At the Social Liberal Forum conference session on equality, one of the points raised by Julian Huppert (pictured alongside chair Mark Blackburn and the other speaker Kelly-Marie Blundell) was that of philosopher John Rawls’ idea of the Veil of Ignorance.
The Veil of Ignorance challenges us to find fairer solutions to policy questions: it asks us to consider what policies we would support if we were ignorant of our place in society, including of what skills and attributes we might have. This might not be possible: this is a challenge not a recipe.
Rawls goes on to deduce that inequality is only justified when that inequality benefits the least well off. This is called the Difference Principle. In practise this would mean that even though capitalism generates more wealth than communism does, it is still only justified if there is sufficient redistribution to ensure that the least well off person is still better off under capitalism. (And putting aside questions of freedom!)
I happened to meet Julian a week earlier, and for reasons that are not important we were discussing the relative merits of classical and Bayesian statistics. Julian is an enthusiastic advocate for the latter. If you can express your beliefs about some unknown fact (say how many people support Brexit) in terms of probability then with Bayesian methods you can refine those beliefs with evidence (say an opinion poll).
A Bayesian may therefore say of a poll showing 40% support for Brexit that there is a 95% probability that the true level of support is between 37% and 43%. A classicist would argue, a little more tortuously, that the true level of support is not random, so either is between 37% and 43%, or is not; but that this sort of poll will get the answer within 3%, about 95% of the time. By using the language of probability to describe the state of our knowledge, Bayesians are making more powerful and useful (if philosophically suspect) statements than classicists can.
Decision Theory deals with the problem of making decisions where the success or failure of our efforts depend on some unknown/random variable. (As distinct from Game Theory, where it depends on the decisions of another strategising agent.)
Two examples of a Decision Rule are the minimax rule, whereby we choose the action whose worst outcome is the least bad, and the Bayes Rule whereby we choose the action which gives the best outcome on average.
The Bayes rule isn’t really an option for the classical statistician because they don’t express their knowledge about the unknown in purely probabilistic terms. So the textbook examples in this field have, perhaps unfairly, the classicists using the minimax rule and the Bayesians the Bayes rule.
In real life, both these rules are a little purist: we are generally willing to take some risk, but we also buy insurance that loses us money on average. We apply Bayes-plus-insurance. (Although an insurance policy may lose us money on average but still gain us welfare on average if it protects us when we are most needy at the cost of money we need less when we are richer.)
Back to Rawls. Suppose I am inside Rawls’ Veil of Ignorance seeking to maximise my own economic well-being in the society I am about to set some policy for. Put this way it is a decision theoretic problem in which the unknown is the position in society that I will hold.
If I assume the worst – that I will be at the bottom of the heap, as per the minimax rule – I will agree with Rawls’ difference principle. If on the other hand I am a good utilitarian (like Mill, Bentham and others) I will apply the Bayes rule, seeking the greatest welfare on average, and I will tolerate a small chance of a somewhat harder deal, if it brings a bigger chance of a much better deal.
So utilitarianism can be seen as simply the application of the Bayes rule from behind the veil of ignorance; the difference principle being the application of the minimax rule. But the minimax rule is a conservative strategy that forgoes opportunities for the sake of the worst case – never leave home in case a tree falls on your head. The difference principle spites the many on behalf of the few.
The utilitarian/Bayes policy is egalitarian in the sense that everyone’s welfare matters the same – everyone has the same weight in the average. Under the minimax rule only one person’s welfare matters, albeit with some trickle-up.
A balanced policy – not pure Bayesian but Bayes-plus-insurance – would weight the less well off more highly in the utilitarian calculus without ignoring the majority altogether.
The difference principle demands a level of taxation for redistribution (and let’s for the sake of argument ignore the rest of the world, or it would be foreign aid rather than welfare) almost but not quite enough to stifle and stagnate the economy. A utilitarian or a balanced policy allows the economy to flourish, creating more wealth, and much better outcomes for everybody in the long run. There is still some redistribution, because the welfare of everyone matters and a given amount of money will have more utility to a poor person, but redistribution is no longer the endgame of improving the human condition.
Now it strikes me that the difference principle is too often accepted, and though I wasn’t able to put this to Julian at the time, I hope a good Bayesian such as he will appreciate why it shouldn’t be.
* Joe Otten was the candidate for Sheffield Heeley in June 2017 and Doncaster North in December 2019 and is a councillor in Sheffield.
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25 Comments
The problem with utilitarianism as a strategy though is that at its extremes it can lead to abhorrent decisions, if a given policy would lead to a tremendous lack of utility for a small minority, with a corresponding small gain in utility for the supermajority, the utilitarian thing to do is to persecute the minority (see for example the “torture vs dust-specks” argument). There are other problems with utilitarianism, too, such as the “repugnant conclusion”.
I think there is an argument to be made that minimax strategies should be in use *until the level of the worst-off person has been raised to a reasonable level*, after which utilitarian strategies should take precedence. There should be a floor beyond which no-one is allowed to fall (unless of course they chose to), but once that is taken care of then the utilitarian argument should be used. An example of putting that into practice would be having a basic income (floor beyond which no-one is allowed to fall) but then letting other policies be geared towards economic growth.
Anyway; back in the real world……
And of course one could also argue that the title of this post is a bit of a misnomer — one could use the Bayes rule to find the action that will result in the highest payoff for the worst-off, just as easily as raising the average. One just has to use the minimax rule as the utility function to be optimised for…
Not sure that’s right, Andrew. The Bayes rule necessarily maximises the expected utility which the veil of ignorance implies is the average utility enjoyed by a member of the society. Now the Wilson-Pickett thesis does indeed attempt to tie the average person’s utility to that of the less well off, but it doesn’t do nearly enough for your needs.
On your previous point, I suspect even a purely utilitarian argument would be sufficient to establish a floor level, for any sensible utility function.
Please apply this to Public Finance Initiative and Climate Change, bearing in mind the Fixed Term Parliament Act.
Thank you for posting this. Some really interesting ideas here, especially about the development of policy, and it would be good to hear from Julian if he would prefer the difference prinicple to be more widely used. What would really help others to understand, however, would be some more thoroughly worked-through examples. Even better if they were not just economic ones. I also suspect that the Bayes approach will require some defending against those who would say that not seeing ‘redistribution as the end game’ is just another way of justifying not doing it.
“The Bayes rule necessarily maximises the expected utility which the veil of ignorance implies is the average utility enjoyed by a member of the society.”
Not necessarily. The veil of ignorance, at least in my understanding, doesn’t necessarily mandate one choosing the highest average utility. An example — you’re behind Rawls’ veil of ignorance and are given a choice of a society where sixty million people live to ninety, or one where fifty-nine million, nine hundred and ninety-nine thousand, nine hundred and ninety-nine people live to ninety years and one day, and one person gets tortured to death aged twenty. The difference in expected utility would be small, and the potential downside for being the person tortured to death so great, that from behind the veil of ignorance one might still reasonably say “I’m willing to trade one day of definite life against a one in sixty million chance of losing seventy years and being tortured”.
“the Wilson-Pickett thesis”
I assume you mean the Wilkinson-Pickett thesis, as in The Spirit Level? The Wilson Pickett thesis is that I’m gonna kiss you girl and hold ya, and do all the things I told ya in the midnight hour 😉
(Sorry, couldn’t resist — precisely the kind of typo I make myself all the time…)
” I suspect even a purely utilitarian argument would be sufficient to establish a floor level, for any sensible utility function.”
One would hope so. Utilitarianism seems to me to lead to fairly abhorrent conclusions when taken to its limits, which suggests it’s flawed — but every other form of reasoning about ethics seems *even more* flawed…
The theme of the SLF session you refer to was actually Privacy, rather than Equality. The latter took place after lunch.
A couple of technical points.
(1) I’m sure Andrew Hickey is right, Bayes rule doesn’t, in itself, maximise expected utility. Bayes rule simply get you to a posterior probability distribution. You can combine that with a utility function to find an expected utility, which you can then maximise, but you aren’t forced to.
(2) The usual decision theoretic justification for insurance is what economists call the diminishing marginal utility of money. Your expected monetary gain from taking out insurance may be negative, but utility is not proportional to money.
Andrew H, indeed, it is the Bayes rule, not the veil of ignorance that mandates choosing the highest expected utility.
We are saved from most of the difficult consequences of utilitarianism when we are talking about redistribution of incomes because redistribution from rich to poor increases rather than reduces utility. (Putting aside the extent to which this weakens the economy.)
Pedant. Ah yes. I should have written this up sooner.
Andrew M, (1) Bayes Theorem gives you posterior probability distributions. Bayes Rule (Or the Bayes Estimator or Action) is about the action that maximises expected utility. I did kind of leap from one to the other in the article. They are connected but not identical.
(2) yes I allude to this. It also creates the utilitarian justification for redistribution (other things being equal).
Where is the evidence for your repeated assertion that redistribution weakens or stifles an economy?
Mark, the assertion, made once, is that it is possible to raise taxes so much that the economy is stifled. I think this is pretty obvious and not worth digressing into in this article.
As I remember the constraints, behind the veil one lacks information that would permit judgments like, the odds of this are greater than the odds of that. So the consideration that “I will tolerate a small chance of a somewhat harder deal, if it brings a bigger chance of a much better deal” is not available to people behind the veil. If this is correct, behind the veil utilitarian reasoning has no purchase and the “issue” you raise is a non-issue. Of course realizing this might lead one to wonder whether the veil of ignorance is too opaque. Speaking for myself, I think Rawls was right to make it opaque.
Echoing other commenters: Bayes Rule is about probability and subjective belief, it doesn’t say anything about making decisions. The decision procedure that maximises the expected value for some quantity is known as VNM-rationality; it’s not hard to prove that any decision procedure that is not VNM-rational will have some very weird properties. Strictly, “Utilitiarianism” is VNM-rationality plus the assertion that what we should maximize is something like “the greatest good to the greatest number”.
See Wikipedia for some of the proofs around VNM-rationality: https://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Morgenstern_utility_theorem
For axioms that yield Bayesianism as well as VNM-rationality, see here: http://lesswrong.com/lw/5te/a_summary_of_savages_foundations_for_probability/
Larry, thanks for your comment. Clearly I go on to disagree with Rawls, so I’m open to argument on what information and intelligence should be available in the veil. For me, the value of the veil is precisely that the agent does not know her place in society, and therefore cannot advantage herself at the expense of others. All other information, knowledge, indeed God-like omniscience, would lead to better policy decisions and should be allowed.
Rawls argues against my assumption that every outcome (i.e. every place in society) is as likely as any other. I am using some sort of forbidden reasoning that challenges his conclusion (the “wrong” kind of probability). But the only alternative to every outcome being as likely as any other is that some outcomes are more likely than others and then the veil is falling apart.
Paul, thanks for your links. I realised in writing this that what I have always called the Bayes (Decision) Rule, others call a Bayes Estimator or Bayes Action. I think this is just a point of terminology. It may be (nearly) the same thing as VNM-rationality, as approached from the field of statistics rather than philosophy.
“The Bayes rule necessarily maximises the expected utility” Right, but the question is how does one measure utility? There’s a law of diminishing returns. A ten pound note found in the street is worth more to a homeless, unemployed person than to a millionaire, for example.
My view is that it’s as important to measure utility correctly as it is to model policy outcomes properly. And that’s a specific application of the general observation that we need two things in politics (a) the right values and (b) competence. Neither is helpful without the other, but (b) without (a) can be positively dangerous.
“The Veil of Ignorance … might not be possible: this is a challenge not a recipe.”
To be clear, Rawls never suggested that the Veil of Ignorance was possible. We are not supposed to treat it as possible. Rawls’ Original Position is no more real than The Social Contract. It is a thought experiment of the kind very common in moral philosophy.
Our economy is presently weakened because it is too unequal. Fascinating though Rawls and Bayes may be, therefore, we don’t actually need them here. We just need to clobber the kleptocracts who are wrecking our economy!
David, I agree that kleptocrats weaken the economy and increase inequality, and that opposing them therefore doesn’t depend on where you stand on this kind of argument. It is surprising we don’t see more of it really – I mean there is Steve Webb’s heroic stand against pension funds salami slicing from us at every opportunity, but who else has given that kind of focus to kleptocrats, how they work and how to stop them?
Your broader point – which I guess is the Spirit Level argument – deserves another article.
Lots of people saying, “never mind all that, we’ve got difficult problems to deal with”, and IMO this is more-or-less right. Questions about the foundations of morality, justice etc. have been being asked for thousands of years and we don’t seem to have uncontroversial, agreed-upon answers, and probably won’t for a long time – in the mean time we have stuff to do, and some of the controversial attempts at answers are more-or-less impossible to apply to anything, at least not directly.
Mill himself – our very own philosopher-MP – had to grapple with this – part of his contribution was to write On Liberty, which is a really good book and full of principles which are both good and applicable. Thing is, Mill claims to have derived the principles from utilitarianism, and lots of people say the principles are good but the derivation isn’t – they claim that his principles actually contradict utilitarianism. Personally… I think given the huge uncertainties involved, it’s hard to say either way for sure.
Personally, I found Mill much more inspiring to read than Rawls (those Lib Dem membership cards with pictures of famous old Liberals on them – I want one with Mill on), but I suspect that’s a matter of taste. I think that reading through philosophy books can help you develop your ideas, but trying to extract and apply neat little formulae from them is a waste of time at best.
If this +3 to -3% is applied to the last round of polls before the general election, how close were they to the overall result?
Oh dear, I do hope the party is not about to go into a period of mental masturbation around angels and pinheads.
Philosophy has its place, indeed it’s kid’s stuff according to Julian Baggini at http://www.pressreader.com/uk/the-guardian/20150728/282196534655230/TextView
Stephen Booth,
As the LibDems claim to be the arbiters and defenders of liberal philosophy they are obliged to engage in such activities. Liberalism is only a philosophy, it is not inherently a political movement. Taking its name for yourself and asserting ownership of it commits you to responsibility for it.
There are plenty of political scientists who interpret actions purely in terms of self-interest. It’s this sort of analysis that leads to the conclusion that voting is rarely a good decision because the chances of changing the result are so minute they’re outweighed by the time and possibly expense taken up by voting. When people act in quite different ways, academics can purse their lips and complain that people are mistaken.
Liberalism cannot be based purely on self-interest. We ask people to do things for the community or for the world – and some of the most community-minded people are those whose benefit from positive changes in the community are severely limited by time – namely old people. Self-interest calculations may be useful to politicians, but they cannot predict how people will vote. Few Liberal Democrat voters in 1992-2010 voted that way for personal or family advantage and hardly any of those many new members joined for such reasons. I’ve hardly ever met a UKIP voter who’d calculated their personal advantage in UKIP policies: the UKIP vote is based on a twisted idealism.
Anderson took 6 for 47 against Australia at Edgbaston and is looking to improve.
Continual improvement is a mentality which is common in sport and in business.
We won the Eastleigh by-election with the Tories third, but they won the seat at the general election.
We need to do better.
Anderson goes on the honours board for getting 5 wickets or more in an innings.
He has the prospect of getting 10 wickets in the match. winning would give England a 2-1 lead in the series.
Results in Australia were bad.