[ExI] Morality and function fitting (Was: Forking)

Anders Sandberg anders at aleph.se
Mon Jan 2 12:07:36 UTC 2012

On 2012-01-01 12:55, Stefano Vaj wrote:
> I do think that utilitarian ethical systems can be consistent, that is
> that they need not be intrinsically contradictory, but certainly most of
> them are dramatically at odd with actual ethical traditions not to
> mention everyday intuitions of most of us.

Of course, being at odds with tradition and everyday positions doesn't 
tell us much about the actual validity of a position.  Which brings up 
the interesting question of just how weird a true objective morality 
might be if it exists - and how hard it would be for us to approximate it.

Our intuitions typically pertain to a small domain of everyday 
situations, where they have been set by evolution, culture and 
individual experience. When we go outside this domain our intuitions 
often fail spectacularly (mathematics, quantum mechanics, other cultures).

A moral system typically maps situations or actions to the set {"right", 
"wrong"} or some value scale: it can be viewed as a function F(X) -> Y. 
We can imagine looking for a function F that fits the "data" of our 
normal intuitions.

(I am ignoring the issue of computability here: there might very well be 
uncomputable moral problems of various kinds. Let's for the moment 
assume that F is an oracle that always provides an answer.)

This is a function fitting problem and the usual issues discussed in 
machine learning or numerics textbooks apply: we could select F from a 
very large and flexible set, allowing it to perfectly fit all our 
intuitive data - but at the price of overfitting: it would very rapidly 
diverge from anything useful just outside our everyday domain. Even 
inside it would be making all sorts of weird contortions in between the 
cases we have given it ("So drinking tea is OK, drinking coffee is OK, 
but mixing them is as immoral as killing people?") since it would be 
fluctuating wildly in order to correctly categorize all cases. Any noise 
in our training data like a mislabeled case would be made part of this 
mess - it would require our intuitions to be exactly correct and 
inputted exactly right in order to fit morality.

We can also select F from a more restricted set, in which case the fit 
to our intuitions would not be perfect (the moral system would tell us 
that some things we normally think are OK are wrong, and vice versa) but 
it could have various "nice" properties. For example, it might not 
change wildly from case to case, avoiding the coffee-mixing problem 
above. This would correspond to using a function with few free 
parameters, like a low degree polynomial. This embodies an intuition 
many ethicists seem to have: the true moral system is not enormously 
complex. We might also want to restrict some aspects of F, like adding 
reasonable constraints like the axioms of formal ethics (prescriptivity 
("Practice what you preach"), consistency, ends-means rationality ("To 
achieve an end, do the necessary means") - in this case we get the 
universalizability axiom for free by using a deterministic F) - these 
would be constraints on the shape of F.

The problem is that F will behave strangely outside our everyday domain. 
The strangeness will partly be due to our lack of intuitions about what 
it should look like out there, but partly because it is indeed getting 
weird and extreme - it is extrapolating local intuitions towards 
infinity. Consider fitting a polynomial to the sequence 1,2,1,2,1,2 - 
unless it is constant it will go off towards positive infinity in at 
least one direction. So we might also want to prescribe limiting 
behaviors of F. But now we are prescribing things that are far outside 
our own domain of experience and our intuitions are not going to give us 
helpful information, just bias.

Attempts at extrapolating a moral system that can give answers for any 
case will hence either lead to

1. Fit with our moral intuitions but severe overfitting, complexity and 
lack of generalization to new domains.

2. Imperfect fit with our moral intuitions and strange behavior outside 
our normal domain. (the typical utilitarian case)

3. Imperfect fit with our moral intuitions and apparently reasonable 
behavior outside our normal domain, but this behavior will very likely 
be due to our current biases and hence invalid.

Not extrapolating will mean that you cannot make judgements about new 
situations (what does the bible say about file sharing?)

Of course, Zen might have a point:
'Master Kyogen said, "It is like a man up a tree who hangs from a branch 
by his mouth. His hands cannot grasp a bough, his feet cannot touch the 
tree. Another man comes under the tree and asks him the meaning of 
Bodhidharma's coming from the West. If he does not answer, he does not 
meet the questioner's need. If he answers, he will lose his life. At 
such a time, how should he answer?"'

Sometimes questions have to be un-asked. Sometimes the point of a 
question is not the answer.

My own take on this is exercise is that useful work can be done by 
looking at what constitutes reasonable restrictions on F, restrictions 
that are not tied to our moral intuitions but rather linked to physical 
constraints (F actually has to be computable in the universe, if we 
agree with Kant's dictum "ought implies can"), formal constraints (like 
the formal ethics axioms) and perhaps other kinds of desiderata - is it 
reasonable to argue that moral systems have to be infinitely 
differentiable, for example? This might not tell us enough to determine 
what kind of function F to use, but it can still rule out a lot of 
behavior outside our everyday domain. And it can help us figure out 
where our everyday intuitions have the most variance against less biased 
approaches: those are the sore spots where we need to investigate our 
moral thinking the most.

Anders Sandberg
Future of Humanity Institute
Oxford University

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