The 2% Rule - And What You Can Do With It.

In my last Blog I suggested in one of the footnotes that when it comes to progression it is not the masses that drive us forward, it is the top 1-2% of every generation that brings about this progression, and that were it not for them, humanity probably would have remained in the Middle Ages. I think that probably requires a Blog post all of its own, so here goes.

There are two sides to that coin; one side is to laud those in the top 1-2% and to be thankful that they were ones that projected us forward.  But the other side of the coin says that we live in a world in which the vast majority of people make no real contribution to the furtherance of the human race. 

That does not mean that people don’t bring many other qualities and benefits to the world (I’ve already mentioned plenty in the ‘overpopulation’ Blog) – I mean simply that around 98% of the people in every generation are not innovators, scientists, economists and great thinkers to whom society owes a great debt in helping humanity leap forward. 

If you have trouble believing this, here’s what you should do. Make a list of everyone you know, and divide them into two groups; those who are innovators, scientists, economists and great thinkers that have made contributions that history will record as being hugely significant to mankind’s progression, and those that haven’t. I’ll bet that those who fall into the ‘haven’t’ group make up a majority that either matches or exceeds 98% of the ratio. 

As a simple test to illustrate the few people that make any mark on history, consider that everybody reading this had 16 great-great-grandparents. I’ll bet that almost no one knows the names of any of them, much less something about their contribution to history that they have left for future generations. 

This, however, is no reason to be downbeat – it is just one of those patterns in the social world (like Pareto’s famous 80/20 rule - 80% of x is the result of 20% of the people) that is a result of nature not being very democratic in her distributions.  People should be rewarded according to their abilities – but let’s not pretend that that is not any fairer than the alternative, because people don’t choose their abilities either.

Many are appalled at the huge wealth divide and the income gap in Britain* – well that is nothing compared with the gap in intelligence between the top few % and the rest. With the wealth gap, at least governments can suppress or compress the factors causing the huge polarity – with intelligence this is not something that can be subjected to external manipulation.

Moreover, there is huge asymmetry in statistics; for example, if you picked two random people off the street and found that their combined earnings were £500,000, the chances are they don’t earn £250,000 each – more likely one earns £480,000 and the other earns £20,000. Similarly, take two random music artists who’ve sold a million records combined and it’s much more likely that one has sold close to a million and the other next to nothing than it is finding two who’ve sold 500,000 each. 

The upshot is, as much as people would like wealth, success, earning, talent, appreciation, intelligence etc to be equitably distributed, it plainly isn’t - and instead of realising and accepting this, they make injudicious comments about how wrong it is that the gap between rich and poor keeps increasing. 

This isn’t the Blog post to list all the reasons why this is misjudged – but suffice to say that free market economics is the primary thing that lifts people out of poverty into prosperity, and in a lot of cases, for that to happen, you are going to see the rich getting richer. 

The whole point about the rich getting richer (which is so often overlooked) is that the poor are getting richer too. In a great many cases the poor are only getting richer because the rich are getting richer – so only complain about the richness of the rich if you have a complaint about the poor prospering too.

The main reason prosperity is increasing is because with the 2% rule we find that with each increase in population the 1-2% of innovators increases numerically too. When there were only 300,000 people in the world, the top slice 2% innovators were only 6000 per generation. In a population of 7 billion, the top slice 2% innovators can be as many as 140 million. Once an idea is conceived, it can be shared by millions. Once cat's eyes are invented, the whole world benefits. Once a computer chip is prototyped by the first innovator, the whole world reaps the rewards, and so on. 

With more competition the talented people strive harder to accomplish things ahead of their competitors, and they learn from each other too. But to borrow an analogy from Horace Mann, most people will change with the course of the popular wind, but there are a few exceptions who, like mountains, actually change the course of the wind.

With the 2% rule I’ve said that the vast majority of people that have ever lived end up living and dying unnoticed by most in the vast prism of history. The question is, given our increased population, will that 2% figure increase in modern times? I think it might. Rousseau identified the foundations for our dependency of leadership – and what logically followed was that because most people make little impact on recorded history, the primary influence used to be left to the minority of charismatic figures that can. 

Rousseau referred to the leadership mandate as being ("the Legislator") whereby figures arise to change the values, ethics, politics and customs of the people. Back then, the fact that only 2% of the people made any major contributions to world history was partly due to the fact that leadership and innovation went hand in hand. Higher figures got to be innovators and innovators got to be higher figures.

But nowadays the shared mental matrix (seen most notably on the Internet) gives people a new power. Instead of their being a 2% minority that do all the innovating, I suspect it will be spread out a little more. Maybe not by much, but enough to see changes in the way things are done – and hopefully with enough intellectual diversity and idea-sharing to help increase the minority to a larger percent.

Lastly, remember something important if you remember nothing else – even those in the top 2% were there only because of hard work and diligent persistence. The scientific and technological innovations of the world can easily give the illusion of brilliance in what instead is really gradual, incremental progression, involving lots of trial and error and cumulative improvements costing us a lot of sweat and mental resources. Our knowledge and our technology is the cumulative effect of lots of time and effort. 

Many of the illusions of individual brilliance comes from caricatures like the ‘light-bulb’ effect, where the image is shown to be hovering over the head to illustrate a ‘eureka’ idea. This was first conceived to represent the inventing of the light bulb by Edison – which is unfortunate because (like all inventions) they do not come to mind as a fait accompli achievement, they involve many proto efforts beforehand. The truth is, the light bulb illustration was never a very good example to begin with, because Edison didn't really invent the light-bulb; it was prototyped a couple of dozen times, the first time nearly a century before. 

What Edison did was refine the filament – but it wasn’t just him – it involved the input of his colleagues too. Even their cumulative effort wasn’t plucked from the air - it owed much of its success to Hermann Sprengel from whom Edison's team learned how to use dripping mercury to create a better vacuum inside their bulb. It was only through trial and error that they could have realised that without that simple chemical vacuum technology the carbon filament burns up.

That is just one example; anyone with a tincture of knowledge of the history of science knows that there aren’t really any eureka moments in isolation from the efforts that preceded them. If you fancy being in the top few percent of your generation, it’s not too late – you just need to be prepared to work as hard and as diligently as the greats that preceded you. You might need a little luck too – and I hope you have it!

 

* Although heaven knows from whence this natural assumption that everyone has similar levels of income came – it is an absurd supposition.

 

Why The World Is Not Overpopulated

In the backwaters of Blogosphere there is nothing worse than speaking the obvious.  The flip side of that coin is that there is nothing better than taking a viewpoint that the majority of people believe to be right and showing it to be wrong.  This is what I’m going to do with the 'overpopulation' myth. The reason that the overpopulation scaremongering seems to be back in vogue is because of the continual literature on climate change, and also because recently the world population exceeded 7 billion (people love a good round number as a catalyst for such pronouncements), which must mean the world is overpopulated and that we are consuming far too many resources. Also Professor Stephen Emmott of Oxford University has been pulling in the crowds with his Ten Billion lecture, which is a proclamation of doom and gloom for the 21st century.

Professor Stephen Emmott is preaching to the choir, because if you ask people whether they think the world is overpopulated, most will tell you they feel sure it is.  There are two reasons for this (well three actually, but I’ll come to the third in a while).  The first reason is that ideas are like memes – they are passed on in the form of cultural viruses (just like the biological analogue).  ‘The world is overpopulated’ is one of those memes – it has been heard so often that people just accept it must be true.  The second reason is a development of the first reason; it is because people start with the natural assumption of overpopulation that they find it very easy to observe evidence to support their view.  Whether it be a huge metropolitan city ring road full of traffic at a stand still, or a London tube station in rush hour, or a crowded African region struggling for food and water, or a diminished animal community on the verge of extinction, it’s easy to assume the world has too many people*.

People are wrong about the over-crowdedness issue in a similar way to how they are wrong about the over-pollution issue – in both cases they have their reasoning backwards.  To see why, we first need to see why it is a good thing that you and I were born – and to do this we must go back to 1798.  The bad idea that “the earth is overpopulated” was started most prominently by Thomas Malthus in his 1798 Essay on the Principle of Population, in which he argues that the population increases geometrically but food supplies only increase arithmetically, which means an eventual and inevitable case of worldwide famine and disease.  I’ll explain what that means in a moment, and why Malthus was wrong.

Now there is no denying that in some parts of the world increased population, poor resources and lack of birth control is a problem.  But that doesn’t mean that the world is overpopulated - it means that the population of people that are alive are not doing as well as they could in aiding those that need more help than they are getting.  It is true that humans do damage to the environment and to other animals, but a countersceptic could point out that animals have been doing harm to other animals for millions of years before humans came about - and also that environmental events have ‘damaged’ parts of the planet for even longer.  If you take the entire history of life that has ever lived on this planet, over 99% of that life lived and became extinct before humans came about – so it seems absurd to suggest that humans being alive is a unique and unprecedented cost to the animal kingdom. 

Here’s what the sceptics fail to realise.  Yes, we certainly can do more to be mindful of other animals, but the fact that there are parts of nature that are worse off because of humans is not an argument that says there are too many humans, it is an argument that humans need to be more mindful of the effects they have on nature, and seek better ways to improve the status quo.  Similarly, the fact that there are so many divorces is not an argument against marriage, it is an argument that humans need to be more mindful in selecting the right partner, and work at being better husbands and wives.  I’m going to show why the solution to the ‘natural’ problems that overpopulation proponents describe is not fewer people, it is more people – which is why I say the world is under populated, not overpopulated.  To see why, let’s look at how Malthus got his reasoning wrong.  Malthus’s distinction between Arithmetical ratios and Geometrical ratios is as follows:

Arithmetical ratios (technology growth) are: 1, 2, 3, 4, 5, 6, 7, 8, 9 etc

Geometrical ratios (population growth) are: 2, 4, 8, 16, 32, 64, 128, 256, 512 etc

What he’s saying is that as the population grows and grows with increased rapidity, the food supply grows at a much slower rate, leaving us eventually over-populated and out of resources.  That’s what the ratios mean.  Malthus was right about these ratios up to the time of writing his essay – but what he didn’t predict was how the world was about to change, most notably with the Industrial Revolution** and later contraception.  The reason Malthus got it wrong was that he didn’t work out that progress in technology is proportional to the number of people alive in the world, which means that technological growth will eventually grow geometrically along with the population.  In simple terms, with more people alive there are more innovative ideas being produced at a greater rate.  Before the world’s big population boom in the past two centuries, technological progress was so slow that Arithmetical ratios and Geometrical ratios were all but indistinguishable, because population increase and technological innovation were slowly and steadily moving along the same coterminous lines in history.  Geometrical ratios become more noticeable when you have a large foundation to facilitate the exponential increase, and that happened after the industrial revolution, and will continue to happen henceforward at an even greater rate.

This is the key distinction between qualitative changing and quantitative changing – the former gives us the real breakthroughs in economic and technological change, the latter only gives us more of the same.  Here’s an example.  It was once forecasted that economic progress in Manhattan was coming to a close because the island had nearly reached its capacity regarding the horses it could contain.  If you’re only focusing on quantitative change your narrow vision only has you looking to see where you can fit more horses; whereas if you’re focusing on qualitative change you look to advance beyond horses to industrial machinery, and eventually from industrial machinery to computers.  Another example, the Great Irish Famine wasn’t just due to unfortunate infestations in potatoes – it was over-reliance on one single crop that severely added to the plight.  Whether it is potatoes for food or horses for transportation, it is important to diversify, because diversity leads to increased qualitative change.  That's another reason why you can be sure that our technology will continue to progress - we diversify our skills and our imagination by not having an over-reliance on too narrow a range.

Consider this in terms of an analogy in which we are recording planetary temperature. Planet A increases its global temperature of 100 degrees at a rate of 1 degree per year (arithmetical), whereas Planet B increases its global temperature of 100 degrees by 1% per year (geometrical).  In one thousand years Planet B, which is increasing geometrically, would be 2000 times hotter than Planet A, and growing 2000 times faster too.  If you looked at the temperature differential in the first few years the difference between the two planets would be minimal – whereas after a couple of thousand years it would be immense.  That’s what is happening with our technological progression – it is getting hotter and hotter because technological progression is increasing like the heat on planet B, not Planet A as Malthus thought.  Our probability of running out of any resources has always been superseded by our ability to advance the sufficient technology or innovation to wean ourselves off the dependency of those resources.  It is the geometrical ratios of both population growth and technological progression that make this exponential progression more or less inevitable. 

If you want some kind of qualification for that, it’s easily done.  I’ll give you some empirical indication based on how the world has gone for the past 200,000 years.  For the past 199,800 years we’ve had low global populations, and humans lived in meagre conditions, with lots of primitivism, low life expectancy and frequent infant mortality.  Until recently in our 200,000 year history we have lived in pretty poor circumstances, just above the subsistence level.  Then a couple of hundred years ago something changed.  People started to become more scientific, more empirically minded, richer, and populations began to increase more rapidly (it’s still going on).  This progression can be explained by a simple rule of thumb – people innovate, improve and provide answers to problems - and the more people, the more innovation, improvements and problems solved.  The more ideas and the more people to share those ideas with, the more humans prosper. 

It’s no coincidence that each half century has been progressively better than the last, and that the most recent times have been the most globally prosperous than any time in history.  That’s largely because we have 7 billion people on the planet – more ideas, more innovation, better technology, improved economic freedom, peak human liberation, and more global communication and potential to help the neediest***.  When the world has 8 billion people it will be even more prosperous; when it has 9 billion, yet even more prosperity.  It’s no coincidence – the recent burst in population in the past 200 years has been the primary cause of our burst in prosperity (200 years is only 0.1% of 200,000 years).  That we have a maximal population and progression dialect in 0.1% of the entire human history suggests that the answer to our worries about the world is that we haven’t had enough children in the past 200 years, not that we’ve had too many. 

It is easy to look at some of the worst places in the world, like Africa****, and say that many of the countries there have too many people in relation to the available resources, and this is true.  But those countries do not amount to an argument that supports the overpopulation proponents – they show that there are places in the world in which the economic conditions are unable to take advantage of the benefits of having a large pool of potential innovators, and fruitful trade potential.  This is usually because the countries in question are run by dictators or oppressive political groups that keep the masses starved of food and knowledge.  They are being denied the very thing my argument says will enrich them – the ability to contribute to their nation, and to the wider world.  If simply having a densely populated nation was inimical to success then Japan and Hong Kong would be as bad as much of Africa. 

It’s good that you were born

Now that’s cleared up, let’s consider the costs and benefits of an individual being born.  First off, you probably know all the facts about the incredibly tiny probability of the unique 'you' being born - 1 in the millions of sperm that made it...same for your ancestors…etc etc - so the upshot is you're very fortunate to be alive to experience a life on this planet. I'm glad you were born, and I don't think you'd wish you weren't here to experience life on this incredible planet.  If you'd never been born, your family would have ever so slightly more resources consumed, due to your not being born to consume them – but your family probably are the ones most glad you were born. 

Notice I said “your family would have ever so slightly more resources” not “the rest of the world would have ever so slightly more resources.  Let’s consider the resources humans consume.  It is thought by many that if you weren’t born the rest of the world would gain from what you don’t consume.  That’s not true.  When you were born you cost the world very little; the only people who would have felt a cost would be the people whose resources (time, energy, economic) you took up – and that would only really apply to your immediate family.  And as I said, your immediate family are the ones who have gotten most pleasure out of you – your parents spent a lot of time, energy and money on your upbringing, but you (and any siblings you have) are probably their greatest joy in life.  If you hadn’t have been born your family would have more resources, and the rest of the world would have the same as before.

It is clear that life has a multitude of net benefits that have no attached costs, as well as costs that do have concomitant attached benefits, and also some net costs too.  I said the main costs you bring are to your family – the reason being is that your external spillover costs mostly have benefits for others, and most people’s net costs that confer no benefits are comparably tiny.  Over-population theorists tend to only see the costs and miss the benefits.  The car in front of you in the morning rush hour is imposing a cost because the driver is delaying your journey slightly.  But he is probably going to his place of work in which the benefits he brings to the company, and to society, far outweigh the costs of delaying your journey by a minuscule amount.  Your partaking in the auction on Sunday helped bid the price up, which was a loss to the eventual buyer.  But the buyer’s loss is simultaneously the seller’s gain.  If you are successful in a job interview the other candidate sees you as a cost to his aspirations, but you succeeded because the interviewers saw that you could bring more to the company than the other candidate.  His loss is yours and the company’s gain.  The upshot is; it is easy to focus on the costs and omit the benefits.

Now then, seeing as though the costs are minimal, let’s look at the benefits to your being born.  Apart from all the obvious benefits you bring to your closest family, look what else you bring to the world; you contribute skills, you earn money, you work, you are a friend to many, a caring neighbour, a parent, a lover, you think up new ideas, you bring a unique perspective based on a unique experience of the world, you bring support, and conversation, and with that comes anecdotes, wisdom, retrospective prudence, humour, and many more things.  The reason why your existence is a blessing to the world is the same reason why increased population has made the world more prosperous; you have brought much more into the world than you have drained from it. 

Now let’s consider the cost-benefit analysis from the point of view of the people who chose to bring you into this world – your parents.  When your parents decided to have you, they knew that you would be a drain on their resources – both their financial resources, and their time and energy.  But I’ll bet having you was one of the best days of their life – and I’ll bet they haven’t regretted it since.  In other words, they focused on all those costs, weighed them up with the benefit of having you, and thought you were worth having, even though they must have overestimated the costs and underestimated the benefits.  I say “underestimated the benefits” because to begin with most parents think of a having a child only in terms of that effect on the family life – they are not taking into account all those benefits I mentioned above, because they are spillover benefits that come later, not direct benefits to your parents.  Hence, they overestimated the costs and underestimated the benefits, and still thought you were worth having – and that single case can be applied to the parents of just about all children.

The ‘overcrowded’ myth

I’d guess by now you’ve now got ahead of me and realised how fallacious the over-crowded argument is.  Crowded cities are popular because people like to live in crowded cities.  They like crowds because crowds have more people, and more people means more of the benefits I mentioned above.  Rural areas are quieter because fewer people like to live in them, and house prices are very expensive in Central London and Manhattan because more people want to live there.  Its simple logic - the reason London has 8.6 million people and rural towns have only a few thousand is because more people prefer to live in London than they do rural towns. The reason being, not only is there is a greater abundance of the aforementioned benefits in more populous areas, there is also better career prospects, higher salaries, better nightlife, greater choices of restaurants, a richer choice of entertainment, more tourist attractions, better public transport, greater diversity of people – the list goes on. 

On the pollution argument, well, my 0.1% observation is a bit like the reverse of pollution.  The benefits of pollution (profits from owning a factory, pleasure from driving a Subaru, etc) are outweighed by the costs of pollution to others, which means polluters pollute too much.  Parents and prospective parents vastly underestimate the benefits that children bring to the prosperity of the world, so they end up having too few children.  Progression and increased population is an inevitable concomitance because each generation reaps the benefits of the inventiveness of its ancestors.  Not only that, but population growth drives technological and industrial innovation, which drives economic growth.  The ‘overpopulation’ proponents have got their reasoning backwards; our improved technological abilities and economic prosperity have both engendered significant population growth as well.  Economic prosperity has continued to increase for the past two thousand years, with every century more prosperous than the last, and this is because there are more people on earth to contribute to the strategic and technological advancements. 

So not only is overpopulation a clear myth – the reverse is true - if you want to help solve the problems of the world like damage to the environment, bad living conditions for the neediest, and the diminishing populations of endangered animal species, you’ve got more chance if you have six kids than if you have none – because one of them just might be the one who puts a better solution in place.

 

 

 

* Not too long ago the entire world’s population could be housed quite comfortably in the State of Texas.

** It may actually be true that things like the industrial revolution had to wait until humans had the capacity to support large-scale innovation.

*** One point of note, despite increases in population it's not the masses that drives us forward, it is the top 1-2% of every generation as a rule. Were it not for the top 1-2%, humanity probably would have remained in the middle ages.  The reason why the model I gave you works is that with each increase in population the 1-2% of innovators increases numerically too.  When there were only 300,000 people in the world the top slice 2% innovators were only 6000 per generation.  In a population of 7 billion the top slice 2% innovators can be as many as 140 million.  That's a lot of people with a lot of ideas - so despite a justified pessimism regarding the overall abilities of most humans, such pessimism doesn't impinge on my model of progression. Once an idea is conceived it can be shared by millions. Once cat's eyes are invented, the whole world benefits. Once a computer chip is prototyped by the first innovator, the whole world reaps the rewards, and so on. 

**** You may also like to note that the countries with the largest populations - China, Brazil, Russia, India (and several African nations) – are actually showing the world’s fastest economic growth rates. 

Happy New Year - You Are Lucky To Be Here!

Happy New Year to you all!  If you are reading this at the beginning of 2013, then you are one of 7 billion people that is astronomically lucky to be alive today.  It is quite common for biologists and religious people to make calculations of the odds of your being born, but it is a largely faulty endeavour because such models only ever focus on a few of the variables, and they fail to take into consideration that many of the contingent facts are post hoc and not amenable to straightforward probability calculations (the picture at the bottom of the page gives exhibition to the same flawed model). So, in trying to tell us the incredibly small chance of any individual being born, they choose a method that underestimates the real chances by a factor much larger than the figures they give us.  That's like a multi-billionaire trying to show off his wealth by emptying the moneybox next to his bedside table.

But that said, it is at least true that despite the flaws in the oft-presented probability models, you had an alarmingly fortuitous journey in being born.  Even if we calculate solely on the direct male line with the figure of your one lucky sperm with the unique set of DNA that makes up your father’s genes you inherited amongst 250 million sperm per intercourse, then going back a mere 40,000 generations you only had a 1 in 1.8 x 10⁴⁰³¹⁶⁷* chance of making it here. 

Now that you have made it here to 2013 after 40,000 generations of 1 x 250 million chances of being the lucky sperm, consider something else – the reality you create by being human is an astoundingly brilliant illusion that requires a human mind to experience it.  Here’s why;

The following things can be said to exist: table, moon, freedom of choice, chair, love, jealousy, the play Hamlet, a dream about the play Hamlet, the sun, gravity, atoms, fear, admiration, generosity, and a hurricane.

If asked to put them into two distinct groups, most would do the following:

Group 1: table, moon, chair, the play Hamlet, the sun, gravity, atoms, a hurricane.

Group 2: freedom of choice, love, jealousy, a dream about the play Hamlet, fear, admiration and generosity.

The demarcation is usually centred around separating things that exist conceptually or as products of mental cognita (group 2) from things that exist in physical form in the external reality out there (group 1) – not dissimilar to how Kant separated noumena and phenomena. 

But I think this is a hugely (and implicitly human) limited view of reality, naturally resulting from our evolution of very limited parts through natural selection.  Natural selection built us to survive and understand a world of hunting and gathering – we are not well equipped to understand the full depths and complexities of reality. 

To understand reality more proficiently is to understand the following. Both of the above groups represent not too dissimilar objects in that the whole of reality with which humans interface is, in fact, a brilliant illusion constructed by the human mind.  That reality is different for every other kind of animal, and maybe without minds to perceive external reality, mother nature would be nothing more than mathematics (or thoughts in the mind of God, as per Berkeley’s Idealism, if your beliefs lean that way).

Either way, the existence of, say, table, moon and chair in the form perceived by humans is no more or less real than the existence of freedom of choice, love and jealousy – in that both sets of objects of study are as they are because of how the human mind interfaces with reality.  It’s a secret not many people know – but outside of human perceptions, the world doesn’t really have atoms, motion, heat, colour, water, rocks, dust and things of that kind.  Yes of course these things existed before humans (and other living things) came along, but they did not, and do not, exist as you know them, outside or apart from how you know them – they exist only in non-reified mathematical form, and they are probably existent in the reality of some kind of mathematical patterning that is able to bring to bear the physical substrate you and I know as the material world. 

As you begin 2013, have a little smile as you consider that at the beginning of the universe there was a vanishingly small chance of your ever being here – and also that having made it here, the whole of reality with which you interface is a brilliant illusion constructed by virtue of the fact that that is how humans perceive reality and make conceptions within it.  If that’s not a reason to marvel at being alive, I don’t know what is. 

* That’s 403,167 zeros

The Best Theoretical Idea In The World?



It’s nearly the end of 2012 – the year I will remember as (among many other things) the year in which I discovered one of the neatest and most brilliant theorems I’d ever heard.  I don’t know how it had not crossed my path before, but I’ve definitely been enriched since becoming aware of it, so I thought it’d be a good Blog subject on which to end the year.  The theorem is called Aumann’s Agreement Theorem.

Here’s how it goes.  You may have noticed (I expect you have) that people in the world disagree about lots of things– religion, politics, ideologies, moral systems, land rights, tastes, facts, and many other things.  And in disagreeing with each other they make points of argument and listen to the counterpoints – back and forth, with each trying to rebut the other’s contentions.  It may seem the most natural thing in the world that opinions vary so widely, but I have long thought that most disagreements are either psychological and emotional, or due to biases, incomplete information, and poor reasoning – so I was delighted to find someone had formally confirmed my suspicions with one of the most elegant mathematical theorems I’ve ever read*.

The idea behind the theorem is that most people disagree on ‘facts’ that are really statements about relations between data points.  Game theorist Robert Aumann stated in his theorem that if two independent computers have the same programs, the same set of data (the input) and the same computational steps, then both computers should display the same output.  Not only that, two computers with different information should still reach the same output provided the computational steps are the same.  Imagine a complex murder scene with 1000 bits of information related to the crime.  The agreement theorem states that if computer A had 500 facts and computer B had the other 500 facts they should both exchange data and come to the same conclusions about who the murderer is.  The probability of their reaching the same conclusion increases further with every single instance of shared facts.  Unfortunately, humans aren't logic machines - they have flawed reasoning skills, misinformation, sensory faults, biases and incomplete knowledge of any situation in its entirety.  If Jill stops John and asks for directions to city hall, and at the end of the journey Jill ends up at the market 2 miles away, we can conclude that either John's information was wrong or Jill didn't follow the instructions precisely.

But despite the many human flaws, the upshot is, two logical, unbiased minds debating a subject (like the computers) ought to soon reach an agreement, either on the right answer, or on how far a human mind can logically accept or deny a set of premises, or else on rare occasions admit a roadblock halts their tracks.   The roadblock may be due to human limitation of knowledge, not having access to all the facts, or it could be that the wrong question is being asked.  But in terms of all the facts, difference in subjective probabilities ought to be solely down to differences in information. This is what Aumann means with the term 'the assumption of equal priors'.  If all disagreements are errors in analysing posteriors then when two people reach different conclusions, we know that one or both may be at fault.  If there is no rational basis on which two people with the same information should disagree, then what two debaters need to do is, first, make sure each has all the information, and second, keep discussing the individual issues face to face with openness and honesty until a resolution is reached. 

This may sound like idealism – but it is idealism only in the sense that we know everyone is not going to start to agree on everything.  That doesn't mean the observation is devoid of genuine power and utility.  One's own awareness of why people diverge in opinions, and the method by which they can understand how to converge, can only be a good piece of wisdom to have. Remember the agreement theorem isn't saying that everyone will agree - it is stating that people can (and perhaps should) in principle converge on an agreement as long ask they honestly wish to find it.  To have that summarised in an elegant mathematical theorem is great if you want a welcome recourse in the face of all those mindless disagreements happening out there.  

I think it is evident that as humans have continued to develop and co-exist the magnitude of disagreement has diminished over time**.  That is to say, the longer humans have been able to develop their knowledge and understanding together, the more closely we have converged in understanding, particularly since the rise of empirical and rationalist paradigms.  The take home lesson is that the reason humans disagree so much is not through lack of availability of data or methods of assimilating that data, which should serve as a signpost for those who genuinely want to enhance their knowledge and understanding, and find themselves in the company of like-minded people who feel the same.  Robert Aumann and Scott Aaronson have given us a mathematical proof that shows this is how knowledge would work if people passionately and intelligently and diligently sought the truth without getting so swayed by emotive or biasing factors.

* Mathematician Scott Aaronson has formalised the agreement theorem by providing a mathematical proof which shows that agreement should be converged upon in fairly quick time.  Aaronson's proof is the best and most comprehensive summary of the theory I've seen. 

** This is offset by the fact that there are now more people, and hence, more things about which to disagree, but proportionally we are increasing our convergence rates.

Don't Ban Guns - Help Prevent People From Becoming Killers

I’ve had about half a dozen people ask my view on this – otherwise I probably wouldn't have blogged on it. After the recent shooting spree tragedy, President Obama wants to get tough on gun ownership and consider future policies to "help prevent more mass killings". Needless to say there are plenty of problems with this.  As tragic as the event was, I don’t think there is a way to legislate against it happening again – and I don’t think the proposed solution of reinstating the Clinton era law against assault weapons is going to be effective. 

The majority seem to be asking for a complete ban on guns, and the sceptics are asking how much good that will do. The sceptics are asking the wrong question – it’s not whether a complete ban on guns will do any good (it is bound to do some good), it is whether the cost of enforcing such a law outweighs the desires of the population and the good those costs could do elsewhere. 

In the first place, I don’t think a complete gun ban will do much good. Here’s why. Let’s first ask, on what grounds do people want guns banned? Is it because when disturbed and psychologically damaged people get hold of them they are dangerous and kill people with them? Many may say ‘yes’, but to me that’s fairly obviously misjudged.

Say we have a maniac intent on killing as many people as possible, but he has no gun. What can he do? He can go into his mother’s kitchen drawer, find the sharpest knife and go on a killing rampage. Are these people honestly saying that sharp kitchen knives should be illegal too? They'll have one objection; you can do a lot more damage with a gun than a knife. Even if that’s true, you can do more damage with a car or van or lorries or a box of matches and a can of petrol if you are that way inclined.

To legislate against the most maniacal killing sprees you would have to ban knives, cars, vans, lorries, matches and petrol if you take it to the limit. Heck, it is easy to kick a person to death with heavy boots – are we going to say that people on building sites have to by law walk around barefoot or with plimsolls on? Of course not. 

So the grounds that guns should be banned because when disturbed and psychologically damaged people get hold of them they are dangerous is not much of an argument at all. A disturbed killer in the making will find the tools with which to commit his or her murders irrespective of the law, just as has proved to be the case many times in the UK where guns actually are illegal. 

Next, let’s suppose for the sake of argument that guns are the only way to kill people – would it then be worth having a blanket ban in the shape of a federal law? That depends on how much people want them banned, which depends on whether they are prepared to pay the cost or whether they think the money could be better spent.

It is hard to get an accurate figure for law enforcement, but as a rough idea it is thought that drug laws in the USA cost between $50-100 billion. So how much would it cost to implement a gun law? I don’t know, but I know that any amount in excess of the minimal requirement for tackling persistent gun crime from recidivists would be too much, because any additional expenditure on gun laws would be better spent in helping to prevent people becoming killers. 

The other reason that the cost of the law would be economically inefficient is that most people causing trouble with guns are the sort of people who are likely to be taking up most of the police’s time anyway, so the costs of targeting the rest of the relatively safe gun owners across the country will be vastly disproportionate to the good any such law will do (remember, I said we can't legislate against maniacs outside the police's radar). Put it this way; would you want the police spending lots of their time and resources going after a large sample group who constitute only 1-5% of the threat, or would you rather that majority group kept their guns with virtually no threat of using them? I know what I’d rather see – particularly as valuable police time will be taken away from more pressing and persistent daily crimes. 

The point is, even with a blanket ban, guns will still be traded on the black market, and someone who is desperate to go on a shooting spree will find a gun from someone, whether guns are legal or illegal. And secondly, given the amount of people that own a firearm, it is obvious that lots of people wilfully choose to own one for protection. This is important for one reason; if you solicit public opinion, you may well find that most people don’t want a gun ban.

So what? you may say – guns play a part in deaths, and the anti-gun folk should get their way. But it’s not that simple; given that it costs (even by a conservative estimate) over 100 billion a year to implement such a gun law, it can be argued that those costs may come at the expense of good law and enforcement in other areas, and in spending money that could be used more wisely for prevention, and confidence building, and restoring self-worth in young people's lives. 

Here's another reason why the economics doesn't favour the gun law. Let’s be generous and say it costs only $60 billion for a gun law enforcement – the costs of enforcement must drain the police force to the tune of $60 billion (unless you want to foot the bill for more police, in which case the cost goes up again). The cost of the law at $60 billion works out to about $200 dollars per person, which is $800 per year for a family of four.

Given the vanishingly small chance that you or your family are going to be the victims of a shooting spree (even if you’re excessive in allowing for 100 deaths in an isolated shooting spree every year*, it’s only one in three million), do you think the family would rather have the money and the one in three million chance of dying, or the probability vanished (don’t forget, threats never vanish anyway)?

I’ll bet most families would choose $800 dollars and a one in three million chance of death, because they already demonstrate similar behaviour every day in what they will or not fork out for safety equipment and risk reduction. If anyone decided they preferred to avoid a one in three million chance of death rather than a certain $200, you’ll know they don’t understand risk or probability.  Most Americans don’t earn $200 per day, and each of them has much less than a one in three million chance of dying when they drive or cycle to their place of work. 

While I have sympathy with people’s call to see guns banned, I think it doesn’t make much economic or practical sense. America needs to learn how to irrigate deserts, not wave axes around looking for trees to chop down. I think what is needed is not a focus on guns – it is a focus on getting to the root of the psychological damage that inflicts so many young people. If you want to do good, focus not on guns but on helping people.

It is tragic that we live in a world in which these isolated incidents come along and wreck entire families. But I can see no way to legislate against these things happening – not without imposing a law that will be almost entirely ineffective, and one that imposes tens of billions of costs that will impinge on other police duties, and do nothing to stop isolated incidents. Shakespeare understood more eloquently than most that you cannot legislatively remove human anomalies out of the system of being human:

Whether 'tis Nobler in the mind to suffer

The Slings and Arrows of outrageous Fortune,
Or to take Arms against a Sea of troubles,
And by opposing end them: to die, to sleep
No more; and by a sleep, to say we end
The Heart-ache, and the thousand Natural shocks
That Flesh is heir to?

* And that certainly doesn’t happen 

The Truth About Working Immigration

A recent report shows that the right-wing anti-immigration UK Independence Party (UKIP) has risen six points to gain 10 per cent of support, which is as good as it has ever been for the party.  Euroscepticism, rises in unemployment and increased immigration are probably the primary reasons for this occurrence.  Of course, the kind of people who support UKIP are the kind of people who think rises in unemployment and increased immigration are causally linked – “If it weren’t for all those bloody immigrants our British folk would have more jobs” is what they assert.  They are wrong.    

Are immigrants really bad for the British job market? That’s the wrong question – the right question is whether immigrants make us economically and culturally richer.  Even that isn’t the nicest question we can ask, because it only views migration by what we can gain, not by what the person coming into our country has to gain (which is usually much more).  But yes immigration does make us richer – both financially and culturally – but it has to be the right kind of immigration.  By ‘right’ I mean the right kind of immigrant – one who is willing to assimilate himself into the UK’s language and culture, not remain aloof in non-English speaking enclaves that are detached from the rest of he country (although I understand their temptation to do this – if you or I went to live in, say, Turkey or Singapore, we’d probably gravitate towards the more familiar English communities if we could find them). 

Here’s one way immigration makes us richer. Say you have a British worker earning £10 per hour, and he won’t work for less.  If an immigrant comes in and will do the same job for £7 per hour, then as a result is Britain better or worse off on the whole?  Purely in terms of economics, Britain is better off because the British worker was being paid £3 too much (in net terms).  Of course, this sort of thing doesn’t reach a low ebb because we have the minimum wage, and it doesn’t even apply exclusively to immigration.  If you have a Mancunian worker earning £10 per hour, and he won’t work for less, and a Liverpudlian comes in and will do the same job for £7 per hour, the nation is better off because we were paying a man £10 per hour to do a job that we could get done for £7 per hour. 

Most right-wing journalists and politicians seem to be under the assumption that the costs of immigration can be measured by the number of British people who leave their jobs as a result.  But this simple caricatured picture of the Eastern European replacing a British worker on a higher salary is pretty much the opposite of what is happening.  Think about it; any employee who leaves his job rather than taking the wage decrease must either be transferring to a job with similar wages, or he must have better alternatives ready at hand.  The employees who cannot easily leave and as a consequence must take a pay cut are the ones hurt the most.    

Every working immigrant is a potential employee, customer, buyer and seller, and provider of services. He bids down wages, but that's a double-edged sword, because while it’s bad for his fellow workers, it's good for employers and consumers.  There is a wider picture though; the costs of immigration are borne by British workers who are hurt by the aforementioned falling wages, and the benefits are reaped by British employers and company owners (who profit from those same falling wages).  The employees’ loss is the employers’ gain, so they cancel each other out.  But there is a wider gain for the British economy because employers and company owners enjoy an additional benefit when the fall in wages enables more profitable expansions to the business, which, nationally, results in lower prices (in some cases) and lower unemployment (in other cases). 

Moreover, and I don’t have any statistical figures to hand, but even when wage drops occur for Brits, they are almost certainly dwarfed (at least in relative terms) by the gains for immigrants.  A Brit who takes a £2 per hour wage drop is probably giving (indirectly) something like a £7 hourly gain to the kind of people for whom that sort of gain is essential for feeding their family. 

So on balance working immigrants don't harm the UK; because immigration makes us richer, not poorer.  Also, in the longer run, the excess profits that immigration engenders get competed away and show up with lower prices for consumer goods. Even consumers benefit here; if your wage falls by 5% while prices fall by 10% you're benefiting. 

Contrary to poplar opinion, the minimum wage doesn’t impact this situation all that much. A minimum wage does two things. It shifts capital from employers in an unstable competitive market to low paid workers, and it induces some employers to let their staff go because they cannot afford the wages. If you’re getting £7 per hour and only bringing £6 per hour worth of benefits to your company, you’ll likely find yourself on the dole. In that sense, it is possible to argue that for the good of low-paid workers there should be no minimum wage at all – which is interesting because the minimum wage is supposed to be for the benefit of the low-paid, unskilled workers.  If you are a lower paid man or woman going from here to there in different jobs, you will find less work available with every rise in the minimum wage – and the higher the rate the more unemployment.

This might amount to a road block for young, unskilled workers and the unemployed – which is why tax credits are a more effective method because they target those who have children or high level benefits, and need high wages to make it worth their while signing off benefits, but who don’t have the skills or experience to command that kind of salary.  An efficient tax credit system will leave such people almost unaffected by immigration, certainly with regard to the economy.

There are some notable costs of immigrants coming into our country; most obviously the issues surrounding sex trafficking, drug gangs, and rise of Islamic fundamentalism – but you don’t have to be an immigrant to be involved in those activities – many indigenous folk get involved too.  Yes the Government needs better border control, but it’s a terribly difficult task for any Government to realistically keep a check on the numbers coming in illegally. 

All in all, immigration benefits a nation, especially working immigrants. Yes there are sceptics, but here’s an amusing way to catch them out.  The next time someone says there are too many immigrants in the UK, ask them how many immigrants there are.  They will usually say they don’t know – to which you can respond by asking how they can say there are too many immigrants when they don’t know how many there are in the first place. If they try to be clever and give you a figure, ask them how they can know the number when apparently the Government doesn’t even know. 

What The Dickens? - Two Kinds of Miserliness

Reading my Christmas edition of The Spectator that arrived this weekend, I came across an article by Toby Young entitled "Dickens and the profit motive" in which he says the following about Dickens's feelings towards the ills of capitalist businessmen:

"In virtually all of his books, from Great Expectations to Hard Times, capitalists are depicted as mean and heartless* - men whose humanity has been eaten away by their relentless desire to make money. Ebenezer Scrooge is a case in point.  When the Ghost of Christmas Past takes him back to his youth, we see Scrooge actively choose his love of gold over his love of Belle, a beautiful young woman"

The trouble is, Toby Young is only focusing on one half of the situation and overlooking the other half.  Plus, regarding the half on which he is focusing, he has rather misunderstood the effects of the actions.  In economics, people are negatively affected not by other people's hoarding of money, but by other people's spending or use of resources.  In terms of how Scrooge's behaviour affects everyone else's financial well-being, he is the opposite of "mean and heartless" because he is hoarding his bank notes and not spending them on resources - which leaves more for everyone else**.  This is because people aren’t rich by having money; they are rich because of what that money buys (goods, free time, holidays, etc).  Scrooge is the opposite of what he is accused of being, because he has the money to be rich, but he keeps it in the attic, away from the many goods, free time, holidays, etc that he could consume.

A hat tip to Steven Landsburg here, but when Scrooge earns a bank note and doesn't spend it, the rest of the world is one bank note richer, because Scrooge produced one bank note's worth of goods and didn't consume them. By not using fuel, there is more for everyone else; by not having a big mansion there is more bricks and mortar for everyone else; by not having servants there are more employment opportunities for those who might wish to employ servants themselves.

I said that in hoarding his bank notes and not spending them on resources, Scrooge leaves more for everyone else.  How are those extra resources shared around?  Well it depends on how the savings are made.  If Scrooge puts £1 million pounds worth of banknotes in his attic and never touches them then everyone else is better off by £1 million pounds, which they'll find by having the prices of goods driven down.  If Scrooge takes his £1 million pounds out of the attic and puts it in his bank, he will bid down interest rates to the tune that others will be able to afford £1 million pounds worth of goods or services.  Conversely if he buys £1 million pounds worth of timber he will bid up the price of timber for everyone else, and reduce the supply too. 

So although Scrooge’s character is "mean and heartless", his effect on the economy is just the opposite – it is full of gains for those who probably didn’t realise they were benefitting from his miserliness.  Of course, the wonderful thing about A Christmas Carol is that its message has a specialness far beyond economic outcomes; it is about the wonders of a personality transformation, after which one sees others in an entirely different light because one can see oneself in a different light.  To this extent, economics is amoral. 

* You'll also find lampooning and ridiculing too; you may recall that relatives of Martin Chuzzlewit are criticised for their collusive attempts to obtain the inheritance; the Lammle family in Our Mutual Friend learn the costs of marrying for money; there's an odiousness about moneylender Daniel Quilp in The Old Curiosity Shop; and there is something pathetically desperate and uenviable about Uriah Heep in David Copperfield.   

** And when it comes to paying wages, I don't even think it can be assumed that Scrooge’s wages to Bob Cratchit were evidently stingy; I mean, from what I can remember, Cratchit's wages were low, but he was free to seek employment elsewhere.  Say Scrooge pays Bob Cratchit £20 per week, and Cratchit is worth £25 per week in labour and skills - why doesn't Fezziwig or one of the other prospective employers offer him £22.50 per week?  Then Cratchit would be £2.50 better off, and Fezziwig would get £25 worth of skill and labour for £22.50.  Maybe Scrooge was only paying Cratchit what he was worth.