Which Brilliant Ideas Are Far Less Widely Known Than They Ought To Be?

It's a great question which a friend and I were discussing over a group dinner Friday night. I can offer plenty of suggestions to whet your appetite; there are numerous ideas that would enrich people's understanding of everyday societal matters that are not currently captured with enough depth to do so. Examples would be things like comparative advantage, that which is seen and unseen, deadweight costs, Coase's theorem, Chesterton's fence and the concept of the invisible hand. Then there are absolutely life-changing ideas such as Aumann's Agreement Theorem and Harsanyi's Amnesia Principle that bear repeating regularly to get them as widely disseminated as possible. All of those ideas make an appearance in this blog from time to time.

However, the idea I'll pick as the idea of choice in response to this blog post's title will be Arrow's Theorem, as a tribute to Kenneth Arrow who died this week. He was, up until a few days ago, one of the greatest living economists. Arrow's Theorem is not the easiest to describe simplistically because it is mathematically dense, and is quite counterintuitive too (I had a go once before using voting as the illustrative template). In fact, past reading of economics has given me the impression that several economist social commentators have described Arrow's Theorem as the hardest complex idea to simplify for a layperson. I'll have a try with a version I typed up yesterday in the hope that you find it both understandable and intriguing.

To do so, let's discuss my favourite dessert - cheesecake. What I'm going to illustrate is that no democratic system, however fair it appears in terms of participants and number of choices, can satisfy all the axioms associated with the preferences. So for example, if there are three, then: if two are satisfied the third must be violated, whether those two are 1 and 2, 2 and 3, or 1 and 3.

Let's illustrate this. Every day, Julie, Frank and Timothy split a cheesecake with one flavour - Chocolate, Strawberries or Lemon. Their preference orderings change from day to day - some days Julie is in the mood for Strawberries, other days the very thought of Strawberries makes her wish she was eating another flavoured cheesecake. Every evening at dinner time they have to call in their first, second and third choice cheesecake orders (let's say the cheesecake patisserie insists that you specify your second and third choices in case they run out of something.) So Julie, Frank and Timothy need a method for translating their individual preferences to a cheesecake order. Now as it happens, on the 22nd on February, their preferences ran as follows:

 

	Julie	Frank	Timothy
First Choice	Chocolate	Strawberries	Lemon
Second Choice	Strawberries	Lemon	Chocolate
Third Choice	Lemon	Chocolate	Strawberries

I’m not going to divulge what system these three were using to determine their order, but I will tell you that on the 22nd they phoned the patisserie and expressed Chocolate as their first choice. On the 23rd, Julie ranked Chocolate over Lemon again (and let's suppose we don’t know anything about Frank’s or Timothy’s rankings). On the 22nd, only Julie ranked Chocolate over Lemon, whereas on the 23rd, Julie plus possibly one or both of the others ranked Chocolate over Lemon. So if the cheesecake order ranked Chocolate above Lemon on the 22nd, then it should certainly have ranked Chocolate over Lemon on the 23rd, no?

In principle, yes (disallowing for a change of mind for variety - not something that's as likely to happen in political voting). Any other result would have seemed unreasonable to Julie, Frank and Timothy, so when they designed their system, they designed it with the following feature. If we list Chocolate over Lemon on our order on one day, and if none of the people who prefer Chocolate over Lemon change their minds about that the next day, then we should list Chocolate over Lemon the next day as well.

Because this was implicit in their system (and because they’d listed Chocolate over Lemon on the 22nd when only Julie had that preference), they always listed Chocolate over Lemon on any day when Julie preferred Chocolate to Lemon. That is to say, Julie was the principal figure on the Chocolate/Lemon consideration - the 'authoritarian', if you like.

Now on the 24th, Julie was in a Chocolate/Lemon/Strawberries frame of mind. Suppose again we don't know much about Frank’s or Timothy’s moods except that they both favoured Lemon over Strawberries. Since everyone preferred Lemon to Strawberries, Lemon was, of course, listed higher than Strawberries in the cheesecake hierarchy. Once again, any other result would have appeared unreasonable to Julie, Frank and Timothy, so they’d built their system along the following lines:

Whenever we unanimously prefer option X to option Y, option X should rank higher than option Y on our order.

First, Julie preferred Chocolate to Lemon, so of course Chocolate ranked higher than Lemon. Second, everyone preferred Lemon to Strawberries, so Lemon ranked higher than Strawberries. Logic says that Chocolate must have ranked higher than Strawberries. Logic also says that when Julie prefers Chocolate/Lemon/Strawberries in that order, and everyone else prefers Lemon to Strawberries, Chocolate must be more preferable than Strawberries.

They also agreed the following:

Our preferences regarding Lemon should not affect the relative positions of Chocolate and Strawberries in the ranking. Therefore, the above should hold if we drop all the Lemon-related assumptions. That is to say, on any day when Julie prefers Chocolate to Strawberries, Chocolate must rank higher than Strawberries.

The next day, the 25th, Julie’s preferences ran Strawberries/Chocolate/Lemon, while the other two both preferred Strawberries to Chocolate. Since they all preferred Strawberries to Chocolate, Strawberries came out higher than Chocolate on the cheesecake order. Since Julie was a Chocolate/Lemon authoritarian, Chocolate came out higher than Lemon. Logic tells us also that Strawberries came out higher than Lemon. And the same would be true on any day when Julie preferred Strawberries/Chocolate/Lemon and everyone else preferred Strawberries to Chocolate.

But the ranking of Strawberries vs. Lemon was designed to be unaffected by how anyone cared about Chocolate, so the Chocolate-related information cannot be relevant. This tells us that on any day when Julie prefers Strawberries to Lemon, Strawberries rank higher than Lemon. She’s not just a Chocolate/Lemon authoritarian and a Chocolate/Strawberries authoritarian; she’s a Strawberries/Lemon authoritarian too.

What we’ve uncovered is that any Chocolate/Lemon authoritarian is also a Chocolate/Strawberries authoritarian and a Strawberries/Lemon authoritarian. Interchanging the flavours, we could have just as easily discovered that any Chocolate/Strawberries authoritarian (e.g. Julie) is also a Chocolate/Lemon and a Lemon/Strawberries authoritarian - and so on as every pair of flavours appear. In other words, despite the table of preferences above, Julie is an absolute cheesecake authoritarian as all of her preferences are entirely reflected in the cheesecake order on any given day.

Now here's the upshot of it all. We started by declaring that Chocolate came out on top on the 22nd. But if Strawberries had come out on top, then using Arrow's model I could have given evidence to show that Frank is an absolute authoritarian, and if Lemon had come out on top, then using Arrow's model I could have given evidence to show that Timothy is an absolute authoritarian. Regardless of what happened on the 22nd, someone must be an absolute authoritarian - counterintuitive as that may have first appeared.

Extending that further, if there had been more people than just Julie, Frank and Timothy, and more flavours than Chocolate, Strawberries and Lemon, then although the argument becomes more mathematically intractable, it is not at heart any further from the nub of the wisdom just covered - that is, if you have a scenario that translates a series of individual preference choices into a single group preference of choice, that scenario will throw up an authoritarian.

Crucially here, we're seeing the distinction between what are very coherent individual preferences (called transitivity), and how at a group level it becomes incoherent (intransitivity). Transitivity is formally expressed as: if A > B, and B > C, then A > C - so in other words, with cheesecake choices, if Julie likes Chocolate more than Strawberries and Strawberries more than Lemon, she should like Chocolate more than Lemon.

Groups, however, don't necessarily have a transitive preference order - they have intransitive 'cycling' of preferences, which means Chocolate beats Strawberries, which beats Lemon, which beats Chocolate, which beats Strawberries, which beats Lemon, which beats Chocolate - meaning for group scenarios you might just as well put the flavours of cheesecake in a hat.

  

When You State It Like This, The Minimum Wage Doesn't Seem Quite So Lovely, Does It?

My local newspaper has a feature that looks to name and shame businesses that are finding ways to get around paying the full minimum wage to employees. The people that should actually be named and shamed are the short-sighted politicians that impose this law on people trying their best to run a business and people doing their best to find work.

I wonder if anyone has ever thought of the minimum wage the other way round, from the perspective of a law against the employee rather than the employer. That is, not of it being illegal to pay someone less than £7.20 an hour, but for it to be illegal to sell your labour for any less than £7.20 per hour. When it’s stated that way round it emphasises the point a bit more of how much of an infringement on our liberties the minimum wage law is.

When you think of Tom, Dick and Harry getting out of bed, eating their breakfast, all ready and willing to go out to their £6.50 an hour jobs - jobs they enjoy - but suddenly being disallowed to go to work because the government decides to slap an extra 70p on their legally mandated price floor, it doesn't sound anywhere near as positive, does it? To compound the point, have a look at a typical supply and demand graph.

   

The equilibrium point is the point at which the supply and demand curves cross - which basically means that it's the one price where the quantity supplied and the quantity demanded are equal. Suppose the graph represents a 25kg sack of potatoes, and the equilibrium price is £6 per sack. That means that if the market price is not at the equilibrium - say at £8 per sack - then the quantity demanded and the quantity supplied would not be equal.

 

The same is true of wages. Suppose the equilibrium price for a gardener is £6.50 an hour. If a government sets the minimum wage at £7.20 an hour then as you can work out from the demand curve, demanders (that is employers) would want fewer gardeners, while suppliers (gardeners) would want more of their labour sold, thus creating disequilibrium. Thanks to this government price floor the suppliers are now not able to sell all the labour they want to. Not only that, but of course, demanders are not happy either because they cannot buy the quantity they would like to, as they prefer a price of £6.50 an hour to hire a gardener, not £7.20.

 

The result: supply and demand for gardeners is at a disequilibrium, and the country has fewer gardeners. What I didn't tell you is that Tom, Dick and Harry are gardeners - or, at least, they were until the former chancellor hiked up the minimum wage an extra 70p an hour, and sent Tom, Dick and Harry, and lots more like them, to the job centre - where there'll join the thousands of other people who are already there, and have been for a very long time having never had a job, because said chancellor has made it illegal for them to sell their labour at the supply and demand equilibrium point.

It Would Be More Surprising If Employers Are *Not* Discriminating Against Muslims

A couple of days ago I saw a feature on the BBC News channel on discrimination against Muslims in the job market - Is it easier to get a job if you're Adam or Mohamed?:

"A job seeker with an English-sounding name was offered three times the number of interviews than an applicant with a Muslim name, a BBC test found. Inside Out London sent CVs from two candidates, "Adam" and "Mohamed", who had identical skills and experience, in response to 100 job opportunities. Adam was offered 12 interviews, while Mohamed was offered four."

The reports conclude that there is 'Significant discrimination' going on in the job market against Muslims. The BBC feature also showed that Muslims are the minority group that find it hardest to obtain employment - a fact that is creating all kinds of social problems in areas with high concentrations of Muslims.

With my economist hat on, I don't find it in the least bit strange that Muslims are being discriminated against in the labour market. Quite the contrary, it would be stranger to me if they weren't being discriminated against, because if there is one thing we ought to be discriminating against it is people's views and beliefs.

I have shown before on this blog how the market weeds out unfair discrimination and how it is foolish for an employer to discriminate on factors that don't affect someone's ability to do a job. But that's just another way of  saying that it is wise to discriminate on factors that do affect someone's ability to do a job. That's why we don't see blind lifeguards and people in wheelchairs working on the top of cranes.

Ah, but hang on, being a Muslim doesn't preclude someone from doing a job, does it?

No it doesn't, not usually, but hang on yourself - we are talking about a more subtle kind of discrimination here - one that I can fully sympathise with. Imagine you're an employer and you're shortlisting for five candidates for an interview based on application forms and CVs. You have 4 shortlisted already and the fifth is between an applicant called Adam and an applicant called Mohamed. All other things being equal, it is perfectly understandable why a prospective employer would pick Adam over Mohamed.

That's not to say that Mohamed would always be worse than Adam - in fact, there may be instances where, in not picking Mohamed, the employer has omitted the strongest candidate of all. But you must understand that picking job candidates is not an exact science, it is a probability estimate that occurs in a fast-paced world with lots of asymmetry of information.

Knowing that Adam the non-Muslim and Mohamed the Muslim are equally qualified, the prospective employer knows that as a broad cross-national probability estimate, Adam provides less of a risk of being a worse employee than Mohamed. Like I said, not always, but all the employer is interested in at this stage is picking the people who he or she thinks constitute the best candidates to be good work colleagues with as few barriers as possible to doing the job.

Unfortunately for Mohamed, he lives in a world in which people's views and beliefs ought to be scrutinised, and judgements ought to be placed on that scrutiny. One should feel no differently about a scientologist, an astrologer, a member of the BNP, a young earth creationist, and so on - not that these views and beliefs always maketh a bad candidate, but simply that they increase the probability of doing so.

They do so on the basis that if you're sort of person to believe things that are obvious to everyone on the outside as being nonsense, or have views that are obvious to everyone on the outside as being socially toxic, you are likely to be the sort of person susceptible to all manner of bad thinking and dodgy beliefs (I've elaborated on how Islam falls into that category numerous time before on this blog).

So while Mohamed may sometimes be the best candidate for the job, he has an increased probability of missing out on an interview due to the socio-cultural stigma of being a Muslim in a place like the UK. And that's because, even if the probability is low, as long as all other things are equal, a prospective employer ought to factor in Islam into the consideration of who to shortlist for the interview. For example, Mohamed may be less preferable than Adam because being a Muslim, he might have a religious needs that disrupt his work more than Adam (going out to pray during the day for example), he might have a troublesome attitude towards female colleagues, he might be disruptive by being overly preachy, he might be more susceptible to other extreme beliefs, he might be politically toxic to the work atmosphere, and although hopefully unlikely, there is perhaps a slim chance that he might be a radicalised Muslim or go on to become one in the future.

The point is not that all Muslims are like this (obviously!!) or even that the things I described are highly representative of Muslims in the UK (they are probably not!!) - it is that in the landscape of employers choosing prospective employees they are going to pick candidates for an interview that have the lowest probability of being bad workers and bad colleagues. And in a straight shoot out between an unknown candidate called Adam and an unknown candidate called Mohamed, it is easy to see why prospective employers would opt for the former over the latter, thereby making the BBC's discriminating statistics unsurprising.

A Libertarian Paradox?

A friend, Tim Reeves, recently came up with what he claims is something paradoxical about libertarianism:

"They claim the market should work for itself as government can't understand its inner workings (which is probably true) and yet how do libertarians know the market will work if no human mind can understand it?"

I've been tentative about the so-called libertarian brand before, but for now let's stick with the populist understanding. While I have sympathy with Tim's interpretation, I don't think his paradox is as much of a paradox as he thinks.

Before I explain why, let me first say that I can think of a couple of elements of libertarianism that could be loosely be thought to be paradoxical. One such example is that libertarians desire the shrinking of political influence to a fraction of what it is now, but in being so averse to the state they may lack the political clout to influence from the inside. Another example, although admittedly a looser paradox, is that the freedoms libertarians welcome involve embracing a society open enough to contain many elements it finds to be inimical to the values it espouses.

But Tim's enquiry regarding how libertarians can know the market will work if no human mind can understand it doesn't strike me as being much of a conundrum, because in being asked to understand how the market works we are only being asked to understand that the market is society's aggregation of individual decisions by buyers and sellers made by people for whom those decisions brought about a mutual benefit.   

That is to say, while Tim is quite right that the free market is too vast and complex for politicians to understand its inner workings, it doesn't follow that because of this libertarians are on dodgy grounds assuming the validity of their position, because all us pro-market people are trying to say is that a free market in action must, by definition, be a system working for its agents, because it is quite simply the accumulation of activities that work for those agents.

There may well be unpleasant things in society that result from free market transactions, and concomitant power laws that cause discomfiture to certain socio-cultural groups, but us pro-market people are not primarily selling the qualities of the market per se - we are trying to advocate the freedoms from which things like the market operate more fruitfully.

The Truthseeking Wheat From The Truthseeking Chaff

Suppose you meet someone for the first time. A way to impress them might be to talk intelligently at them for a while, reeling off a litany of impressive knowledge and reasoning. But while you might impress, you wouldn't learn much from the other person. On the other hand, you could meet that person and spend your time listening and learning, forgoing opportunities to impress them with your own conversational gifts.

Ideal conversations are probably about half and half - with both agents having roughly equal listening and talking time. While on my day I could make an impact on an interlocutor with some impressive knowledge and reasoning, I find what generally happens when I converse with a stranger is that I tend to allow the conversational output to be largely about the other person, because I want to 'soak up' as much new knowledge within that brief window as possible.

Here's why. Suppose you get chatting with a stranger and the chances are you won't get to do it again any time soon. Yes you could impress them by talking intelligently at them for a while, but equally you could use the opportunity to learn something from someone who knows more about a subject than you. Any stranger is going to have areas of knowledge that surpass yours, be it knowledge related to their job, their hobby, or simply a keen interest of study.

Consequently, then, if you and I meet as strangers, there's a good chance that I'll be highly interested in something you know about that I can add to my knowledge stock - be it plumbing a bathroom, working as a solicitor, your superior sporting talent, your experiences in a foreign country, an author you've read that I haven't, or numerous other areas of knowledge you have in which mine is less prodigious.

Being willing to soak up other people's expertise is a rewarding pursuit, and well worth resisting the temptation to predominate a conversation. And don't worry about not getting your chance to express intelligence - taking an interest in others and asking sharp and incisive questions will give exhibition to an intelligent mind at work.

For further consideration, there's another element to this. Being better informed isn't a panacea against being wrong. Given that even well informed people have faulty reasoning, it is not a good assumption to say "You are well informed therefore you're probably right". A better question to pursue would be "If I knew as much as you do on the subject, would I agree with your conclusions?". If your interlocutor says 'yes' it may show confidence that they think they can back up their position. If on the other hand they say 'no' it may well be an indication that they hold that view for different and possibly fragile reasons.

Suppose Jack and Jill disagree on five things. In four of the five cases Jack says that if Jill knew as much as he did on those subjects she would agree with him. But in the other case Jack admits that if Jill knew as much as he did on that subject she'd still disagree with him. On which of these scenarios do you trust Jack the most: on the four cases in which if Jill said 'show your work' there would be enough to convince her Jack was right; or in the one case where if Jill said 'show your work' there would not be enough to convince her Jack was right? In all probability it would be the former.

It has to be said though, there is a difference between evidence showing someone to be wrong and that person actually changing their mind. For example, it would very easy to provide the scientific evidence to show that evolution is a fact, but that doesn't mean a young earth creationist would change their mind when presented with it. It would also be very easy to provide the economic evidence that import tariffs are bad for the economy, but that doesn't mean a politician will suddenly stop supporting them. Bias and self-interest are powerful tools of motivation even in the face of contra evidence.

It's very likely is that if a person believes something that is not true, and doesn't appear very bothered about the evidence connected to showing the falsity of the belief, their reasons for believing it are motivated by very strong and influential non-empirical factors, like being part of a cult or wishing to deceive large swathes of the population. This is why in any consideration of truths and facts, open, honest, rigorous dialogue that presents evidence and the weight of arguments from both sides is always going to be the best course of action.

That is why, if anyone disagrees with me about anything, I am always enthusiastically wishing to debate openly about it, and have all the arguments from both sides laid out like a buffet on a dining table. My experience tells me that the 'buffet' standard is a pretty reliable standard for separating the genuine truth seekers from those who believe what they want to believe irrespective of truths and facts.

The Best Way To Be Right Is To Not Mind Being Shown You're Wrong

One of the kindest things a regular reader once said to me was how consistently he thinks I get things right. "The thing about your blogs is that you're just so damn right about everything". Let me assure you, I always try. And the secret, as I'll explain, and as the title indicates, is in not being afraid of being wrong. You'll usually notice something reassuring about genuine truth-seekers: if someone shows them they are wrong about something, or offers them a better way of looking at things, or imparts some wisdom that comes from superior reasoning skills, they never mind having these things pointed out.

Genuine truth-seekers are more likely to rigorously explore both sides of the argument, and only opt for the position they think makes most sense, and best conforms to reason, logic and evidence. Because the truth is, throughout your life, every time you're open enough for someone to show you where you're wrong is equally a time when you've been given the opportunity to be right about something new.

Suppose you were brought up in the Bible Belt in America and you used to believe that the earth is only a few thousand years old, that humans do not share a common ancestor with other apes, and that the eye is too complex to have evolved. Then in a particularly enlightening day someone manages to show some good evidence why all three of those propositions are false.

In being shown to be wrong, you have learned at least three new things - the real age of the earth, the process by which natural selection can bring about eyes through a cumulative ratchet process (I once blogged about this here), and how our understanding of DNA demonstrates common ancestry (I once blogged about this here). Being shown how the old you was wrong ought to be positively embraced, because it also shows the new you how you are right.

It's not that difficult in life to be self-assured in your views and argue with confidence in debates, exposing your opponents with all the aplomb of a sniper picking out targets. You just have to follow these guidelines: be wedded to facts and truths, not emotional feelings or in-group biases. Also, don't seek security in the consensus - it doesn't mean these people are right just because there are a lot of them.

Consider bookmakers as an illustration. Bookmakers' odds are about probability of outcomes before the event. They are, in a sense, the pre-fact likelihood of future facts - asking who will win an upcoming horse race, presidential election or football match. The odds a bookmaker offers on a sporting event are not based on a general public consensus, they are based on the consensus of a proportion of the population that knows about sporting probability, and on the behaviour of people who are willing to bet money on these outcomes.

The bookmakers don't always get their odds right, but on average you'll find they do - where on average means over the long term they get a lot more right than they get wrong. That the betting public get on average a lot more wrong than right means the bookmakers stay in business.

Learning how to be right is a bit like this - it's about playing the long percentage game and not being taken in by any fads or hyperboles. It is about mastering methods of thinking that can hold you in good stead in front of any proposition. Of course, in a civilised society it is often good that our democratic views are implemented - be they views on which party should govern us, whether we should be in or out of the EU, and so on - but that should not be confused with empirical investigations.

Just because the majority of people think we should not frack or that London needs rent controls doesn't matter one jot if there are good logical and evidential reasons why the consensus is wrong. “Have you ever noticed when you’re driving that anybody driving slower than you is an idiot, and anyone going faster than you is a maniac?” observed the comedian George Carlin. It's a nice bit of awareness-raising, because one thing you must forever keep at the forefront of your consciousness is that in being human you see the world through a series of you-centred biases, and those biases shape how you think, the views and beliefs you have, and how you formulate arguments.

I wish everyone always had that at the forefront of their minds, because instead of thinking everyone wrong and themselves right about everything, they could perhaps consider more readily that they might, in fact, have plenty to learn, and plenty of ways in which a change of mind will be good for their arsenal of reasoning. I’m not immune to that criticism either – it’s always good to be self-critical, however confident you are that you’re right.

I think the thing that gives me such confidence when I write as I do is in part because I’ve thought about these things a *lot*, and always tried to put myself in the place of the opposition and argue well for their side of the argument (a good tool to use in any debate). But the other major factor, in my view, is that I really don’t care what the results are as long as it’s true, logical, evidential, and conforms to reason.

I have no need for denial, no dog in any fight, no in-group or tribal affiliation, and no concern for whether what’s true is thought true by the majority, by some people, or by hardly anyone – I’m only interested in what is correct. If a genie appeared and showed me where I was wrong about x or y I’d be genuinely fascinated and delighted at this fresh illumination. That’s the only way to be, and why, as the title suggests, the best way to be right is to not care about being wrong.