Liberty & Social Policy: Blackstone's Ratio, And Type I & II Errors

                                                                                  

Recently I asked this on Facebook.

Somebody puts a gun to your head and forces you to spin a coin:

If it lands on Heads then ten randomly selected innocent people in the UK, aged between 25 and 40, are sent to prison for five years.

If it lands on Tails then ten randomly selected criminals about to serve five years in prison in the UK, aged between 25 and 40, are set free.

Do you hope the coin lands on Heads or Tails?

Not one respondent said Heads. Everybody who answered seriously said they hope it lands on Tails, or that there are no winners in this scenario.

In the 1760s, a lawyer named William Blackstone famously declared that it’s better for ten guilty people to go free than for one innocent person to suffer. For the next 240 years, most legal systems have paid dutiful regard to this sentiment. I don't know why so many people blithely advocate the principle, nor do I know what William Blackstone thought so special about the number ten as the optimum number of guilty people we should set free for the sake of the innocent. Why isn't the optimum number six or fourteen; why ten? And why is it better for a guilty person to be set free than for an innocent person to suffer - why aren't they both equally undesirable?

The answer, of course, is that nobody ever says. They make these assumptions without ever considering a proper trade off. Moreover, in both scenarios, there is suffering of innocents - either innocents going to jail, or innocents suffering by criminals not being in jail. The right way to measure a preference of false convictions over false acquittals (or vice-versa) is to try to imagine how both would affect the majority of lives, and how much people would be willing to pay to avoid a false conviction or being the victim of a criminal who received a false acquittal. And we lack the information to do a proper calculation on this. Perhaps it would be better for one innocent man to serve time in prison rather a violent man being set free and causing physical harm to six women during the same timeframe. In this case, it may be better to convict just one innocent person rather than letting one guilty person go free. If the conviction of one rapist prevents a further ten rapes, then in this case Blackstone's ratio may be backwards.

There is also a discussion to be had about what constitutes a healthy reasonable doubt. If I'm 90% sure that Fred committed a murder, then I should be 100% sure that I'd vote guilty. But if I'm only 60% sure that Fred committed a murder, how sure am I that I'd vote guilty? I don't know with any degree of confidence. And in any scenario I envisage, the percentages change when the stakes are altered. If the crime is minor vandalism that carries a six month prison sentence, then it's probably never worth convicting an innocent person to see that several guilty people get convicted. But in the case of murder, it may be worth the odd false conviction if it increases the probability of a string of rightful convictions of people who committed murder.

The above scenarios are hypothetical, but there are many real life scenarios where we frequently have to assess a trade off. Should we place people in lockdown during Covid or pay the price of extra deaths in order to avoid absolute economic decimation? Should we live with the ecological consequences of capitalism or risk intervening and costing many more lives through the stifling of economic development? Should we risk the death of some civilians to bring an end to a warmonger's dictatorship? Even though most people never properly consider questions as trade-offs, the world is full of them.

When it comes to policy, then, there are two questions one always needs to ask:

1 Have I got the reasoning right? If yes, go to number 2

2) If my reasoning is right, will my solution actually work?

If yes to 1 and 2, consider implementation. If no, to either, abort.

Alas, so many political decisions fail both criteria. The reasoning is faulty, either because they’ve not undertaken a proper cost-benefit analysis or they misunderstood some statistics, or they treated a complex problem over-simplistically. But even if they got their reasoning right, that still doesn’t mean they should enact a policy, because many policies have negative 'unseen' effects as a result of the changed incentives brought about by the policy's introduction (in economics this is called the law of unintended consequences).

For example, the minimum wage is a state-enforced increased cost to employers, but businesses respond by passing those costs on to consumers with higher prices or fewer jobs, so it does more harm than good. Policies like rent controls and tighter regulations that try to make life better for tenants have such an adverse effect on landlords and property developers that tenants find it harder to rent at affordable prices. Increased taxes on high earners in the hope of raising more money for the treasury can have the unintended consequence of reducing tax revenue as entrepreneurs reduce their capital investments. Subsidies and bailouts increase risky behaviour as firms know they won't be so heavily penalised for their mistakes. The list goes on.

Type I & Type II Errors
It's perhaps wise to think of this in terms of type 1 and type 2 category errors. A type 1 error is the incorrect rejection of a null hypothesis that is true. An example would be, as above, when a jury delivers a guilty verdict in the trial of an innocent defendant. A type 1 error is generally an error that infers an effect or correlation or causality that doesn't actually exist (a false positive).

A type 2 error is the failure to reject a false null hypothesis. An example would be, also as above, when a jury delivers an innocent verdict in the trial of a guilty defendant. A type 2 error is generally an error that fails to infer an effect or correlation or causality that does actually exist (a false negative).

Generally, although not always, we feel that a false positive is less harmful to society than a false negative. An anti-virus system that wrongly thinks a benign program is a virus is better than an anti-virus system that wrongly thinks a virus is a benign program. An airport security system that wrongly thinks an innocent man might be a terrorist and pulls him in for questioning is preferable to an airport security system that wrongly thinks a terrorist is an innocent man and sees one of their planes blown up.

Preferences like this are built into our evolutionary hardwiring, and for good reason, as most people know with the following popular example. A rustling in the bushes may be the wind, but it may be a predator. It's less costly to assume it's a predator and find out it's the wind than to assume it's the wind and find out it's a predator. So over the years we have been primed for false positives - to sense potential danger, patterns and breaks from normalcy, and ascribe them to something causal or deliberate or predatory, even when such things are not there.

But….there is a but. I'm fairly sure that on balance it is usually best to adhere to the opposite approach: that is, it is best to err on the side of individual liberty and pay the relatively small prices when things are sub-optimal, rather than erring on the side of suppression of liberty and suffering the relatively great opportunity costs of doing so.

Let's explore some real life examples, and I'll try to show why we should err on the side of freedom and do very little to intervene.

Take the debate about censorship of free speech as a prime example. Aside from the standard legal prohibitions (making threats of violence, slander, perverting the course of justice, etc) the negative utterances that emerge under a system of freedom of expression are a price worth paying for the astronomical benefits that come from the free exchange of knowledge and ideas. The same for causing offence: we have to be able to risk offending others as a gateway to exploring truths and facts - no one has a right not to be offended.

Or take the free market as another good example. The relatively small costs we would pay for a much freer market would be astronomically dwarfed by the advanced standards of living, enhanced innovation and increased prosperity we would enjoy.

People base their assumptions on all sorts of crazy whims and misunderstandings based on the aforementioned type 1 and 2 errors. If they go unchallenged then they are not getting the correctives they do deserve, and they are getting the latitude they don't deserve.

Or take the issue of whether trans women should compete in women's sports: of course they shouldn't. They have an unfair advantage, and that undermines the sport because it's grossly unfair to the women competitors. It's better to inconvenience a minority of trans people and invite them to compete in a separate trans category in their sport than it is to undermine the whole category of women's sport by letting in a few dominant trans people. Ironically, a lot of the people who want trans people to compete in non-trans people's sport divisions are the same people who support protectionist political institutions that hinder developing countries in competing more fairly in the wider global marketplace. Real life is often more farcical than situation comedy.

At a busy airport, we all have to go through lengthy security checks to make sure we are not terrorists or drug smugglers. Every time you or I go through an airport security system, the airport makes a Type 1 false positive error. It is deemed to be worth the high number of false positives in order to avoid the Type 2 false negative error where the airport fails to detect a terrorist or a drug smuggler. To know which policies are best, we need to ascertain the statistical probability and weigh up the costs of execution against the outcome of a false negative error. If the resultant bad outcome was something like a terrorist attack that killed thousands of people, then a system like an airport security that allows a large number of false positives in return for a low number of false negatives is probably justified.

A system, on the other hand, that sought to protect offence by banning lots of expressions of free speech would be making a catastrophic error, because whatever your beliefs about any subject, the ability to communicate those beliefs - in speech, in writing, in art - is not just the bedrock of society, it is the bedrock of being human! The capacity to express yourself is the very basis of turning the vortex of our inner thoughts into a coherent order, whereby beliefs are formulated and opinions are articulated and challenged. Language is like a tree that plants its roots into our inner-most being, and allows knowledge, thinking, creativity and feeling to spring out in a way that connects humanity as the most advanced species on the planet. And it is the duty of every thinking human to stridently oppose the attempts to uproot that liberty with their emotionally stultifying and intellectually oppressive agenda.

Society is riddled with these examples: from the attempts to restrict free speech and free thought; to attempts to equalise society when the inequalities are based on free choices; to acceding to the demands of the dozens of gender neutral pronouns that have been constructed; to supporting the multi-billion pound climate change crony capitalist industries - and the glaring truth they all miss is that it is far far better to let liberty run its course and deal with any problems when they arise, than it is to stultify liberty in the hope of achieving the narrow outcome you think you want.

On Being Certain God Exists

As I was editing the final draft of my book, I felt a huge sense of God speaking to me. I felt Him challenge the general assumption that we should act as though we believe He exists but never assert that we are certain He does. I felt that He called for a revival of confidence for Christians in the world, where we proclaim that we are certain He exists, because He has made Himself known to us in so many ways that are more compelling to us than the ways we feel certain about other things.

Now obviously this is still a complex consideration that took a while to contemplate - not least because I wanted to test it with more prayer and supplication to the Holy Spirit. And I was also aware that even if this is something of which God approves, there are going to be wise and unwise ways to go about discussing it. After all, the Old Testament is full of occasions where God hides His face from a sinning Israel; and even in the New Testament, where Christ is referred to as 'the image of the invisible God', there are accounts in scripture of Christ's time on earth where He actively avoided the crowds and didn't make a big spectacle of His miracles. Moreover, our basis for faith is said to be on what is 'unseen' (Hebrews 11:1, 2 Corinthians 4:8), so on what grounds might we be permitted to declare that we are certain God exists? On the other hand, if we claim to feel certain about some things, then there is a prima facie case to be made that we ought to be able to feel certain that the God we have a relationship with actually does exist.

There is also a profound distinction between feeling certain God exists, and the faith one has in Christ. To have faith in Christ doesn't necessarily mean one is not certain of God's existence - in fact, one may have faith in Christ precisely because we feel certain God exists and can be found through Him. Or in other cases, one might feel certain that God exists because one has faith in Christ and sees God in Him. I know God exists - by which I mean that of all the things I know, the proposition related to the God of the Bible's existence is known by me as strongly as the other things I know most strongly.

In order to explain that, I need to talk about the different things I know and how I go about knowing them. Here are three examples of things I know. I know that 2 + 2 = 4. I know that Brazil has a larger land mass than Turkey. I know I prefer fried scampi to fried onion rings. These three bits of knowledge are constituent parts of what one could call my worldview. I use the term worldview to mean the aggregation of all the things I know, think, believe and feel, based on the totality of my life experience. That life experience has led me to know that mathematics is reliable; that the land masses of countries are measurable to an accurate degree; that my tastes inform me about what I like and dislike; and that it is possible to compress lots of complex data to formulate succinct theories about the world. It is possible, of course, to challenge some of my knowledge. For example, although I know I prefer fried scampi to fried onion rings, it might be possible to manipulate my neuronal activity to alter my brain states and tastes. Private experiences, as Wittgenstein reminds us, are shaky justifications on which to proclaim knowledge.

When I consider what it involved for me to become a Christian, I am able to declare with confidence that knowing the Christian God exists is something I know as well as I know anything. I know Christianity is true just as I know all the other religions are made up human constructs. You may find this hard to digest, but I think I know why. When you hear someone say they are a Christian, you don't have access to the rich diversity of experience, thoughts and contemplations that went into their becoming a Christian. I think for a non-Christian it is impossible to fully understand how a Christian arrives at their knowledge of God - not least because our knowledge of God is not just of our own doing, it is through God's own Holy Spirit revelations in a daily relationship with us. It is a minute-by-minute awareness of what it means to be in a relationship with God - an awareness to which every Christian reading this will be able to testify.

To know God exists means knowing a lot of other things about how we can know God exists. We are so used to thinking of faith in God through a pretty furtive, circumspect lens that any claims that we know God exists are bound to be met with derision. There came a point in my journey when I started to wonder why this was so. You see, every Christian I know feels certain God exists. Yes we have moments of doubt, we have struggles, and we have emotional and intellectual challenges. But the truth is, we don't just believe God exists, we are certain He does.

Perhaps the reason you don't hear us speaking in terms of knowing God exists is, I suspect, because 1) It is very difficult to articulate what knowing God's existence actually means; and 2) One can't know God exists until one has revelation from the Holy Spirit, so trying to justify the knowledge to non-Christians is rather like justifying Mozart's best symphonies to someone who has never heard music. But whether or not it is possible to articulate this, the fact is, I am certain that God exists - I'm certain with as much confidence as I am certain of anything. Knowing God exists involves taking a whole lifetime's worth of experience, knowledge and comprehension (and dare I say wisdom?) that can be used to formulate a proper understanding of all the things necessary to have certainty of God's existence.

I think we also need to draw a distinction here between certainty and proof. There is no proof of God’s existence, so proof is not what I’m considering here. You may recall in Tennyson’s Ancient Sage, his terrific line “Cleave ever to the sunnier side of doubt”. The point of the distinction is that I think we can feel certain of things we can’t prove. Proof is something that can be demonstrated to others, but it only really belongs in mathematics. Certainty is something we can’t demonstrate to others in isolation, because it conveys how we feel about something. If we try to demonstrate certainty to others, then we enter the realms of requiring evidence or proof. I can demonstrate that I feel certain about mathematical sums by proving them with a pen and paper. I can demonstrate that I feel certain that biological evolution is factual by providing thousands of pages of supporting evidence. But if we claim we feel certain God exists, what we are actually doing is sharing a summation of a complex worldview built on a repertoire of experience. We have to be careful not to undermine the profound contemplations that work alongside faith and humility, but we don't have to discount certainty on the basis of discounting proof. They belong in different categories.

Finally, we can know something exists in a way that we cannot know that something doesn't exist. Given that certainty has to be a feeling based on a proprietary state, the category of positive certainty has to be operating on a higher level to negative certainty. Let's take human love as an illustration. The man who feels certain that love doesn't really exist could spend his whole life being single or in bad relationships and always feel certain there is no such thing as love. Conversely, the man who finds love with his beloved has the experiential mandate to feel certain love exists. In fact, love is one of those profound things whereby once you have it, you sense there is no real greater certainty in your life, because there is nothing on earth that can change that feeling while it's alive and well. That's why being certain God exists can be valid in a way that being certain He does not exist cannot possibly be. Another reason why this is true is purely down to the informational content. Even if it were possible to feel certain God does not exist, such certainty would take immeasurably more information and cognitive computational resources than feeling certain God exists, which could come about through a much more direct channel, and in much less execution time.

In closing, I am mindful that as Christians, even if we feel certain inwardly, we mustn't alienate people by coming across as being overconfident and potentially strangling the oxygen out of fruitful dialogue. But to be certain, we have to be convinced that the set of all possibilities within our spatio-temporal existence (call it N) has been sufficiently contravened by a Divine power (call it P) who has the qualities to act in a way that seems to us evidently outside of that existence. I do not mean anything that gets entangled with dangerous assumptions like God of the gaps, Clarke's third law etc, I mean a deeper understanding of certainty - a power that God has given us so that He has done enough in our individual lives to enable us to feel certain that He exists. Those Divine contraventions that constitute P could be anything from prophecies, healings, internal revelations, events that we believe to be powered from outside of space and time, and so forth. Of course, our faith is a worldview based on our life experience, so those 'sufficient contraventions' are built on our experience of others' experiences too in a complex join-the-dots epistemology. But it may remain one of those strange elements of Christianity that continues to linger in the abyss - in that most Christians feel certain that God exists, yet rarely feel the confidence to declare it.