From: king@reasoning.com (Dick King)
Newsgroups: sci.med
Subject: Re: Inoculation aggro
Date: 13 Nov 92 18:10:13 GMT
Organization: Reasoning Systems, Inc., Palo Alto, CA

In article <1992Nov13.072854.437@news.wesleyan.edu> RGINZBERG@eagle.wesleyan.edu (Ruth Ginzberg) writes:
>In <2199@snap> paj@uk.co.gec-mrc writes:
>
>> A more interesting problem is as follows:
>
> [interesting problem about maximizing one's outcome given certain
>probabilities]
>
><*heh,heh*>  This was about the best version of the game-theoretic puzzle, known
>to philosophers as the Prisoners' Dilemma, as I've ever seen!  I think I'll use
>it in for my intro ethics classes...
>
>BTW, the usual point of such examples is exactly to point out the differences
>in strategies when one takes one's desired outcome to be "maximizing OUR
>chances for survival" rather than "maximizing MY chances for survival".
>
>Interesting, huh?

This is NOT Prisoners' Dilemma .  This is Tragedy of the Commons.

Prisoners' Dilemma as it is usually phrased in textbooks is that two
accomplices have been arrested.  If exactly one of them squeals, he gets out of
jail and the other gets ten years.  If they both hang tough they plea-bargain
for one year -- the cops don't "have the tickets".  If they both squeal it's
seven years in the slammer each.  The key point is that no matter what the
other guy does, you're better off squealing than clamming up, and that the best
SUM of the two players' results come from both prisoners clamming up.  The key
fact is that each player has the option of screwing the INDIVIDUAL who screwed
him last time.

In Iterated Prisoners' Dilemma the "game" is "played" for many rounds.  The
generally recognized result is that the optimal strategy, both from the
societal and individual perspective, is "do unto the other as he has done unto
you last time [and give him the benefit of the doubt the first time - otherwise
the two of you will be needlessly shafting each other forever [and screw him
the last time no matter what has gone on before]].  Tournaments have been held
in which individuals were invited to write strategies and mail them to an
arbitrator in the form of FORTRAN programs; this strategy has always done very
well, winning against everything except a few bizzaire programs that have
little significance to ethics*.  This is a benign game-theoretic puzzle, in
that self-interest and societal interest almost coincide.

In Single-Round Prisoners' Dilemma, there is no next time, so there is no point
to being nice to any other player because they have no credible threat.  


In Tragedy of the Commons if you act in a selfish way you gain, and each of a
large number of other individuals lose less than you gain, but the sum of the
others' losses is greater than your gain.  Consider, for example, 100 rancers
sharing a pasture which can support 1000 head of cattle comfortably.
Specifically, if N head of cattle are raised, each will end up providing
max(1000, 1E9/N^2) lbs. of high-quality meat.

If every rancher is raising ten head they each get 10,000 lbs. of meat, for a
total of 1E9 lbs.  If one rancher adds an eleventh the whole pasture generates
only 998,000 lbs; there is a loss of 2,000 lbs, the one antisocial rancher gets
10978 lbs while everyone else gets 9980 lbs.  The generally recognized result
is that this is a bad situation -- it severely punishes behavior that most
would regard as social.  

Commons tend to get trashed, and the usual solution is to "privatize" the
commons [in this case, for example, by dividing the large pasture into 100
parcels or, perhaps, inventing an abstraction known as a "grazing right" if the
physical situation rules that out].  As another example, the recent moves
towards a market in pollution rights is likely to work out well, because it is
a privitization of the atmosphere's pollution sinking capacity.

If i decline to vaccinate i'm imposing a very small risk on everyone else while
incurring a medium-sized risk, and most importantly if one of my neighbors
vaccinates and the other doesn't i can't choose to half-vaccinate in such a
manner that i only expose my non-vaccinating neighbor to increased risk.  The
commons here is "herd immunity" -- by not vaccinating, if most neighbors are
vaccinated, i am adding one more infection source and the commons's ability to
absorb such infection sources has a limit.


The optimal result is to compute the number of non-vaccination right and
allocate them in a sensible manner.  A market would appeal to purists, because
the right to not vaccinate might be worth more to some people than others.  In
fact, this is close to what is done in practice -- some vaccinations are
mandatory, but you can get an exception if you can show yourself to be in a
high-risk category.


Of course, schools insist on a few vaccinations that can't be justified on the
basis of risks to others.  Tetanous comes to mind.  But the real purpose of
requiring Adam to have a polio vaccination is to protect, not Barbara who could
protect herself just as well by doing the same, but Charley who has something
wrong with him that makes polio vaccene too risky.

-dk

* where a few authors send programs such that one program recognized
  confederates by an early sequence of plays, and the confederate programs then
  act in a very benign way.