=========================================================================
Date: 24 November 1993, 17:11:22 EST
From: JBS      at YKTVMV
To:   usenet-poster at polecat.newsgate.ibm.com
Newsgroups: sci.environment
X-Post-Me: Yes
Subject: Re: Insurance rates and actuarial risks
 
         Carl J. Lydick posted:
>Please note that insurance companies are generally subject to government
>regulations which often prevent them from setting premiums on a strictly
>actuarial basis.
         Len Evens responded:
>Can you give some examples and references?   I know that there has been
>a lot of controversy in some notorious cases, such as automobile
>insurance rates in some states,  New Jersey and California, in
>particular.    However, courts, particularly those with judges
>appointed by Republicans---which means most federal judges and many
>state judges---are not very sympathetic to regulations which require
>businesses to run at a loss.   I doubt very much that insurance
>regulations often prevent insurance companies from setting premiums
>on a strictly actuarial basis, particularly for weather related
>damage.
         Lydick is correct.  Regulators require departures from strict
actuarial rates in at least two ways.
         1.  Forced subsidization of high risks by low risks either
via pooling or limitations on allowable rate differentials.
         2.  Limitations on changing the terms of existing policies
at renewal time.
         Note neither implies a requirement that insurance companies
run at a loss.  Examples of both abound.
         1.  I am unaware of any cases where insurance companies are
allowed to base rates on race, religion, ethnic background or national
origin even when significant actuarial differences exist.
         2.  Different rates based on sex are under attack and have
I believe been prohibited in many cases.
         3.  Rates based on age may not be allowed to fully reflect
actuarial differences (ie young people may underpay for auto, overpay
for medical etc.)
         4.  Rates based on geography may not be allowed to fully
reflect actuarial differences (ie rural drivers overpay, urban drivers
underpay etc.)
         5.  In many cases high risks are placed in "assigned risk"
pools and given subsidized rates with losses made up by assessing
companies based on the amount of premiums they collect (or some
similar basis).
         6.  There are often restrictions preventing companies
from refusing to renew (or only renewing under significantly
different terms) existing policies.
         Regarding Andrew, the storm disturbed insurance companies
not just because it affected their estimate of the correct rates
but also because it drastically raised their estimate of the losses
possible from a single storm.  Insurance companies do not want to
be exposed to the possibility of bankruptcy (or even loss of a large
portion of their capital) from a single event even if their rates are
high enough that their expectation is positive (this is why casinos
have bet limits).
                          James B. Shearer
=========================================================================
Date: 24 November 1993, 18:41:52 EST
From: JBS      at YKTVMV
To:   usenet-poster at polecat.newsgate.ibm.com
Newsgroups: sci.physics.fusion,sci.environment
X-Post-Me: Yes
Subject: Re: Global warming
 
         Bruce Scott posted (in response to a query as to why current
models of global warming justify large policy changes):
>Second, the reason is that preventable risk should be prevented. ...
         It is this mindset that tempts many people to dismiss the
environmental movement as antirational.  Obviously (to me anyway)
preventable risk should be prevented if and only if the costs do not
exceed the benefits.
                     James B. Shearer
=========================================================================
Date: 24 November 1993, 19:28:10 EST
From: JBS      at YKTVMV
To:   usenet-poster at polecat.newsgate.ibm.com
Newsgroups: sci.physics.fusion,sci.environment
X-Post-Me: Yes
Subject: Re: Global warming
 
         Michael Tobis posted:
>A good strategy integrates the costs and benefits of all possible outcomes
>for each strategy, weighted by best estimates of the probablity of such
>outcomes. In situations where the maximum possible loss is very large, but
>the likely loss is quite small, the maximum possible loss carries a lot of
>weight in evaluating the optimal cost strategy.
>
>Should we really be focussing on the *most likely* outcome? Are we doing so
>because so many people focus on the *best* plausible outcome and we feel a
>need to rebut them? Shouldn't cost-benefit assessments take the *worst*
>plausible outcomes into account as well?
         I believe things are not so simple as you suggest above.  I
have the following questions.
         1.  The above appears to assume that outcomes should be
arithmetically averaged.  Why is the arithmetic average to be
preferred to the geometric average?
         2.  What is the function we are maximizing?
         3.  What is the definition of a "plausible" outcome?
         4.  Is the best plausible outcome no effect?   What
probability would you assign to the following scenario?  Anthropogenic
CO2 prevents another ice age.
                          James B. Shearer
=========================================================================
Date: 24 November 1993, 21:33:04 EST
From: JBS      at YKTVMV
To:   usenet-poster at polecat.newsgate.ibm.com
Newsgroups: sci.physics.fusion,sci.environment
X-Post-Me: Yes
Subject: Re: Global warming
 
         Michael Tobis posted:
>The final concentration seems likely to be very sensitive to the level
>at which emissions stop increasing, if we assume that sudden decreases
>in emissions are unlikely.
         What is the basis for this statement?  A naive model predicts
the final concentration will be a linear function of the steady state
emission level.  Incidently why are sudden decreases unlikely?  It
would seem to me that emissions are likely to decrease at least as
fast as they rose as fossil fuel supplies are exhausted.
 
         Michael Tobis again:
>By the way, a sudden decrease of *emissions* by some 80% is NOW required
>to hold CO2 *concentrations* to current levels.
         Again what is the basis of this statement?  The naive model
suggests a 50% reduction would suffice (assuming 50% of anthropogenic
CO2 has remained in the atmosphere).
                          James B. Shearer
=========================================================================
Date: 24 November 1993, 22:00:40 EST
From: JBS      at YKTVMV
To:   usenet-poster at polecat.newsgate.ibm.com
Newsgroups: sci.physics.fusion,sci.environment
X-Post-Me: Yes
Subject: Re: Global warming
 
         Michael Tobis posted:
>The models that Dale so insistently questions are among several streams of
>evidence indicating that the time for concern in this matter is upon us.
>Policy is typically made on the basis of far less widely held opinions on
>the part of economists, a far less precise discipline than physical
>climatology. Why should climatology be held to a standard of proof so much
>higher than economists' when the indicated policy of the two disciplines
>(apparently) disagree?
         I have some problems with this.
         1.  Why do you believe that economists currently have any
significant influence on policy?  For example most economists believe
the law prohibiting the export of Alaskan oil harms the economy of the
United States for no good reason.  Nevertheless so far as I know the
law remains in effect.
         2.  On what basis do you characterize economics as a far less
precise discipline than physical climatology?
         3.  In what way is climatology being held to a higher
standard of proof than economics?
         4.  How can either economics or climatology have a indicated
policy regarding global warming in isolation from the other?
                          James B. Shearer
=========================================================================
Date: 28 November 1993, 00:18:33 EST
From: JBS      at YKTVMV
To:   usenet-poster at polecat.newsgate.ibm.com
Newsgroups: sci.environment
X-Post-Me: Yes
Subject: Re: Global warming
 
         I posted:
|>          Bruce Scott posted (in response to a query as to why current
|> models of global warming justify large policy changes):
|> >Second, the reason is that preventable risk should be prevented. ...
|>          It is this mindset that tempts many people to dismiss the
|> environmental movement as antirational.  Obviously (to me anyway)
|> preventable risk should be prevented if and only if the costs do not
|> exceed the benefits.
         Bruce Scott replied:
>Well, I agree with this last, and if you are reading anything else into
>what I said, it is according to your own prejudice. It is just that I do
>maintain that the cost of dislocation is outweighed by the risk which is
>incurred by doing nothing. Why do I have to repeat things which are obvious,
>just to satisfy reflexive, nonrational people?
         Maybe it is obvious to you, however as you should be aware
there is a large part of the environmental movement (in my opinion by
far the dominant part in the real world although perhaps not in this
group) which vigorously resists cost/benefit calculations.  This is
because they believe protecting the environment is a moral imperative
not a pragmatic choice.  If you do not wish your views to be confused
with theirs you need to add the distinguishing qualifiers.
 
         Bruce Scott (concerning moving from fossil to fission
power plants):
>BTW, it seems to me that a certain population of environmentalists is
>going to get their sincerity tested: in the long run, it is not very
>ecophilic to oppose reflexively the very thing which can rather painlessly
>remove the risks of global warming, is it?
         A devout environmentalist believes industrial civilization is
evil.  Expecting him to support nuclear power as a lesser evil is like
expecting a puritan to support distribution of condoms in schools.  In
fact like the puritan he may oppose it with particular vigor.  This is
not a question of sincerity.
                          James B. Shearer
=========================================================================
Date: 28 November 1993, 01:05:00 EST
From: JBS      at YKTVMV
To:   usenet-poster at polecat.newsgate.ibm.com
Newsgroups: sci.environment
X-Post-Me: Yes
Subject: Re: Decision theory
 
         I said (in response to a post of Michael Tobis which
attempts to reduce choosing between policy choices to a math-
ematical calculation):
>         1.  The above appears to assume that outcomes should be
>arithmetically averaged.  Why is the arithmetic average to be
>preferred to the geometric average?
         Len Evens replied:
>From the internal evidence of what you say in (1), it appears
>that you are lacking
>in knowledge about conventional decision theory.
>In that theory, one uses the so-called expected gain which is the
>sum of the probability of various outcomes multiplied by their
>costs.  Under sufficiently restricted conditions, this is a rational
>thing to consider.   Michael was trying to set up a rough model
>along these lines.   I would like see some further attempts to
>quantify this, although as I remarked in an earlier posting,
>there are some real problems with this.
         Actually I believe I do have some knowledge of decision
theory which is why I asked the question.  In investment theory
it is usual to average outcomes geometrically for reasons I find
persuasive.  This explains for example why you shouldn't place
all of your money in the investment with the greatest expected
return or why you should insure against large losses even if
your arithmetic expectation by so doing is negative.  What does
"conventional decision theory" advise as the "rational" thing to
do in these examples.
                          James B. Shearer
=========================================================================
Date: 29 November 1993, 16:57:52 EST
From: JBS      at YKTVMV
To:   usenet-poster at polecat.newsgate.ibm.com
Newsgroups: sci.environment
X-Post-Me: Yes
Subject: Varieties of doom (was Global warming)
 
         Steinn Sigurdsson posts:
>You have to be careful when considering extreme outcomes.
>A comparable issue is the question of how much effort we should
>expend on defending the Earth from asteroid and comet impacts.
>There is a 3\times 10^{-7} - 3\times 10^{-8} probability per
>year of an impact large enough to wipe out humanity. Expected
>cost is infinite. How much effort should we expend to prevent this?
         Where did these numbers come from?  I would put the probability
below 1e-10 per year myself.  Your numbers predict 15-150 such impacts
in the last 500 million years contrary to observation.
         It is also questionable whether the extinction of humanity
should be assigned an infinite cost.
                          James B. Shearer
PS:  Sorry if this appears twice (let me know if it did).
=========================================================================
Date: 29 November 1993, 19:38:06 EST
From: JBS      at YKTVMV
To:   usenet-poster at polecat.newsgate.ibm.com
Newsgroups: sci.environment
X-Post-Me: Yes
Subject: decision theory
 
Message-ID: <2dan3v$dji@news.acns.nwu.edu>
References: <19931127.222540.671@almaden.ibm.com>
NNTP-Posting-Host: schur.math.nwu.edu
 
         I said (in response to a post of Michael Tobis which
attempts to reduce choosing between policy choices to a math-
ematical calculation):
>         1.  The above appears to assume that outcomes should be
>arithmetically averaged.  Why is the arithmetic average to be
>preferred to the geometric average?
         and in response to Len Evens:
>         Actually I believe I do have some knowledge of decision
>theory which is why I asked the question.  In investment theory
>it is usual to average outcomes geometrically for reasons I find
>persuasive.  This explains for example why you shouldn't place
>all of your money in the investment with the greatest expected
>return or why you should insure against large losses even if
>your arithmetic expectation by so doing is negative.  What does
>"conventional decision theory" advise as the "rational" thing to
>do in these examples.
         Len Evens comments further:
>My background in `decision theory' is a graduate course taught
>many years ago by a leading mathematical statistician and cursory
>but ongoing discussions with my colleagues who are experts in
>this or related areas.  I think you will agree that the concept
>of expected gain (or loss) is the conventional approach.
>The usual argument for it is that if you repeat such
>decisions many times, your actual gain will be likely
>to be pretty close to your estimated gain.   Of course,
>there are some philosophical questions about how to apply
>this if you do it only once.
>
>I don't remember seeing any arguments for geometric averaging.
>Could you outline such arguments or perhaps provide an easily
>accessible reference?  I would be specially interested in
>whether there are theoretical reasons for arguing that geometric
>averaging (by which I assume you mean taking the product of
>payoffs raised to exponents which are their probabilites)
>are preferable or if they just give more reasonable looking
>results in certain cases.
>
>There are well known paradoxes about using expected gain to
>make decisions, the most well known of which is the so-called
>St. Petersburg paradox.  These typically involve situations in
>which very large payoffs (or losses) are associated with very
>low probability events.   I find the reasoning in these matters
>to be very subtle and confusing, but fortunately I have a colleague
>who is very knoweldgeable about such matters and regularly
>reexplains them to me.   It was my impression that there are
>acceptable methods using conventional concepts to resolve these
>paradoxes, but I will go back and ask him again.
>
>The most important point my colleague made to me in our most
>recent discussion was that the use of decision theory in societal
>decisions is not valid, or at least fraught with peril, bcecause
>different people or groups have different utility functions.
>Your personal utility function may place greater
>value on the ease of your commuting than on  concerns
>about climate change, while my utility function may do the opposite.
>In such a situation, ultimately the decision is made politically,
>and the best we can hope for, in a democratic society, is that
>people are knowedlgeable and have an accurate understanding of
>the facts on which they base their decisions.   Unfortunately,
>political decisions by most people are made with very short
>time scales.  People may support a candidate or candidates
>who strongly pursue a policy they disagree with because of issues
>they feel are more important just then, and they
>feel they can always switch.   Unfotunately, in some cases,
>decisions made now may have highly undesirable consequences in
>the future.   This is a paradox without easy resolution.
         Carl Lydick also commented:
>Yes, when you're dealing with compound interest, and decisions as to when to
>do something, geometric means are appropriate.  When you're dealing with
>decisions as to possible choices to make at a given time, arithmetic means are
>appropriate.  Please note that the former reduces to using arithmetic means for
>expected value.  If that's NOT what you meant, then please take the time to
>tell us what you're talking about, giving explicit examples.
         I will give an example.
         Suppose you can invest all or a portion of your wealth in
something such 50% of the time you lose your entire investment and 50%
of the time you receive back three times your investment.  For
simplicity assume your initial wealth is 1.  Let x (0<=x<=1) be the
amount you invest.  Then 50% of the time you end up with wealth 1-x
and 50% of the time you end up with wealth 1+2x.  The arithmetic
average of the outcomes is 1+.5*x which is maximized when x=1.  Thus
you maximize your arithmetic expectation by betting your entire capital.
However in the real world few people would feel this is a reasonable
stategy.  The geometric average of the outcomes is sqrt((1-x)*(1+2x).
This is maximized when x=.25.  This suggests you should bet 1/4 of your
capital which seems more reasonable.
         It can be shown that betting 1/4 of your capital is optimal
in the sense that if you face this choice a large number of times you
are almost certain to do better betting 1/4 of your capital each time
than by betting any other fraction.  However you still maximize your
arithmetic expectation by betting it all every time.
         The original poster, Michael Tobis, appeared to be measuring
outcomes in dollars.  If you introduce utility functions the question
of whether to use geometric or arithmetic averaging on outcomes is
largely moot since (assuming positive utility functions) maximizing
the geometric expectation of F is equivalent to maximizing the
arithmetic expectation of log F.  So in the above example you can
adopt a log wealth utility function and maximize the arithmetic
expectation of that if you prefer to look at things in that way.
                          James B. Shearer
================================================================================
Date: 30 November 1993, 21:55:38 EST
From: JBS      at YKTVMV
To:   usenet-poster at polecat.newsgate.ibm.com
Newsgroups: sci.environment
X-Post-Me: Yes
Subject: Varieties of doom
 
         I asked (regarding Steinn Sigurdsson figures for the
probability of an impact which wipes out humanity):
>    Where did these numbers come from?  I would put the probability
>  below 1e-10 per year myself.  Your numbers predict 15-150 such impacts
>  in the last 500 million years contrary to observation.
         Steinn Sigurdsson replied:
>The probability is substantially greater than 10^{-10}/y.
>The main uncertainty is in judging how big an impact would
>extinguish humanity at a given technology level (in the broadest
>sense of technology).
         I don't see the point of estimating this for other than
the current level of technology.
         Steinn Sigurdsson again:
> "Dinosaur" killers seem to hit about every 50 million
>years, and would certainly do the trick. We don't know the
>mass function for Earth crossers nor do we know how small an
>impact would knock us out. I will however happily concede the
>higher end and accept 10^-8 to 3\times 10^-9 /y if you prefer.
>Oh, numbers are from memory of the summary of the NASA workshop
>on impacts a few months ago.
         What makes you think we are as easy to kill as the dinosaurs
were?  As for Nasa I believe this is the organization which estimated
that the probability of a space shuttle failure at 1E-5.  This would
suggest their numbers are not always to be trusted.  Be that as it
may I would be interested in a summary of this report if someone has
it.
         It is my understanding that the fossil record indicates that
there have been no impacts in the last 500 million years (and probably
none in the last 3 billion years) which would kill off humanity if
they occurred now (or even come close).  Given this I see no reason
to change my estimate that the probability is between 0 and 1e-10.
                       James B. Shearer
=========================================================================
Date: 2 December 1993, 18:54:25 EST
From: JBS      at YKTVMV
To:   usenet-poster at polecat.newsgate.ibm.com
Newsgroups: sci.environment
X-Post-Me: Yes
Subject: Re: Is economics zero-sum
 
         Carl Lydick posted (reformatted)
>There are flaws.  In particular, there's a flaw in your understanding
>of the term "zero-sum game."  A zero-sum game is defined by the
>condition that for one player to increase his payoff requires that at
>least one other player's payoff be decreased.
         This is NOT the definition of a zero-sum game.  In a zero-
sum game the sum of the payoffs to the players is 0.
 
         Carl Lydick again:
>If that's what you're trying to do, then either use the term "zero-sum"
>properly or don't use the term.
         I suggest you follow your own advice.
                       James B. Shearer
=========================================================================
Date: 3 December 1993, 17:26:36 EST
From: JBS      at YKTVMV
To:   usenet-poster at polecat.newsgate.ibm.com
Newsgroups: sci.environment
X-Post-Me: Yes
Subject: Re: Is economics zero-sum
 
         Carl Lydick posted (reformatted)
=>There are flaws.  In particular, there's a flaw in your understanding
=>of the term "zero-sum game."  A zero-sum game is defined by the
=>condition that for one player to increase his payoff requires that at
=>least one other player's payoff be decreased.
         I replied
>         This is NOT the definition of a zero-sum game.  In a zero-
>sum game the sum of the payoffs to the players is 0.
 
         Carl Lydick again:
=>If that's what you're trying to do, then either use the term "zero-sum"
=>properly or don't use the term.
         Me again:
>         I suggest you follow your own advice.
         Carl Lydick retorts:
>Care to cite a source for your rather bizarre definition of "zero sum"?
 
         "The Compleat Strategyst", J.D. Williams, McGraw Hill, New
York, 1954, p.15
         "The above two cases illustrate a fundamental distinction
among games: It is important to know whether or not the sum of the
payoffs, counting winnings as positive and losses as negative, to all
players is zero.  If it is, the game is known as a ZERO-SUM GAME."
                          James B. Shearer
=========================================================================
Date: 3 December 1993, 18:01:14 EST
From: JBS      at YKTVMV
To:   usenet-poster at polecat.newsgate.ibm.com
Newsgroups: sci.environment
X-Post-Me: Yes
Subject: Re: environmental junk mail
 
         Stephen Best complains:
>   It's a luxury to be able to complain about something
>without having also the obligation to solve the problem.
 
         This doesn't seem to bother environmentalists when they are
complaining about others.
                          James B. Shearer
=========================================================================
Date: 7 December 1993, 16:21:33 EST
From: JBS      at YKTVMV
To:   usenet-poster at polecat.newsgate.ibm.com
Newsgroups: sci.environment
X-Post-Me: Yes
Subject: Re: Cost of environmental regulation
 
         Michael Tobis asks:
>And I still don't understand what "costing the economy as a whole" really
>means. A dollar spent here is the same dollar as a dollar spent there!
>Somebody still has the dollar! Could someone explain this to me, slowly and
>plainly, as if to a Bear of Little Brain? Thanks.
 
        Others have already replied to this, however I will try as well.
Suppose a kid throws a brick through your windshield.  Suppose it costs
you $250 to get it fixed.  (For the purposes of this example we will
ignore other costs such as the inconvenience involved.)  We may approx-
imate the cost to you as $250.  (There are a bunch of quibbles which
indicate the cost is not exactly $250 which we will disregard.)  What
however is the cost to the economy as a whole?  This can also be approx-
imated as $250.  You may object that the cost to you is offset by
the benefit to the person you paid $250 to fix your winshield.  How-
ever this is wrong for two reasons.  First the person you pay $250
does not benefit by the entire amount since in return he has to fix
your windshield.  (Another way to see this is to ask why you can't get
your windshield fixed for $200.)  Second if you had not had to repair
your windshield you would have had $250 to spend on some other good or
service so whatever benefit there is to the windshield repairer is
offset by the cost to the person supplying this other good or service.
(Again there are quibbles that this is not exactly correct).
         Now suppose we wish to approximate the cost to the economy
as a whole of windshield vandalism.  Suppose 100000 windshields are
vandalized each year and they cost an average of $250 to repair.  Then
it is reasonable to approximate the cost to the economy as a whole as
25 million dollars.
         Finally suppose the government enforces a new auto "safety"
regulation which requires the replacement of 100000 windshields per
year.  Suppose for the purposes of this example that there is no actual
safety (or any other) benefit from replacing these windshields.  Then
the effect on the economy as a whole is similar to that from windshield
vandalism and may be approximated as 25 million dollars.  (I repeat
for the purposes of this example we are only considering the cost
of installing a new windshield.)
         This is the sort of reasoning used in arriving at figures for
what regulation costs the economy.  Of course regulations may have
benefits in which case they should be estimated as well.  You may
object that such reasoning ignores many things (which I have dismissed
as quibbles) and hence is imprecise.  However such objections apply
also to the climate models which you have been defending.  In both
cases one needs to be aware that there is some uncertainty in the
results obtained however I do not believe this justifys totally
ignoring them (as has been advocated in this group).
                    James B. Shearer