzing the data in order to prove the result. This requires relatively more time and less insight. If the production function of empirics requires in its input mix more time per unit of insight than the production function of theory, then smarter people have a comparative advantage in theory. They are endowed with more insight, but everyone has the same amount of time.
The amounts of theory and empirical research produced per unit of insight need not be related in any way for the above comparative advantage result.
Based on comparative advantage, I should switch to empirical research 🙂
Some empirical research methods are quite simple, but modern theory requires complicated math. Due to this, empirical research requires more time per unit of methods knowledge in its input mix. People with a stronger methodological background (better education) thus have a comparative advantage in theory. This suggests graduates of universities with more (advanced) coursework should be more likely to do theory.
Individual scientists do science because it is fun and pays the bills. Why would society finance this? I think it is done to achieve prediction and control. Control over whatever can be controlled (physical things, people, abstract concepts) and prediction of what cannot be controlled (weather, earthquakes, evolution of the universe).
Control is something evolution has made people desire (control is commonly used to change the environment to improve people’s survival and reproduction). Prediction allows people to adjust themselves to aspects of the environment that they cannot change to suit themselves. Prediction is also part of learning to control: predict a response, take an action, observe if the response to the action is the one predicted.
If prediction and control are the goals humanity sets science, then scientists and fields of study should be evaluated based on their contribution to these goals. For example, studying history is useful if it helps predict or control future history.
A small contribution of science may be entertainment (popular science shows and news), which may justify financing interesting and entertaining science even if it does not contribute much in other respects.
When evaluating an artwork, the guilt of a suspect or the quality of theoretical research, the usual procedure is to gather the opinions of a number of people and take some weighted average of these. There is no objective measure of the truth or the quality of the work. What weights should be assigned to different people’s opinions? Who should be counted an expert or knowledgeable witness?
A circular problem appears: the accurate witnesses are those who are close to the truth, and the truth is close to the average claim of the accurate witnesses. This can be modelled as a set of signals with unknown precision. Suppose the signals are normally distributed with mean equal to the truth (witnesses unbiased, just have poor memories). If the precisions were known, then these could be used as weights in the weighted average of the witness opinions, which would be an unbiased estimate of the truth with minimal variance. If the truth were known, then the distance of the opinion of a witness from it would measure the accuracy of that witness. But both precisions and the truth are unknown.
Simultaneously determining the precisions of the signals and the estimate of the truth may have many solutions. If there are two witnesses with different claims, we could assign the first witness infinite precision and the second finite, and estimate the truth to equal the opinion of the first witness. The truth is derived from the witnesses and the precisions are derived from the truth, so this is consistent. The same applies with witnesses switched.
A better solution takes a broader view and simultaneously estimates witness precisions and the truth. These form a vector of random variables. Put a prior probability distribution on this vector and use Bayes’ rule to update this distribution in response to the signals (the witness opinions).
The solution of course depends on the chosen prior. If one witness is assumed infinitely precise and the others finitely, then the updating rule keeps the infinite and finite precisions and estimates the truth to equal the opinion of the infinitely precise witness. The assumption of the prior seems unavoidable. At least it makes clear why the multiple solutions arise.
If the environment changes, then there is a fitness benefit to being an adaptable organism. On the other hand, adaptability is costly (bigger brain for adjusting behaviour, various backup systems in the body like the camel’s hump need to be carried around). So adaptability gives a net benefit if the environment changes sufficiently rapidly.
If periods of change alternate with periods of constant environment, then it would be useful to have the ability to switch adaptability off for a while. This is adaptable adaptability. The ability to switch adaptability off is in turn costly. It is useful to have if periods of environmental change alternate with periods of stability sufficiently rapidly. It would be good to have an ability to switch off the ability to switch adaptability off if changes and stability alternate with different frequency over time. Even more complex patterns may necessitate the ability to switch the ability to switch the ability to switch adaptability, etc. Hierarchies of abilities controlling abilities arise.
Perhaps after an infinite hierarchy, there is some meta-ability that can switch all lower order abilities. Self-awareness or something similar.
Ronald Fisher analyzed signalling in biology through traits that do not confer direct fitness advantage (higher survival or fecundity), but are desired by the opposite sex. This attraction is an equilibrium in a coordination game – if a potential mate has traits desired by the opposite sex, then the offspring with that mate are likely to have these traits as well and succeed in attracting the opposite sex. The traits confer a mating advantage, which is part of a fitness advantage, justifying the desirability of the traits.
It is a coordination game, because in a different equilibrium, traits without a direct fitness advantage are not desired. Then these traits do not give a mating advantage to the offspring and therefore do not have an indirect fitness advantage either. Then it is not fitness-enhancing to desire them. In summary, if a trait is expected to be desirable in the future, then it is desirable now, and if a trait is expected to be neutral or undesirable, then it is neutral or undesirable now.
Fiat money is inherently worthless, but in one equilibrium of the money game, has positive value in terms of other goods. If everyone expects that others will accept money in return for goods in the future, then it is useful to obtain money now. So everyone is happy to deliver goods in return for (a sufficient sum of) money now. The money game is a coordination game, because if everyone expects money not to be accepted in the future, then they do not give goods for money now. If money is expected to be worthless, then it is worthless, and if money is expected to be valuable, then it is valuable.
An overview of signalling in biology is at http://en.wikipedia.org/wiki/Signalling_theory and Fisher’s theory at http://en.wikipedia.org/wiki/Fisherian_runaway
The coordination game of money is studied by Kiyotaki and Wright (1989, 1993): http://www.jstor.org/stable/1832197 http://www.jstor.org/stable/2117496 and more simply explained in van der Lecq “Money, coordination and prices” https://books.google.com.au/books?id=r1r40SB0Wn8C&pg=PA29&lpg=PA29&dq=fiat+money+coordination&source=bl&ots=iI0M96m-qz&sig=lRHBAWIXYZs2V5S-iNFeH-2yar8&hl=et&sa=X&ei=d3lqVeneJ8TvmAX4vIGgDg&ved=0CEoQ6AEwBw#v=onepage&q=fiat%20money%20coordination&f=false
If only those who fail are allowed to retake an exam and it is not reported whether a grade comes from the first exam or a retake, then the failers get an advantage. They get a grade that is the maximum of two attempts, while others only get one attempt.
A simple example has two types of exam takers: H and L, with equal proportions in the population. The type may reflect talent or preparation for exam. There are three grades: A, B, C. The probabilities for each type to receive a certain grade from any given attempt of the exam are for H, Pr(A|H)=0.3, Pr(B|H)=0.6, Pr(C|H)=0.1 and for L, Pr(A|L)=0.2, Pr(B|L)=0.1, Pr(C|L)=0.7. The H type is more likely to get better grades, but there is noise in the grade.
After the retake of the exam, the probabilities for H to end up with each grade are Pr*(A|H)=0.33, Pr*(B|H)=0.66 and Pr*(C|H)=0.01. For L, Pr*(A|L)=0.34, Pr*(B|L)=0.17 and Pr*(C|L)=0.49. So the L type ends up with an A grade more frequently than H, due to retaking exams 70% of the time as opposed to H’s 10%.
If the observers of the grades are rational, they will infer by Bayes’ rule Pr(H|A)=33/67, Pr(H|B)=66/83 and Pr(H|C)=1/50.
It is probably to counter the advantage of retakers that some universities in the UK discount grades obtained from retaking exams (http://www.telegraph.co.uk/education/universityeducation/10236397/University-bias-against-A-level-resit-pupils.html). In the University of Queensland, those who fail a course can take a supplementary exam, but the grade is distinguished on the transcript from the grade obtained on first try. Also, the maximum grade possible from taking a supplementary exam is one step above failure – the three highest grades cannot be obtained.
In many countries, farmers have managed to obtain free insurance from the government – if there is a bad harvest (due to drought, flood or anything else), the government compensates the farmers using tax revenue. On the other hand, if the harvest is unusually bountiful, the farmers do not pay a windfall tax to the government (which would reduce the tax bill of other people or provide more public services). There is thus no premium for the insurance that the rest of society provides to agribusiness.
A thought experiment: the insurance for the agricultural industry is bought from some insurance company who has to pay the farmers if the harvest is bad. The premiums paid to the insurer are taken from the general tax revenues each year. If the insurance company just breaks even (perhaps due to enough competition between insurers, profits are driven to zero), then the movement of money is the same as in the case of “free” insurance by the government.
Agribusiness has managed to pump some money out of other taxpayers with the free insurance. Their success is explained by the classic lobbying theory: if the benefits of lobbying go to a small group, each member of which gets a large sum, then each member of that group has an incentive to put in the effort and money for influencing politicians. If the cost of lobbying is borne by a large group (say the taxpayers), each member of which only pays a small amount, then members of the paying group do not find it worthwhile to make the effort to counterlobby. The savings are too small to be worth the time and money.
If some politician tries to reduce the subsidy to farmers, they are targeted with intense negative publicity. The agricultural industry claims itself to be necessary for “food security” or “feeding the people”. Nevermind that large amounts of food are currently shipped worldwide. Only the import barriers to foreign-produced food are keeping it out of the domestic market. And food security – who takes a country by blockading it into submission these days? A force large enough to surround the country and cut off food import is large enough to take it by storm, which is considerably quicker. Food security really means preventing the rise of food prices. But this is a financial problem and has a financial solution – insurance against a price rise.
If reducing the farming subsidy does not work, a similar effect can be achieved by providing the same subsidy to everyone and raising taxes. Only the administrative costs are higher than in the case of reducing the subsidy. Other industries could argue that they are affected by the weather or other “national emergencies” and deserve compensation from the government. For example, rainy weather reduces ice cream sales and tourism revenues, so the ice cream sellers and the tourism industry could lobby for the same free insurance as the farmers get. If the world price of some natural resource falls, the miners of that could claim an event beyond their control is threatening them with bankruptcy and ask the government for help. If the tastes of the public change so that some form of entertainment is no longer profitable (theatre, opera, classical music), the providers of that can claim to be important for preserving the national culture and the very civilization itself and ask for taxpayer support… wait, that already happens. It is described in the Yes, Minister and Yes, Prime Minister books.
Of course in reality, the subsidies differ across industries, depending on their lobbying prowess. But if the subsidies were proportional to the tax payments of their receivers, they would neatly cancel with the extra taxes levied to finance them. So the government could abolish subsidies by enlarging the set of receivers to include everyone.
By providing free or subsidized insurance, the government is crowding out private insurance – why insure and pay premiums if the government compensates the loss without premiums? This is especially a problem for risks that are common to many voters. For example, a flood is likely to affect the whole neighbourhood, not just one house. In case of flood damage, the people in the neighbourhood can jointly lobby for the declaration of a disaster zone and a public subsidy for rebuilding. So no need to buy flood insurance. With very few buyers, insurance companies stop offering the product.