In preparation for seeing
why it's irrational to agree to disagree about facts and truths, consider the
following scenario. Suppose Jack & Jill have a disagreement. Jack explains
his view, so does Jill. They both still disagree. So Jack takes another turn at
convincing Jill. Jill retorts and still disagrees. Jack now has to consider something
new. Jill has heard Jack's reasons for holding his view, and an argument
against her response, yet she still disagrees. The difference between
their initial positions and now is that they have had one round of questioning,
so each holds their initial belief, plus the extra strength of that position in
withstanding their opponent's objection.
This process goes on and
on through several rounds, with each getting more confident about their
position, because they know that the view they have has now faced the gamut of
multiple counter contentions. After several more rounds of debate, Jack and
Jill should each hold onto their view with even greater confidence.
Have you spotted something
funny about that scenario? The above scenario I described shouldn't happen at all. If both Jack
and Jill are honestly open to changing their mind, consistent with the facts, you should not see two people
stubbornly and emotively arguing their position and becoming
even more strongly wedded to defending their own position and undermining that of
their opponent as each round passes. What you should see as the rounds of analysis progress is that
one of them should become less and less confident that they are right, and the
other one should become more and more confident that they are right, with the
natural end being agreement.
Suppose both Jack and Jill
start with a conviction value of 10. Every time there is a round of analysis
where one person's view is undermined, the conviction value should increase for
one person and decrease for the other. Suppose for simplicity's sake there are
10 rounds of this kind, and suppose that the debate is whether evolution
happened, meaning Jill the evolution supporter is right, and Jack the evolution-denier
is wrong. Here's what you should see:
Start: Jack 10 - Jill 10
Round 1: Jack 9 - Jill 11Round 2: Jack 8 - Jill 12
Round 3: Jack 7 - Jill 13
Round 4: Jack 6 - Jill 14
Round 5: Jack 5 - Jill 15
Round 6: Jack 4 - Jill 16
Round 7: Jack 3 - Jill 17
Round 8: Jack 2 - Jill 18
Round 9: Jack 1 - Jill 19
Round 10: Jack 0 - Jill 20
Naturally, this rarely
happens, but if both were honest truth-seekers and fact-finders, that outcome is what we should expect.
When it comes to facts and truths, then, it is irrational to agree to disagree.
The person we have to thank for this is Nobel Prize winning mathematician
Robert Aumann.
When it comes to truths
and facts (not subjective things, obviously) Aumann's Agreement Theorem shows
that it is nigh-on impossible for two honest, rigorous and diligent
truth-seekers and fact-finders to agree to disagree (see my blog
post on it here). In addition, computer scientist Scott Aaronson's mathematical paper
showed that these two honest, rigorous and diligent truth-seekers and
fact-finders can be expected to reach an agreement in pretty quick time.
That's all very well, but this doesn't mean people
will suddenly start agreeing, does it?
No. Let's be clear, the
agreement theorem isn't saying that everyone will agree - it is showing that
people can (and should) in principle converge on an agreement as long as they honestly
wish to get to the truth. That is to say, the reason humans disagree so
much is not primarily down to lack of availability of data or methods of assimilating
that data (although it can be), it is down to factors inhibiting that person's
honest, rigorous search for the truth.
But we wouldn't want to stifle diversity and
uniqueness of thought, though right?
It depends on what kind of
diversity and uniqueness of thought you mean. Hitler was quite diverse and
unique, but it's good that his aims were stifled (albeit too late for many
people's survival). The upshot is, Aumann's theorem is a beautiful and elegant
contribution to humankind that when considered properly has the potential to be
very enriching. The diversity and uniqueness of thought that the theorem can
encourage people to help discontinue is stuff that's unhelpful to the human
race, either by being factually wrong, or immoral, or retarding progress.
Take the morality one as
the most obvious example. Is diversity and uniqueness good in moral situations?
Sometimes yes, but often no. Applying Bayesian thinking to issues of ethics,
you'd find that if you gathered in a hall the most diverse people in terms of
their ethics there would be a lot of views you'd find pretty repugnant.
Diversity in one sense is great, but alas not always in all senses. Under the
terms of being factually wrong, or immoral, or retarding progress, the human
race prospers far more when diverse elements - that is, the elements that are
factually wrong, immoral or an impediment to press - are weeded out. That's not
to deny, of course, that there are numerous ways that diversity of thinking,
culture, imagination, creativity, passions, tastes, experiences and talents
enrich the world.
Oh I see, a lot of it is about pre-empting thin end of
the wedges?
It's
important. There is a lot of deception, manipulation and propaganda out there,
which evidently engenders a reservoir of lazy thinking in society, which has
the knock on effect of causing lots of unnecessary disagreement, disharmony,
resentment and, when left to fester, extremist conflict that can lead to
horribly brutality. The Agreement Theorem encourages us to try to cut it out at
source.
Is there a danger, though, that this realisation will
make us want to be right all the time?
I actually find it
incredible how often people are so unenthusiastic about getting things right. I
think we are so blessed to have the faculty of language, the multiplicity of
words, and the most advanced cognition we know about in the universe (of all the
created things, I mean). Besides, just about everyone wants to think they're
right - they just differ on the particulars.
For example, meet Jeremy:
he works in the lab to improve our understanding of cancer in order to help
ameliorate its pernicious effects on people; he believes in driving on the
correct side of the road consistent with the highway laws; his view is that people
should be faithful to their partner; he is passionate about ending animal
cruelty, and he thinks people should be respectful of their neighbourhood and
not drop litter anywhere except in a bin.
Upon hearing those things,
you don't immediately think it's such a shame that Jeremy thinks he's right
about those things, and regrettable that he would like it if more people thought like he
did. Presumably most people reading this have no problems with those examples
of claiming to be right: it is very important to do all we can to diminish the
effects of cancer, and end animal cruelty. Infidelity is hugely damaging;
litter makes the streets look messy; and there would be catastrophe if people
decided to drive on whichever side of the road they fancied.
The point is, it's easy to
support unanimous concurrence on things like cancer treatment and keeping our
streets tidy, but it's also fairly easy to support unanimous concurrence when
it comes to all matters of fact and truth. Yet one meets people who are less
comfortable with this: they do not like it when social commentators express
views they think are correct and when they lament because more people don't
agree with them. But like cancer treatment and keeping our streets tidy, facts
and truths are enriching to human progress - in fact, it's only because of
facts and truths that we even know that cancer treatment and keeping our
streets tidy are preferable to the alternatives.
So to any charge us social
commentators face that "You want everyone to agree with you all the
time" - well yes, of course we do, because we value fact-finding and truth-seeking
as being hugely beneficial to the human race, so why would we want it any other
way? But more to the point - be under no illusion - you are the same as us -
you believe that the things you think are objectively true and morally right
are things others should believe too - it's just that you think the facts and
truths we propound belong in a different category to the ones you propound. In all sorts of ways you value the unanimity of
concurrence as much as we do - it's just that we think there are a
lot more things about which we should agree if people can only train
themselves to override their cognitive biases and emotional skews.
* Note: The issue of what qualifies as a fact and as truth is not unimportant, but we'll save that for another day, as the essential drift remains, and at no cost to the principles this blog post is endorsing.
When dealing with questions about whether something can justifiably be called a fact, or when tackling a complex area of consideration that may or may not have a justifiable consensus, the agreement theorem still does its work, because the process by which we should agree on facts or truths is the same process by which we should agree on the above issues I just mentioned.
For example (as one person mentioned economics), economics does deal with a very dynamic set of data points, but there are plenty of routes by which two people can arrive at an agreement, even if that agreement involves concurrence on degrees of intractability and open-endedness. Here are a few examples. The law of diminishing marginal utility will indicate that when it comes to consumption of a banana, the first unit of consumption (the first banana you eat) yields more utility (is more beneficial and enjoyable) than the tenth banana. It's quite reasonable to agree that by the ninth banana one might be quite sick of them. Extrapolating from the law of diminishing marginal utility, it would be easy to agree that paying a second cleaner to clean your apartment an hour after the first cleaner has cleaned it is a poor use of resources.
Last example, when there is elasticity in the final product demand, wages will likely increase, which consequently knocks on to affect the quantity and level of the demand. Again, two politicians may argue about this all day, whereas two unbiased economists would have no trouble understanding that this is because under those conditions the wage elasticity of demand for that category of labour will be high.
* Note: The issue of what qualifies as a fact and as truth is not unimportant, but we'll save that for another day, as the essential drift remains, and at no cost to the principles this blog post is endorsing.
EDIT TO ADD: As a response to the
response, it's worth pointing out that some of the issues mentioned, such as
what constitutes truth, what qualifies as a fact, what can reasonably be
posited as consensual, and how to deal with complex analyses and intractable
considerations, are all able to be dealt with by Aumann's theorem.
When dealing with questions about whether something can justifiably be called a fact, or when tackling a complex area of consideration that may or may not have a justifiable consensus, the agreement theorem still does its work, because the process by which we should agree on facts or truths is the same process by which we should agree on the above issues I just mentioned.
For example (as one person mentioned economics), economics does deal with a very dynamic set of data points, but there are plenty of routes by which two people can arrive at an agreement, even if that agreement involves concurrence on degrees of intractability and open-endedness. Here are a few examples. The law of diminishing marginal utility will indicate that when it comes to consumption of a banana, the first unit of consumption (the first banana you eat) yields more utility (is more beneficial and enjoyable) than the tenth banana. It's quite reasonable to agree that by the ninth banana one might be quite sick of them. Extrapolating from the law of diminishing marginal utility, it would be easy to agree that paying a second cleaner to clean your apartment an hour after the first cleaner has cleaned it is a poor use of resources.
Another
example, the Laffer curve measures the relationship between how much a
government taxes us and the resultant government income. Two people who
disagree on the optimum level of taxation for the fifth quintile could easily
come much closer to agreement if they both carefully analysed the evidence.
Another example, we expect increasing returns to have a positive effect on
productivity when there is increased growth in output. Two opposing politicians
could argue all day about the best way to achieve this, whereas two economists
(without a political agenda) would likely agree quite quickly.
Last example, when there is elasticity in the final product demand, wages will likely increase, which consequently knocks on to affect the quantity and level of the demand. Again, two politicians may argue about this all day, whereas two unbiased economists would have no trouble understanding that this is because under those conditions the wage elasticity of demand for that category of labour will be high.
The
upshot is, whatever the area, be it economics, science, faith, psychology,
politics or philosophy, Aumann's Agreement Theorem doesn't just bring to bear
the routes by which we can agree on facts and truths, it also factors in all of
the anomalies (complexity, intractability, human failings, different levels of
intelligence, asymmetry of information, etc) that need to be redressed or
overridden. So irrespective of anything that can militate against agreement,
Aumann's model gives exhibition to the pathways by which people 'can' agree as
long as the enquiry is honest and rigorous.
