The Spectre of Math

November 26, 2014

Law of large numbers: idiots, monkeys, CEOs, politicians, and nuclear war

Filed under: Economics,Mathematics,Politics — jlebl @ 1:26 am

Something that seems to be ignored by many people is the law of large numbers.  Suppose you take an action that has 99% rate of success.  That’s 1% chance failure.  Tiny!  Well do it enough times, and failures will happen.  Given enough candidates with 1% chance of winning, one of them will win.  Then everybody is surprised (but shouldn’t be).  Suppose that in the 435 seats for congress, there were all candidates that according to polls had 99% chance to win, and there was always a second candidate with 1% chance of winning.  I would expect 4or 5 of the underdogs to win.  If they didn’t we were wrong about the 99%.

Or how about entrepreneurs.  Suppose you take 100 idiots.  They each get a totally whacky idea for a new business that has 1% chance of success.  One of them will likely succeed.  Was it because he was smart?  No, there was enough idiots.  We should not overvalue success if we do not know how many other similar people failed, and how likely was success.  What if you have a person who started two businesses that had 1% chance of success.  Was that person a genius?  Or did you just have 10000 idiots.  You have surely heard that giving typewriters to monkeys will eventually (if you have enough monkeys and time) will produce works of Shakespeare.  Does this mean that Shakespeare was a monkey?  No.  There weren’t enough idiots (or monkeys) trying.  Plus the odds of typing random sentences, even if they are grammatically correct, and ending up with something as good as Shakespeare are astronomically low.  Shakespeare was with a very very very high degree of confidence not a monkey.  I can’t say the same for Steve Jobs.  The chance of Jobs having been a monkey are still somewhat smaller than your general successful CEO.  Think of the really important decisions that a CEO has to make, there aren’t that many.  If we simplified the situation and went simply with yes/no decisions on strategic things, there are a few in the lifetime of a company.  Most decisions are irrelevant to the success, and they even out: make a lot of decisions that make a small relative change and you will likely be where you started (again law of large numbers).  But there are a few that can make or break a company.  Given how many companies go bust, clearly there are many many CEOs making the wrong make or break decisions.  So just because you hired a CEO and he made a decision to focus on a certain product and drop everything else, and you made it big.  Does it mean your CEO was a genius?  Flipping a coin then gives you 50% chance of success too.

Same with stock traders.  Look and you will find traders whose last 10 bets were huge successes.  Does it mean that they are geniuses?  Or does it simply there are lots of stock traders that make fairly random decisions and some of them thus must be successful.  If there are enough of them, there will be some whose last 10 bets were good.  If it was 10 yes/no decisions, then you just need 1024 idiots for one of them to get all of them right.  They don’t have to know anything.  Let’s take a different example, suppose you find someone that out of a pool of 100 stocks has for the last 3 years picked the most successful one each year.  This person can be a total and complete idiot as long as there were a million people making those choices.  The chance of that person picking the right stock this year is most likely 1 in 100.  Don’t believe people trying to sell you their surefire way to predict the stockmarket, even if they are not lying about their past success.

OK.  More serious example of law of large numbers: Suppose your country does a military operation that has 99% chance of success and 1% chance of doom to your country.  Suppose your country keeps doing this.  Each time, it seems it is completely safe.  Yet, eventually, your country will lose.  You start enough wars, even with overwhelming odds.  Your luck will run out.  Statistically that’s a sure thing.  If you want your country to be around in 100 years, do not do things that have even an ever so tiny chance of backfiring and dooming that country to failure.  You can probably guess which (rather longish) list of countries that I am thinking of, which with good odds won’t be here in 100, 200, or 500 years.

Let’s end on a positive note:  With essentially 100% probability humankind will eventually destroy itself with nuclear (or other similarly destructive) weapons.  There seem to be conflicts arising every few decades that have a chance of deteriorating into nuclear war.  Small chance, but positive.  Since that seems likely to me to repeat itself over and over, eventually one of those nuclear wars will start.  It can’t quite be 100%, since there is a chance that we will all die in some apocalyptic natural disaster (possibly of our own making) rather than nuclear war.  Since there is also a small chance that everybody on earth gets a heart attack at the same exact time.  Even if we make sure we don’t do anything else dangerous (such as nuclear weapons), civilization will end one day with a massive concurrent heart attack.

February 27, 2014


Filed under: Economics,Politics — jlebl @ 12:43 am

When reading news, one should do some quick calculations to test for ridiculousness.  It really makes reading news far funnier.  Let us look at the 19 billion dollar deal where Facebook bought WhatsApp.  It is especially hilarious if we interpret this as how much do we as a society value WhatsApp versus some other things.  These are based on just quick googling, but they are for just eyeballing the thing, not to be taken exactly.

1) Minimum wage hike.  There are about 3.6 million people at or below mimimum wage [1] (2012 data).  If we suppose that they would work 250 days a year for 8 hours a day, the current $2.85 proposed hike ($10.10-$7.25) would amount to 2.85 \times 8 \times 250 \times 3,600,000 = 20,520,000,000.   So about the same.  Facebook could have paid everyone on minimum wage the hike for a year.  But of course I’ve overestimated I doubt everyone on minimum wage works 8 hours a day 5 days a week.

2) NASA budget is about 16 billion in 2013 [2].  So WhatsApp is actually worth more than all that NASA does in a year.

3) Nominal GDP [3].  Czech Republic is about $196 billion.  Ten WhatsApps is the GDP of the whole country of 10 million people (where WhatsApp has 55 employees, so 10 of them have 550 employees).  Jamaica has nominal GDP of $13 billion or so.  WhatsApp is way more than that.  OK, you say, that’s just one year.  Suppose that WhatsApp (what it does) works out to working for 5 years before it becomes obsolete.  That’s 3.8 billion per year.  The GDP of Cayman Islands is $3.3 billion.  And that’s where Facebook is taking its profits to avoid paying taxes [4].

4) The University of California budget for 2013-2014 is $6.2 billion [5].  WhatsApp would fund the UC for 3 years.  WhatsApp apparently produces so much good for our society that it equals about the output of the entire UC system for 3 years.






November 8, 2012

Economy and elections

Filed under: Economics,Politics — jlebl @ 6:55 pm

I have a theory as to why did the economy improve over this summer and into the fall, which led to Obama winning the election. I bet a part of this was the money spent on the campaigns. That was 2 billion dollars that went to very targeted places like Ohio. No wonder economy in Ohio is doing quite well. If it weren’t for the election, Sheldon Adelson would not spend 100 million on random stuff over the period, he would sit on the money. This way he spent it to elect Romney improving the economy in battlegound states which led to Obama winning.

Yes it is a bit of a stretch, but it should not be totally dismissed. Apparently the campaigns spent approximately 190 million just in Ohio [1]. That means that GDP of Ohio went up by 0.04 percent just because of the election (the GDP is 477 billion [2]). That’s not much but it’s not negligible. Also note that it wasn’t spread out over the whole year it was rather concentrated. Further note that state spending is 26 billion [2], so this is 0.73 percent of what the state spends in a given year. If the state gets say 5 percent of that money in various taxes (just pulling a number out of a hat; a reasonable estimate in my layman opinion based on state budget versus GDP) that would mean approximately 10 million extra tax revenue for the state. Not at all bad.

So, Sheldon Adelson was really rooting for Obama! Sneaky way to do it too.


April 23, 2012

CS costs too much

Filed under: Economics,Mathematics,Politics — jlebl @ 1:35 pm

Apparently computer science is not too interesting and costs too much.  $1.7 mil at University of Florida apparently.  So obviously we cut it, so that the athletic department (costing $99 mil) can get an extra $2 mil a year.  It’s obvious where our priorities are as a society.  Even if nothing got cut, 1.7 vs 99 is pretty bad.

April 13, 2012


Filed under: Economics,Politics — jlebl @ 6:26 pm

Two things I saw recently 1) NASA budget for climate research is 1 billion (for all those satellites and all that), 2) Facebook buys instagram for 1 billion.

Now we can see where our priorities (as a society) lie. What I don’t get is, that instagram has software that a reasonably good programmer could have done in a few weekends of binge hacking. It does nothing really new. You could even take fairly off the shelf things. Perhaps the servers and the online setup might be costlier, but still, nothing all that strange. To think that this is worth to us as much as figuring out where the next hurricane will hit, or when will the ice caps melt is “interesting”.

Though it is not totally out of sync with what else is happening. When the entire UC system which is responsible for several nobel prizes and innumerable new cures for diseases and leaps in terms of understanding the world, not to mention educating a huge number of students, when that system has a budget hole the size of one CEOs bonus, and it’s a huge hit for the university. Something is off in priorities. Actually there is a very good likelyhood that this CEO will die of some cancer that wasn’t cured because we don’t fund science enough.

February 22, 2012

Exponential growth (and CEO pay)

Filed under: Economics,Mathematics,Politics — jlebl @ 11:17 pm

So CEO salary has increased by approximately 9.7% adjusted for inflation every year between 1990-2005 [1] (that is approx 300% increase over that time, so 4 times what they had in 1990). Anyway, that has a doubling time of \frac{\log 2}{\log 1.097} \approx 7.5 years. Now median CEO (among the top 200) made approximately 10 million a year in compensation in 2010 [2]. In 2009 there were about 8.3 trillion dollars in existence [3]. Anyway, approximately a CEO makes a 1 millionth of the money in the world, or in other words, if we had a million CEOs we’d exhaust our money supply. It takes about \log_2 1000000 \approx 20 doublings to get a million. Hence in 20\times 7.5 = 150 years one CEO will make all the money in the world. And this is all inflation adjusted.

But we don’t have to go so far to get into trouble. Now we did talk about the top 200, so when would the top 200 make all the money in the world. Well that requires only \log_2 \frac{1000000}{200} \approx 12.3 doublings so 12.3 \times 7.5 \approx 92 years. OK, so in less than 100 years, the top 200 CEOs will suck out all the money in the universe.

Anyway, the problem is the following: The companies are not rewarding an individual CEO for good performance. They are rewarding all future CEOs. The thing is, that there is no “starting salary.” A CEO that just started is (statistically) making about the same as the one who’s been around for quite a while. If you would start all CEOs at a base salary, then one particular CEOs salary could rise at 10% a year because he’d be with the company only a fixed number of years, the problem would be manageable. Now to whatever extent there is anything like a “starting salary” the increase an individual CEO makes is even higher than 10% a year. Essentially the starting salary is increasing at 10% a year.

Let’s look at even a more realistic example of how quickly do we get into trouble. The CEO salary can easily be even 1% of the revenue for the company [4]. In fact some small private colleges are paying 1% of their budgets to their university president, a group where similar thing has happened. Well, now think about this doubling. If it is 1% now, it will be 2% in 7.5 years, 4% in 15 years, 8% in 22.5 years, 16% in 30 years, 32% in 37.5 years, 64% in 45 years, and we get 100% at less than 50 years. So in less than 50 years the entire revenue would have to support the CEO. Now you say, well but the revenue is also growing. Not so fast, the 10% pay increase is overall, that includes companies that did badly and those that did well. One would think that the growth of revenue on average (including failed companies) is not that much more than inflation. And this is adjusted for inflation. In any case CEO is definitely growing a lot faster than the economy (and hence your average revenue), and hence you hit the wall sooner or later. Even if we lob off another 2% to adjust for growth, the doubling time for CEO pay is still 9 years.

Of course a problem would appear a lot earlier than in 50 years. So it’s not only the “rich get richer” and “things are not fair” argument. This state of affairs is actually unsustainable even in relatively short period of time (within our lifetimes). I think people don’t understand that exponential growth is really really fast. That’s why pyramid schemes never work. It’s why Ponzi schemes usually fail far quicker than the perpetrator hoped. 10% increase a year does not seem like much (just like 10% return on investment doesn’t seem like that terribly much).

[1] (better sources exist, but I am too lazy to search further).




January 21, 2012

When will the beheading start

Filed under: Economics,Politics — jlebl @ 10:40 pm

It is always good to know when will other people want to cut off your head. Let us look at when were most heads cut off: that was probably the French revolution. OK, what made people want to cut off other people’s heads? Extreme inequality. OK, what was the Gini coefficient? Well, one estimate is 59 [1]. OK, so if we look at the US Gini coefficient it seems to be rising approximately linearly since 1980. In particular, US Census Bureau (via Wikipedia [2]) has the following data:

1980 40.3
1990 42.8
2000 46.2
2009 46.8

Let us do linear regression to obtain:

2020 50.0
2030 52.4
2040 54.8
2050 57.1
2058 59.0
2060 59.5
2070 61.9
2080 64.3

So, I guess people will start trying to cut other people’s heads off around 2058. We’re all safe till then.

[1] Christian Morrison, Wayne Snyder The income inequality of France in historical perspective, European Review of Economic History, 4, 59-83.

[2], Gini Coefficient.

December 9, 2010

Estate tax

Filed under: Economics,Politics — jlebl @ 4:44 pm

Just watching Morning Joe complaining about estate tax being immoral. In my opinion the estate tax should be as high as possible. In this respect I am a complete capitalist. I believe everyone should get the money they earn. Being born to the right parents is not “earning” money. I hope my parents burn through all their (now considerable amount) money before they die. Similarly, I don’t care if the government takes all my money when I die and leaves nothing for Maia. I hope she learns that she has to take care of herself.

December 16, 2009

dude! … where’s my healthcare (part deux)

Filed under: Economics,Politics — jlebl @ 10:13 pm

So apparently now we will get a healthcare reform that does two things 1) mandates everyone to have insurance (sounds good) 2) gives subsidies to poor people to buy insurance (sounds good). But …

However, it does nothing to make costs go down. All it does is that the taxpayer pays for some of the costs. The money ending up in the private insurance sector as overhead can grow arbitrarily large as it does now. In fact, perhaps it can grow faster as part of the money is spent “invisibly.” Example (think in recent history if you haven’t seen such an example): If the government starts giving everyone $1000 towards a purchase of a new car to make new cars cheaper, very soon the price of a new car will be $1000 more than it used to be. The car buyer suddenly pays the same, but the car dealers make $1000 extra.

And I did say overhead, since the money is not be spent on “healthcare.” It is spent on the insurance sector. So apparently all that we are doing is making sure that the insurance companies are very profitable and can continue to raise costs, need not compete.

A good nonprofit (public or not) health insurance is about spreading the cost of healthcare with the minimum amount of overhead (health insurance is purely about spreading the cost, in the end at least slightly more money has to be paid in premiums than is paid for the actual health care). In the current system, the money that flows into the health insurance is a LOT more than flows out (and the difference is rising).

There is some sort of a religion in this country that anything that’s a private enterprise is good, and anything that has anything to do with government is bad. If we all believe in capitalism, why are we afraid of competition. If it does happen that the government can run a health insurance better and it drives the private insurers out of business, then so what? Don’t we in the end want our lives to be good? To be able to pursue happiness? Why are so many millions of Americans concerned with the well being of rather a small number of health insurance executives, who might be losing out on their 20 million dollar salaries?

The current status quo is good for those few rich executives. The new “reform” is good for them as well. Everyone else is getting screwed over (and many of those people willingly out of paranoid fears about their grandmothers being put in Obama-death-camps).

I think perhaps it would be better to let the whole thing go. Leave public option in, let the bill die. The current bill does nothing about the amount of money spent on health insurance and healthcare. It just moves some of the money to be paid from tax revenue. But without any measure to reign in the exponentially rising cost. So all it does is it postpones the day when the system implodes. And makes the implosion probably more spectacular. The insurance will get unaffordable for the average family maybe 5,10,15 years later, but by that time a large part of the bill is also paid by the taxpayer. So not only will we not be able to pay for health care, but we’ll have a huge taxpayer bill. All the time we are feeding an incredibly inefficient system with billions of dollars.

I mean have you dealt with a private health insurance lately? The inefficiency of the system is multitudes beyond any braindamage that a government bureaucrat can even begin to imagine. We’re just going to spend more money keeping that system afloat, making the stockholders and executives in those companies rich. In capitalism, one is supposed to get rich by making a superior product. The insurance companies make the worst product imaginable, wrap it in shit and charge an arm and a leg for it, and we’re afraid that they might go under, so we’ll make sure that they don’t have to improve their product?

Why are we not afraid of driving private security companies out of business by having a taxpayer paid police force? I mean, poor Tony Soprano, if we make police be government run, maybe he’ll be out of business of “protecting us.”

So why not let the bill die. At least the moderate Republicans and the conservative Democrats will have a black eye next election, because trust me, the shit is hitting the fan. By 2010 maybe not yet, but in 2012 or 2014 the situation with healthcare will be so unbearable for such a huge proportion of the population that Republicans will be the ones proposing expanding Medicare. The current bill just moves the fan a little further, but keeps it in the flightpath of the shit, and it throws an extra one or two new pieces of shit at it.

October 19, 2009


Filed under: Economics,Personal,Politics — jlebl @ 4:42 pm

I’ve been thinking about why it is hard to explain ones political views to certain other people. Especially people I think are smart and logical. I think the main point is motivation. If you are a person who’s main motivation for doing anything is some sort of material reward, then you will not understand how socialism works. On the other hand, if motivation by material reward is not the most important thing for you, then you have a hard time understanding the first kind of people (Let us call first kind the set of material-motivation people and second kind the complement of that set). And both will lead to the one side thinking that the other side is either stupid or evil.

The first kind of person will be unable to comprehend how anything could possibly work if there is no material compensation. And humans are very good at dismissing any objective evidence that doesn’t agree with their world view (whatever it is). So the first kind of people will try to look for other motives of the second kind of person who is suggesting something that requires people to work without material compensation (or at least sufficient material compensation). That there is ample evidence that a large proportion of the populace is not at all motivated by simple material compensation seems irrelevant. For example, take things like free software, wikipedia, any sort of volunteer work. But even cases when people take lesser jobs because the jobs are more fulfilling to them.

The second kind of person will, on the other hand, think that the first kind of person is just a greedy bastard who wants as much for himself as possible. And that’s not necessarily true. There are many of the first kind of people who are just plain scared that if you make a world where not everything is compensated materially, then the world will collapse. They do not necessarily lack compassion.

I think the problem for most economists is generally that they are the first kind of person. Capitalism in its pure form can only work if everyone is materially motivated. I will not improve my product to sell more if I truly don’t care about selling more. I would say the proportion of each kind of person is on some fuzzy scale about evenly distributed. So capitalism breaks down precisely because of the erroneous assumption that everybody is motivated by personal material gain. At the same time communism breaks down for the opposite reason. True believing communists, somewhere deep inside think that the majority of population is not motivated only by personal material gain, but that only a small set of greedy bastards are. So if you could just remove those greedy bastards, you could have a just society. That doesn’t work either (mostly because those greedy bastards generally ended up running the show).

I’ve had a tough time explaining my motivation for doing certain things. For example, working on GNOME at one point, or perhaps writing up my differential equations notes and letting them be freely distributable. I’ve had to resort to saying to the first kind of people that it was “for fame” and to “feed my ego” (and perhaps there is some truth in that). But that’s not primarily why I did both things. I did both things because I thought they should be done. Why do you clean up your desk? Why do you do laundry? Why do you mow the lawn? Because those things should be done. I wanted to have a decent desktop without having to keep paying a single company for delivering a crappy one. So I thought GNOME needed to be done. Lately I thought that buying moronically priced books leads to increase in the education spending, leading to a bigger barrier to education for lower income students and leading to larger debt (always a bad thing IMO) in the population because of student loans. So writing freely distributable textbooks needs to be done. I had the opportunity so I did it. I don’t want to sound like I’m trying to save the world, I’m too cynical to try to do that. I also liked doing both of the things mentioned. But the motivation was not monetary gain.

I also did a lot of things for material gain. I have nothing against that. I don’t think capitalism is evil, just like communism also isn’t evil. Anyway … just rambling … I saw the latest Moore flick … maybe that’s why.

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