Late-Night Musings on Probability

What is probability?

Sure, I’m an engineering major, I know how to work with probability. I know about expected values and joint CDFs and autocovariances and Markov chains, and all these things tie into each other in ways that make perfect sense to me. I know they can be used for practical purposes and yield real results. But what does it all mean?

Suppose I have a perfectly weighted six-sided die. The odds I’ll roll, say, a three with this die are exactly one in six.

What I’ve been taught this means is that if I roll the die 6000 times, a three will come up approximately 1000 times. If I roll it 60,000 times it will come up approximately 10,000 times, and so on, with the (relative) error bars coded into the word “approximately” shrinking and shrinking as my number of rolls increases; eventually, as my number of rolls approaches infinity, the proportion of threes rolled approaches exactly one-sixth.

There are serious problems with this definition, though – the most obvious one being that I don’t really have time to roll the die an infinite number of times. Suppose I settle for 6000 rolls and roll 991 threes. I write down that the chance of rolling a three is 991/6000. The next day, I roll the die another 6000 times and roll 1012 threes. I write down that the chance of rolling a three has mysteriously increased to 1012/6000. I’m wrong both times, because this is in fact a perfectly weighted die, whose probability of rolling a three is exactly one in six: 1000/6000. But if I don’t have any idea what to expect from this die and try to figure out its probability distribution from scratch, what else can I do than roll it a lot, and count how often it lands on each number?

Another problem is that a parameter defined as “the limit of x as y approaches infinity” doesn’t seem to tell you anything useful about the outcome of a single die roll. Take another die, which is so absurdly unbalanced that the probability of rolling a three is one in 10 million. If you’re about to roll the die once, what does this tell you? You either roll a three, or you don’t – whether the probability is one in six or one in 10 million. There’s no way to be sure beforehand.

And yet people will happily step into a plane with a one-in-1o-million chance per flight of falling out of the sky and killing everyone on board, but they won’t come near a plane with a one-in-six chance. Clearly, probability means something.

Right now, as I’m typing this, I’m trusting my life to the very low probability that the floor will collapse under me and drop me into the neighbours’ living room in a neck-breaking sort of way. When I go to sleep (which I should have done a long time ago) I’ll be trusting my life to the very low probability that something in my room will randomly catch fire during the night and burn the building down. Every day, when I cycle to class, I trust my life to the very low probability that any driver around me is a murderous psycho and/or on heroin.

And it goes further. Engineers make cost-probability tradeoffs all the time: if a system (like a plane, or a train, or a nuclear power plant) has a potential for catastrophic failure, how high do we allow the probability of such a failure to be? How much money are we willing to spend to drive it down by a factor of z? Depending on the career choices I make, I might have to make tradeoffs like that at some point.

So we have this weird parameter whose very definition is vulnerable to measurement error, and which intuitively sounds like it doesn’t tell us anything more than “X might happen or it might not” – and yet we trust our lives to it and hang price tags on it and feed it into all kinds of complicated mathematical models as if it were as meaningful and quantifiable as the number of apples in a basket.

Now I’ve been told that the definition above is called “frequentist”, and there’s another view called “Bayesian” which interprets probability as the certainty with which a belief (e.g. “this plane will not fall out of the sky and kill everyone on board today”) is held – but on the face of it, that makes even less sense. If a friend of mine takes the perfectly balanced die and, by freak accident, gets 1200 threes out of 6000 rolls, does that mean the die’s probability of rolling a three changes to one in five whenever he’s looking at it? If a devout Christian is 100% certain that God exists, does that prove the existence of God beyond a shadow of doubt? How do you quantify an abstract psychological concept like “certainty”, anyway?

Me, I’m just about ready to start believing that probability is some kind of mystical property of the die itself – or maybe that there really is a Random Number God.

Posted in Philosophy | Leave a comment

De Eerste Kamer moet nog veel ingewikkelder

I

Gemopper over de Eerste Kamer is van alle tijden. De laatste paar jaar zijn de klachten alleen wel 180 graden gedraaid. Stond de senaat eerst te ver van de burger af en stelde hij politiek te weinig voor (de term “slaapkamer” viel regelmatig), nu is hij juist “te politiek” geworden. Het is ook nooit goed!

Toch hebben de klagers een punt. Vergelijk de NOS-uitslagenavond van vorige week woensdag eens met die van de Tweede Kamerverkiezingen in 2012 – een mooi potje zoek-de-tien-verschillen. De voorspelde zetelverdelingen, het slotdebat, het gepuzzel met meerderheden: wie als leek beide uitzendingen achter elkaar zou bekijken, zou na afloop niet vermoeden dat de twee Kamers überhaupt van elkaar verschillen. Door de wankele positie van het huidige kabinet worden de verschillen inderdaad steeds kleiner.

II

Er gaan dan ook veel stemmen op om de Eerste Kamer helemaal maar af te schaffen; wat heb je aan twee Kamers die zich vrijwel hetzelfde gedragen, en elkaar door hun verschillende samenstellingen vooral in de weg zitten? Zo ver wil ik niet gaan. De Eerste Kamer heeft een belangrijke taak: íemand moet wetsvoorstellen grondig inhoudelijk doorlichten, en er een streep doorheen halen als ze niet deugen. Die rol kun je niet overlaten aan de Raad van State of aan een “Constitutioneel Hof” – de bevoegdheden van de wetgevende macht horen nou eenmaal niet thuis bij de (ongekozen!) rechtsprekende macht.

Houden dus, die Eerste Kamer. Maar hoe zorgen we er dan voor dat hij zich weer meer gaat gedragen als een “Raad van State met bindende adviezen” in plaats van een “Tweede Kamer met minder leden”?

Ik zie maar één oplossing: de Eerste Kamerverkiezingen moeten ingewikkelder. We moeten zo’n complex systeem in elkaar zetten dat ze het zelfs in België te onoverzichtelijk zouden vinden. Alle dynamiek moet eruit. De afstand tot de burger – en daarmee tot de wereld van televisiedebatten, uitslagenavonden, peilingen en landelijke campagnes, oftewel de “waan van de dag” – moet groter, niet kleiner.

III

Hoe gaan we dat aanpakken? Spreiding is het toverwoord – spreiding in de tijd, om te beginnen met de Provinciale Statenverkiezingen. We hebben twaalf provincies; Statenleden worden voor vier jaar gekozen; er kan dus elke vier maanden één provincie naar de stembus.

Die Statenleden mogen dan vervolgens ook weer op verschillende momenten hun stem uitbrengen voor de Eerste Kamer. Tot 1983 hadden we een mildere versie van dit systeem: toen koos steeds de helft van de provincies de helft van de senatoren. In 1983 werd ook de termijn van senatoren ingekort, van zes naar vier jaar – draai dat terug.

Laat verder een deel van de Eerste Kamer niet door Statenleden, maar door gemeenteraadsleden kiezen. Daar valt heel wat voor te zeggen: de gemeenten zijn als bestuurslaag veel belangrijker dan de provincies. Als de raadsverkiezingen dan net als de Statenverkiezingen onderling uit de pas gaan lopen, en de “Eerste Kamerverkiezingen voor raadsleden” óók, is het feest compleet.

De samenstelling van de Eerste Kamer zal dan heel traag veranderen, met hooguit vijf of zes zetels tegelijk. De zetelverdeling is dus geen momentopname meer van de politieke actualiteit (“waan van de dag”), maar een soort schuivend gemiddelde over een langere periode. Grote verschuivingen die het een kabinet in één klap veel moeilijker kunnen maken, zijn ook niet meer mogelijk.

Ondertussen is de Eerste Kamer nog net zo democratisch als in de huidige situatie (want nog steeds gekozen door de gekozenen) en dus bevoegd om wetgevende macht uit te oefenen.

IV

Als gemeentelijke en provinciale verkiezingen niet meer allemaal tegelijk worden gehouden, maar één voor één, zou dat nog een probleem oplossen: die verkiezingen worden dan niet meer “gekaapt” door de landelijke politiek, zoals nu steeds gebeurt. De raadsverkiezingen in Gouda kunnen over Goudse kwesties gaan, de Statenverkiezingen in Zeeland over Zeeuwse. Het effect op de landelijke politiek blijft beperkt tot een minieme rimpeling bij de Eerste Kamerverkiezingen, maanden of jaren later, slechts zichtbaar voor verwoed rekenende partijstrategen.

We houden dan (als je het Europees Parlement niet meerekent) één landelijke verkiezing over. Eén moment dat we allemaal tegelijk naar de stembus gaan, dat het circus van lijsttrekkers, lijstduwers, campagnestrategen, campagnevrijwilligers, debatleiders en opiniepeilers mag schitteren. Dat zijn de Tweede Kamerverkiezingen – en zo hoort het ook.

 

Posted in Netherlands, Politics | Leave a comment

Pillarisation on Steroids – Against Atomic Communitarianism

I

In Archipelago and Atomic Communitarianism, Scott Alexander describes his idea of a utopian society. Put briefly, it consists of several isolated communities of like-minded people, who maintain a small common government to ensure peace and stability, but otherwise leave each other alone as much as possible. He calls this utopia “Archipelago”, and the principles on which it is built “atomic communitarianism”.

Utopias have a habit of being impossible to put into practice, and Archipelago is no exception. Scott is smart enough to realise this, and he doesn’t suggest we actually try to build Archipelago in the real world. He does propose some concrete policy goals, though:

So although Archipelago is an interesting exercise in political science, a sort of pure case we can compare ourselves to, it doesn’t look like a practical solution for real problems.

On the other hand, I do think it’s worth becoming more Archipelagian on the margin rather than less so, and that there are good ways to do it.

[…]

One way we could become more Archipelagian is just trying not to yell at people who are trying to go off and doing their own thing quietly with a group of voluntarily consenting friends.

But I think a better candidate for how to build a more Archipelagian world is to encourage the fracture of society into subcultures.

Okay, that’s a clear enough proposal. Now if I may put forward a popular Bible quote:

The thing that hath been, it is that which shall be; and that which is done is that which shall be done: and there is no new thing under the sun.

– Ecclesiastes 1:9

Humanity has a long, long history, and we’ve tried all kinds of social and political models. Name a policy, and there’s a good chance it has been tried, somewhere, at some point.

Atomic communitarianism is no exception. I’m from the Netherlands, and from about the 1870s to the 1960s, our society was divided into several communities called “pillars”. The exact number of pillars depends on which historian you ask, but if you count generously, there were five: Catholic, two flavours of Protestant, Socialist, and Liberal or “neutral”.

II

Although these pillars weren’t geographically isolated – our country is far too small for that – the social segregation went deep. Pillars formed their own schools, sports clubs, hospitals, newspapers, radio stations, political parties, trade unions, employers’ organisations… In short, there were few aspects of life that weren’t “pillarised”.

On the face of it, pillarisation was a very succesful proof of concept for atomic communitarianism. There was no violence between the pillars, nor were there any serious attempts to disrupt each other’s community life. As Abraham Kuyper – a Protestant leader from the early years of pillarisation, who strongly encouraged the process – put it: each pillar was ‘sovereign within its own sphere,’ a principle which was generally respected by everyone. Perhaps most surprisingly, we managed to keep a democratic central government running with little difficulty. (This was possible because the members of each pillar put a great deal of trust into “their” political leaders, and most of those leaders got along well enough behind the scenes. The culture of murky compromises, shady backroom deals, and pragmatism-before-principles that has kept this country going since before it was a country and will continue to do so until the bones of the last Dutchman sink into the soggy ground – that culture really worked its magic during pillarisation.)

So, atomic communitarianism has been proven to work and we should implement it everywhere right away. Case closed!

Then why do so few Dutch people today have anything but negative associations with the word “pillarisation”?

III

I can think of a few reasons. Within each pillar, there was great social pressure to fit in – to vote for the right parties, read the right papers, send your children to the right schools, and shop at the right shops. (I remember, from my secondary-school history book, a picture of an advertisement: ‘Fellow party members! Show that you are Liberals in every way – buy stuff at Shop X!’ This kind of thing was far from uncommon.) Social contact between members of different pillars was heavily frowned upon, and intermarriage was right out. In theory, you could “leave” your pillar if you really wanted to, but it would cost you your contact with family and friends, and even in your new pillar you’d forever be seen as “that weird guy who came in from another pillar.” The pillars mistrusted each other, and developed a complex system of mutual prejudice: ‘Protestants are puritan moralists who want to impose their rules on everyone!’ ‘Socialists are dangerous revolutionaries who want to throw away everything we hold dear!’ ‘Catholics are mindless sheep who always follow their clergy unquestioningly!’

Scott considers his Archipelago ‘the culmination of liberal principles’, but pillarisation, as it existed in real life, was a conservative thing. It created tight-knit communities which exerted strict control over individual members’ personal lives, and within each, it drummed up a sort of tribal hostility towards other communities. Small wonder, then, that the Dutch Liberals of the age strongly opposed pillarisation, and vehemently denied being a pillar of their own.

IV

Now that we’ve seen a quick case study, let’s turn to the principle of the matter. I have three main objections to atomic communitarianism – that is, to the utopia of Archipelago, but also to Scott’s practical proposal to ‘encourage the fracture of society into subcultures.’

The first, and the most serious, is the hostility that would arise between communities. It is well-known that ignorance breeds mistrust; it’s all too easy to be prejudiced against, say, Catholics if you never talk to an actual Catholic. The more isolated you are from the Catholic community, the more likely your image of Catholics is to consist entirely of propaganda and stereotypes (and looking at Scott’s description of Archipelago, in which communities can choose to ban “foreign” radio and TV broadcasts, his point seems to be ‘the more isolation, the better’.) This problem becomes all the more pressing when the different communities voluntarily separated because they didn’t like each other in the first place.

In the Dutch case, these kinds of hostilities remained relatively tame – likely because the pillars weren’t geographically or economically isolated, and thus still ran into each other every now and then – but if left unchecked, they can quickly turn ugly. It’s not that hard to imagine how communities can go from ‘not talking to each other’ to ‘not trusting each other on anything’ to ‘bashing each other’s skulls in.’

Of course, that’s an extreme consequence. I don’t think ‘encouraging the fracture of society into subcultures’ would immediately lead to civil war, but I do think it would decrease human beings’ ability to understand, respect, and trust those who think differently from them.

My second objection is that it would make people intellectually lazy. Why bother debating your opponents, when you can just say, ‘Well, if you don’t agree with how we do it here, you can always pack up and leave?’ Over time, many people would lose, through atrophy, the ability to defend their own beliefs.

Atomic communitarianism doesn’t encourage people to debate their opponents and learn from each other, it encourages them to sort themselves into isolated circlejerks. It doesn’t create a marketplace of ideas, it creates local monopolies, enforced by protectionist measures like the aforementioned optional broadcasting ban.

(Really, that broadcasting thing – ‘preventing memetic contamination,’ as Scott calls it – is bothering me a lot. Perhaps it’s because I can think of a few places where foreign media are or were banned, none of them very nice.)

My third objection is that communities overlap. Scott mentions several possible communities for his fractured society, including a libertarian community, a Christian community, a lesbian community and a community of weight watchers. But what if I’m a Christian, libertarian lesbian who wants to lose weight? Where do I go?

(I guarantee you that somewhere out there among those seven billion people is a Christian, libertarian lesbian who wants to lose weight.)

For another example, suppose I’m a hippie living in a vegetarian environmentalist community. I agree with my community’s positions on pretty much every issue, but the problem is I really love Wagner. Very few of my fellow hippies like Wagner, and in fact many of them will argue that listening to Wagner is ‘like, not cool, dude’ – so if I ever want to see a Wagner opera on stage, I have to move to a more conservative community, where I’ll have to hide my political views and generally be miserable. And the same goes for anyone who likes anything that’s impopular in their community.

V

To a considerable degree, the whole point is moot. Society fractures itself into subcultures just fine, whether you encourage it or not. It’s human nature to seek out like-minded people and avoid those with different opinions (in the words of Billy Joel: ‘Only speak to those who will agree, and close your mind when you don’t want to know’). I’m definitely guilty of this myself. My point, however, is that the impulse should be tempered, not encouraged.

Atomic communitarianism does precisely the opposite. As a result, it becomes harder to meet people with different perspectives, to be tolerant and accepting of those different perspectives, and to enjoy things that aren’t the norm in your community. It becomes easier to be prejudiced against others, and to hold beliefs without ever having to think about them.

Those aren’t outcomes I want, and from what I’ve read of Scott’s writings I don’t think he wants them, either.

Posted in History, Netherlands, Organisation of Society | Leave a comment

Bismarx, the blog Europe probably doesn’t need

Bismarx is now live.

I should probably tell you what the point of this blog is, but first, some background: I am a Dutch electrical engineering student. Although I’m very fond of engineering and the mindset that comes with it, I also have a considerable interest in “softer” topics like politics and history. I have blogged before, but that was always in Dutch; it was mostly about specifically Dutch issues, so it would have been silly – and strongly limiting – to use any other language.

However, there are also some thoughts I’d like to share with a more international audience. Much as I’d like to do so in my native language, I have to admit our neighbours across the North Sea beat us at the colonialism game, and thus I will use English.

And here we get to the point of Bismarx. I have written things in English before, but they’re spread out across several places – mostly, various corners of Reddit and the TV Tropes forums. With this blog, I now have a single place where I can collect and share any thoughts I write down in English.

That’s not to say I guarantee this blog will be 100% English-language. There will almost certainly be Dutch domestic issues I want to comment on in the future, and I will have no qualms about posting about them in Dutch here. I might even post a few things in my third language, German, once I’m able to write longer pieces in German without checking the dictionary twice a sentence. (‘Wait, what was the gender of Ostpolitik again?’)

Now that that’s out of the way, I should give this first post some actual content. Here goes:

The Internet as a discussion forum is heavily US-centric. Articles and blog posts commenting on specifically American issues, or commenting on universal issues from an American perspective, are shared the world over. European bloggers, too, often refer to American debates, American speeches, American studies – even when they’re writing in a language other than English. In most European countries, it’s easy to follow American presidential races or budget negotations in great detail on the websites of national media, and in fact many Europeans do. In short, in serious online discussion as a whole, the American frame of reference is dominant.

The problem is that it’s so one-sided. I often read articles from The Atlantic or Slate about American domestic issues, and I know many more Europeans do, but how often do Americans read about issues that are specific to the Netherlands, or Italy, or Sweden? How detailed is CNN’s or the Washington Post‘s coverage of German domestic politics? Where was the lively discussion on François Hollande’s inaugural speech in America?

Another problem is that the American frame of reference can overwrite your own, if you let it. European bloggers who write about American issues a lot must take care to remember that America is vastly different from any European country: it has a different social model, a different political culture, a different set of controversial issues – which means discussions there do not always map nicely to anything that’s relevant here. I can recall two specific articles in Dutch – one on the gender gap in higher education, another on hiring discrimination based on first names – that examined an issue from a specifically American perspective, citing American studies, without noting this or pausing to wonder if the situation in our own country might be different. (Hint: In the Netherlands, discrimination against people named Achmed is slightly more of a problem than discrimination against people named DeShawn.) We’re all living in Amerika, Amerika ist wunderbar…

I’m not going to kick off this blog with some kind of grand “mission statement”; that would only serve to make me feel guilty for not living up to it. But if Bismarx can contribute to a little more Europe and a little less America in online debate, that would be really nice.

Posted in Europe | Leave a comment