Rawls, uncertainty, etc.

[Clay Shentrup]

I'd really like Warren's feedback on this one.

I have a very intelligent coworkers who's not a utilitarian, and has a philosophy degree, and can go to mind-shattering lengths to provide approximately sensible-seeming (at least, very intellectual) rebuttals to utilitarian arguments.

He talked about a Rawlsian notion of the "veil of ignorance", which is basically Harsanyi's point about wanting to be a utilitarian if you're uncertain of your identity. But he suggests the Rawlsian interpretation that this leads to a maximin position, rather than maximum-expected-utility position.

I countered that this doesn't work, because e.g. people drive their children around, thereby increasing their chance of death in expectation of benefits like "being able to go to the store to get groceries without having to pay for a babysitter." (Also, you don't see parents with their hands above their kids' heads, trying to protect them from falling meteors.)

He counters that this only works with known probabilities. E.g. we know that dying on a plane is very unlikely. But he says that in the face of uncertainty about the mere probabilities themselves, we want maximin.

E.g. a box has either a grenade in it, that explodes when you open it, or it has some money in it. You don't know how likely either option is. In this circumstance, I said you are still a utilitarian, and you just treat the probabilities as being equal. Because, in the absence of any evidence to the contrary, those events are equally likely from your point of view. He says there's no "point of view" in probability. E.g. a fair die has a 1/6 chance of landing on 1. I countered that this is only because you lack information about the rotation and velocity with which it's thrown. If you asked how likely that fair die is to land one 1 given information on its position, speed, distance from the ground, etc., then I could say something more like "95%". Probability is fundamentally about how much information you have.

In any case, I contend you do have to treat unknown probabilities in the manner I described. You can't just say, "I refuse to open the box, no matter how much money is in it, because I have no idea how likely it is that the grenade will kill me." Maybe the grenade event has a really high negative utility. But in that case, you still do the calculation based on equal likelihood.

This seems obviously correct for the same reason that we treat all possible "apriori" probabilities as equally likely when doing confidence intervals.

My assumption is that Warren probably has an elegant thought experiment which would lead to a contradiction in my friend's views. At the very least, I hope he or Andy or some other math expert can speak to the "how to treat unknown probabilities" question.

Thanks.

[Warren D Smith]

I do not understand the question.

--
Warren D. Smith
http://RangeVoting.org <-- add your endorsement (by clicking
"endorse" as 1st step)

[Clay Shentrup]

On Monday, May 6, 2013 1:44:49 PM UTC-7, Warren D. Smith (CRV cofounder, http://RangeVoting.org) wrote:

I do not understand the question.

Well, there are basically two aspects.

1) He argues that you can only be utilitarian about risks you're aware of. E.g. a 1 in 10,000 chance of dying in a plane crash. As for risks of unknown probability, he cites Rawls's argument for maximin. E.g. given two sets of options, you want the set with the maximum minimum. I argue that you still have to be a utilitarian; it's just that your estimates of probability are going to be very inaccurate. But all you can do is make the best guess based on the information you have. The answer is not to necessarily pick the set with the maximum minimum utility.

2) Part of his justification for this is the notion that you can't treat unknowns as being equally likely. E.g. say you can either be in universe X or universe Y. In X, everyone either has utility of 5 or 6, whereas in Y everyone either has utility 4 or 1000. I contend your expected utilities here are 5.5 and 502, respectively. Because, given no evidence about the probabilities of these options in either universe, your expectation is for them to each be equally likely. He counters that you can't just treat probabilities as being equal just because you're ignorant about them. That seems, to me, to run completely counter to the foundation of probability.

[Dale Sheldon-Hess]

If your REALLY have no idea of the odds, you can reason to almost any
answer you want. If the method for picking your random variable isn't
well defined, the resulting probabilities aren't necessarily going to
be either.

http://en.wikipedia.org/wiki/Bertrand%27s_paradox_%28probability%29

--
Dale

[Warren D Smith]

On 5/6/13, Clay Shentrup <cl...@electology.org> wrote:
> On Monday, May 6, 2013 1:44:49 PM UTC-7, Warren D. Smith (CRV cofounder,
> http://RangeVoting.org) wrote:
>
>> I do not understand the question.
>>
>
> Well, there are basically two aspects.
>
> 1) He argues that you can only be utilitarian about risks you're aware of.
> E.g. a 1 in 10,000 chance of dying in a plane crash. As for risks of
> unknown probability, he cites Rawls's argument for maximin. E.g. given two
> sets of options, you want the set with the maximum minimum. I argue that
> you still have to be a utilitarian; it's just that your estimates of
> probability are going to be very inaccurate. But all you can do is make the

> best guess based on the information you have. The answer is *not* to

> necessarily pick the set with the maximum minimum utility.

--well, seems like every choice you can make has the SAME
min-possible-utility outcome, namely something like "somebody kidnaps
you, tortures you to death"
which clearly occurs with nonzero probability no matter what you do, eh?
So the "maximin" operation does not discriminate between options at all.

> 2) Part of his justification for this is the notion that you can't treat
> unknowns as being equally likely. E.g. say you can either be in universe X
> or universe Y. In X, everyone either has utility of 5 or 6, whereas in Y
> everyone either has utility 4 or 1000. I contend your expected utilities
> here are 5.5 and 502, respectively. Because, given no evidence about the
> probabilities of these options in either universe, your expectation is for
> them to each be equally likely. He counters that you can't just treat
> probabilities as being equal just because you're ignorant about them. That
> seems, to me, to run completely counter to the foundation of probability.

-- seems like
http://www.rangevoting.org/OmoUtil.html
is a decent argument, and your pal is going to be out-evolved. Just
wait another 100 million years.

[Abd ul-Rahman Lomax]

At 02:58 PM 5/6/2013, Clay Shentrup wrote:
>I'd really like Warren's feedback on this one.
>
>I have a very intelligent coworkers who's not a utilitarian, and has
>a philosophy degree, and can go to mind-shattering lengths to
>provide approximately sensible-seeming (at least, very intellectual)
>rebuttals to utilitarian arguments.

The argument seems to be premised on an idea that there is a "true"
way of looking at things, and then a "false" way. You can fall into
that, Clay. You will move further, and more rapidly, if you can drop
this concept.

There are *models*, and models are of greater or lesser utility. Ah,
utility! It means that models have a *function*, and that they may
enhance life or they may inhibit, and they may do this with greater
or lesser effectiveness.

>He talked about a Rawlsian notion of the "veil of ignorance", which
>is basically Harsanyi's point about wanting to be a utilitarian if
>you're uncertain of your identity. But he suggests the Rawlsian
>interpretation that this leads to a maximin position, rather than
>maximum-expected-utility position.

What's being considered? How people *actually* make decisions? Or how
people *should* make decisions? And, then, "should" implies some
standard. Without an agreed-upon standard, arguments can rage forever
without any resolution except each side, enamored of its own
arguments, and rejecting the arguments of the "other side," becomes
more and more convinced that it is "right."

>I countered that this doesn't work, because e.g. people drive their
>children around, thereby increasing their chance of death in
>expectation of benefits like "being able to go to the store to get
>groceries without having to pay for a babysitter." (Also, you don't
>see parents with their hands above their kids' heads, trying to
>protect them from falling meteors.)

Here, you are arguing from actual practice. We can assume that actual
practice is functional, or those practicing it would, over time, be
selected out of the population. However, it's also well-known -- or
at least commonly thought -- that there are what might be called
"errors" in actual practice. Gambler's fallacy, for example.
Gambler's fallacy is based on a behavior that functions well in the
natural world, but fails in situations where an outcome is carefully
controlled to be random. We are evolved to deal with the natural
world, and "games of chance" are an invention that sets up something
that is artifically outside that world.

>He counters that this only works with known probabilities. E.g. we
>know that dying on a plane is very unlikely. But he says that in the
>face of uncertainty about the mere probabilities themselves, we want maximin.
>
>E.g. a box has either a grenade in it, that explodes when you open
>it, or it has some money in it. You don't know how likely either option is.

You have set up a situation that is highly artificial. I *actually*
have a box here in my office. Many, actually. Among an effectively
infinite number of probabilities, it has a grenade in it, rigged to
explode when I open the box, or it has a bundle of cash.

Actually approaching the box, one possibility doesn't even occur to
me, indicating very low probability, on average. The other would be
unusual, but is a realistic possibility, and, in fact, I actually do
find money in boxes occasionally. Usually not much. Once, an uncashed
check from an insurance company for $780, from years before. (And
then I was able to obtain that money.)

Clay, you are arguing about an extremely abstract and not
well-specified situation, and are you arguing about how people
*actually* would make decisions in a situation like that (which may
be a meaningless question), or about how we *should* make decisions,
and what are the standards by which to judge that.

It seems that you are arguing for one norm, you call utility theory,
and he is arguing for a different one, maximin. I have no confidence
that I understand this. In my training, I'd look at the underlying
and unstated goals of each participant. The most common one in
intractable arguments is a desire to be right or to avoid being
wrong, next comes a desire to avoid domination. These are survival
programs, and when survival programs are running, the intellectual
centers are subservient to them. Our intelligence is turned to the
task of making up arguments as to why we are right, for example.

> In this circumstance, I said you are still a utilitarian, and you
> just treat the probabilities as being equal.

People don't like being told what they are, Clay. They prefer to
declare that themselves.

> Because, in the absence of any evidence to the contrary, those
> events are equally likely from your point of view.

You made that up. In fact, most of what is being discussed is made
up, whether individually by you and your friend, or by others, and
accepted by you or your friend.

Do we have a "point of view" without *any evidence*? I'd say that's
an oxymoron. Now, "evidence" doesn't necessarily mean logical or
rational evidence, and it can be simply, for example, a different
point of view that we take as applying. I.e., perhaps your friend is
a Republican, and we have a point of view that Republicans are wrong,
and therefore we have a "prior" that he's wrong. And then we find
reasons to support that idea. This *is* how we actually think, until
and unless we distinguish it and begin to operate in a different realm.

> He says there's no "point of view" in probability.

I suspect he's pointing out that "probability" in scientific usage is
based on experience and specific definitions. Another writer here
pointed to Bertrand's paradox, which I don't see as a paradox at all.
It depends on an unspecified meaning to "random."

However, we *estimate* probabilities, but when there is no evidence,
we *ignore* them. You can claim that this is based on a utilitarian
estimate that a probability that we will ignore is likely small, or
very small, but that is intellectualization. We behave just like all
other animals in this respect. We ignore what we have no experience
with or instinct about.

I've seen that people who try to rationalize this process, to make it
more "logical," can drive themselves nuts. A common application is to
imagine a *terrible* outcome, and effectively to assign it an
infinite negative utility. If the utility is infinite, and even if
the probability is very small, the expected utility is also
negatively infinite, and *therefore our whole life should be devoted
to averting that outcome.*

You can't reason your way out of a paper box, but you can reason your
way into one.

That infinite negative utility was made up. There is no absolute
definition of utility, we *choose* to assign value to outcomes.

Utility analysis wrt voting systems was originally rejected because
utilities were generally arbitrary and incommensurable, or thought to be so.

However, what that rejection missed was that we'd expect a good
voting system to function well when studied as voted by people with
utilities that are defined to be commensurable. It's an abstraction,
but it is also possible to test it in limited real-world
circumstances where utilities are naturally defined. And this is what
Warren did.

If we go on and try to justify "rational utilitarianism," the
Dhillon-Mertens term for range voting, as somehow being "true," we
will get stuck in a morass of philosophical arguments that miss the point.

> E.g. a fair die has a 1/6 chance of landing on 1. I countered that
> this is only because you lack information about the rotation and
> velocity with which it's thrown.

That's a 19th century concept, and particularly before chaotic
systems were better understood.

Yes, if you have information about position and velocity, you can
make a different prediction, *maybe.* Maybe not. It may also depend
on when you obtained that information and how much opportunity there
is for unknown forces to act on the die.

Probability depends on sample space. We say that a die and the
throwing process is "fair" if experience shows that the ratio of one
side coming up to all tosses *approaches* 1:6 as the number of tosses
increases.

So I'd guess that your stand is that your "point of view" determines
the probability. That's a rather idiosyncratic definition of "point
of view." Rather, our *experience* -- which includes all such things
as knowledge of position and velocity, and knowledge of the laws of
physics -- is the basis on which we calculate probabilities, and if
we are accurate about probabilities, we also know that they are
approximate, because our experience is only a limited set of
experiences and so the measured ratio will have a deviation from some value.

But in reality, we normally don't have much information. This isn't a
"point of view," it's just a condition which might create a point of
view. If I have a point of view -- a judgment or conclusion -- that
the die is fair and the tossing is fair -- then, yes, I predict 1/6.
If I have a point of view that someone is trying to trick me, I might
conclude quite differently.

It would seem, though, that your friend may have a view of reality
that there is something called "probability" that is an *absolute.*
That's part of a whole world-view that has been invented -- or that
grew like Topsy.

Is it true? No, I'll say, which is not to claim that it's wrong.
World-views are not "truth." They are models. They are either useful or not.

> If you asked how likely that fair die is to land one 1 given
> information on its position, speed, distance from the ground, etc.,
> then I could say something more like "95%". Probability is
> fundamentally about how much information you have.

You *think* you could say this. You made it up. You don't have that
experience, and you have no evidence for it other than certain
*expectations.* I.e., you think "it could be done." Right? Do you
have any idea of how difficult that would be under normal die-toss
conditions? Remember, the prediction is being made *before* the die
is tossed, not after it's, say, almost ready to stop rolling!

By not specifying any of this, an argument can be maintained
indefinitely with no resolution.

>In any case, I contend you do have to treat unknown probabilities in
>the manner I described.

Or they will shoot you.

What, really? "Have to" implies some coercion, or, more colloquially,
as I think you are saying this, it implies that if you don't do this,
you will suffer some Bad Consequence.

But we, as humans, have no difficulty at all dealing with truly
unknown probabilities. We ignore them.

Yes, it is possible that the unknown probability will eat us. But we
don't walk around in fear of being eaten by unknown probabilities,
and if we did, our *fear* would be eating us. Essentially, if we want
to rationalize this, we set those probabilities at *zero*. I do *not*
run outside, holding out my arms, to catch the bundle of cash someone
may have tossed from an airplane, or spend my days watching for the
possibility.

I confine my choices to possibilities where I have some *cause* to
consider them. As we developed the capacity to imagine things we have
never experienced, which is very human, we also had to develop
defense mechanisms against being hijacked by our own imaginations. In
some people these mechanisms break down, and we generally consider
these people insane. But normal thinking can allow the consideration,
abstractly, of possibilities with unknown probability, and then
normal actual process *rejects* most of them as preposterously unlikely.

> You can't just say, "I refuse to open the box, no matter how much
> money is in it, because I have no idea how likely it is that the
> grenade will kill me."

We properly consider such a person as crazy *unless they have
evidence that there is *actually* a grenade in the box.*

>Maybe the grenade event has a really high negative utility.

Yeah, but it would typically only be one human life, unless we are in
a crowd or others are close. That may run about to the limit of
personal negative utility. I can imagine higher negative utility, say
the end of all life on the planet.

And we *actually* risk these things. If we want to hold to
utilitarianism as "actually" being used, we obviously do not assign
infinite value to these outcomes, or we must assign zero probability.

For example, what is the probability of major damage to human life
and other life from global warming? Does anyone see it as *zero*?

(Some may well do this, but, then, *they must have a very reliable
model of climate.* Or an unshakeable faith in the ability of human
beings to deal with whatever.)

>But in that case, you still do the calculation based on equal likelihood.

*Who* does? Clay, I recommend becoming, practicing being, very
precise, if you are going to engage in arguments over this.

>This seems obviously correct for the same reason that we treat all
>possible "apriori" probabilities as equally likely when doing
>confidence intervals.

If it's obvious to you, why not to him? What is obvious to you, Clay,
will come from your personal history, including your history of
thinking on the topic. It fits together *for you*. But there may be
-- indeed almost certainly are -- large chunks of possibility that
are missing from your own experience, so they don't pop up for you.

Your friend has a philosphy degree. If it's an advanced degree, he's
established as an *expert* on what he's talking about. Let me
recommend that you never assume an expert is caught in some stupid argument.

It's quite true that experts sometimes have blind spots, and it's
actually possible you may detect one. However, in attempting to point
it out to him, if that's not done with high skill, you will trip over
many, many ignorances of your own, and he'll see this. You absolutely
cannot argue with an expert as if you know and he doesn't. A method
that may work is the Socratic method, practiced sincerely. Seek to
learn from him. Acknowledge his experise *and respect it*.

That doesn't mean believing that he is "right." Rather, what you have
to learn from him is why people like him might reject utilitarianism.
The better you understand this, and in the case that you actually do
know something he doesn't, the more skillful you will become at
transforming thinking on the topic.

If you start with an assumption that he *must be wrong* because
*utilitarianism* is "right," you'll get absolutely nowhere, you will
learn nothing, and you'll end up convincing your friend that you are
hopelessly ignorant.

>My assumption is that Warren probably has an elegant thought
>experiment which would lead to a contradiction in my friend's views.
>At the very least, I hope he or Andy or some other math expert can
>speak to the "how to treat unknown probabilities" question.

I'm just noticing your premise here, that the fellow is wrong.

It's true that Warren is an expert, but not actually on this topic.
He's a mathematician, not an expert philosopher, and you were really
dealing with philosophical issues.

On the other, hand, asking others for comment can be highly useful.
You may learn something.

I'm not getting any clue that your philospher friend is well-grounded
ontologically, but I do realize that I'm learning about him through
you, and you might not recognize such grounding, focusing instead on
where you disagree with him.

I don't know if you have noticed this yet: agreement is far more
powerful than disagreement. If you really want to reach someone with
an idea, agree with them to the maximum extent possible, then extend
the agreement into new areas.