Now I think that paul was right. How is it that when Paul writes on one thing what he says is true of lots of things ? Does God talk to Paul. If so, Paul sure talks back.
My old thought was if Blaise was wrong then when you lose you can not lose real big. Does this mean that the one strange rule guys were right ? No. If Blaise was wrong then when you win with one strange rule you do not care, so when you win you win real small. Thus while when you lose, you don't lose real big the one strange rule is close to right for you aim is close to log wealth. This is just what Paul said.
To show this you need to have that the risk is just the same sort of risk each time.
OK so what is that in bigger words ? Paul is Paul Samuelson, who once argued that it is not necessarily a good idea to buy the portfolio with the highest geometric mean return even if you have a very long time horizon. He chose to argue this in a paper which contained no words of more than one syllable (except for the last word which was syllable). He called geometric mean portfolio approach proposed by Latane and (independently) Haakonsen "one strange rule". Their argument was that, by the law of large numbers, one would almost surely have higher end of period wealth if, each period, one maximized geometric mean return than if one always bought a different portfolio. this is true, but, as Samuelson pointed out, "if you lose you could lose real big".
In an earlier post, I wondered if the right (possibly changing) portfolio would have to be close to geometric mean maximizing almost all of the time if the utility function were bounded above and below. This means that, although you can lose real big in Euros or dollars, you can't lose real big in utils. With one syllable words "if the utility function is bounded above and below becomes "if Blaise [Pascal] was wrong".
Recently I thought again. The formal problem is time is discrete, each period there are risky assets with iid returns. The player aims to maximize a concave function of time T wealth which is bounded above and below. Does the geometric mean argument make sense in this case ? That is, is the time varying optimal portfollio chosen in t close to geometric mean maximizing for almost all t ? In the old post, I concluded that either it was or the derivative of the utility function with respect to wealth at T was almost certainly very close to zero.
So assume that the utility function is bounded below (wlog by zero) and above by Umax
To make the question simple, assume that one must distribute wealth across assets the same way each period so an iid random variable is added to log wealth each period. Is the right portfollio geometric mean maximizing ? Well , for any other portfollio P, by the law of large numbers as T goes to infinity, the chance that the geometric mean maximizing portfolio will give higher end of period wealth than P goes to 1. Chose T so this chance is 1-epsilon/umax for some small epsilon. If the utility function is bounded above and below, what happens in the other cases can give P utility minus expected geometric mean maximizing utility of no more than epsilon.
with probability 1-epsilon/umax the geometric mean maximizing approach gives higher wealth. This means that, on average, this can matter only
epsilon/(1-epsilon/umax) utils. does this mean that the optimal portfollio P must be very close to geometric mean maximizing ?
Already in the old post, I realised that if the marginal utility of wealth was very low, then the difference in wealth might be very large but matter very little.
Now I realise that bounded utility, iid returns and constant portfolios,means that the marginal utility of Log wealth is almost certainly tiny that is (Wealth)(dU/dWealth)must be tiny. For utility to be monotonic in wealth and bounded above and below (Wealth)(dU/dWealth) must go to zero as Wealth goes to zero and infinity.
With iid returns (with finite variance) (log Wealth - log initial wealth)/root(T) will have a normal distribution so |log(Wealth)| will almost certainly go to infinity so (Wealth)(dU/dWealth) will almost certainly go to zero. This means that there is no implication for optimal P must be close to geometric mean maximizing.
The assumption that "if you lose you can lose real big" is sufficient but not necessary for Samuelson's conclusion. posted by Robert
permalink and comments7:55 PM
Tuesday, December 16, 2003
There were no 0 zero proposed answers to the Monty Redux problem.
I give my answer below. New bits are in ** old bits are in "".
Recall, the Monty Hall paradox from “Let’s Make a Deal” an old game show. The last step in the game show was guess which of 3 boxes contains a big prize. There are three large boxes, box 1, box 2 and box 3, one contains a very valuable prize, the other two contain prizes of small value. The contestant guessed a box. The assistant (Carol Marol or was she on truth and consequences) opened one of the other two boxes showing that it didn’t contain the big prize. Monte Hall offered the contestant the chance to switch to pick the remaining unopened unselected box.
Now all contestants must have noticed the pattern that the assistant always opened one of the boxes which had not been chosen and that box always contained a small prize. "
*This, I think is the, often unstated, assumption that makes the problem such a dread dinner party troll. If there is no information that a box with a small prize is always opened, there is no way to solve the problem. It might be that a box is opened only if the contestant guessed right the first time (so better to not switch and win for sure ) or only if the contestant guessed wrong the first time (so better to switch and win for sure) or anything in between. It was clear on the show that a box was always always opened.*
"I am going to add another assumption to make the assistant follow a well defined rule. I assume that the assistant opens the box which 1) has not been chosen by the contestant 2) does not contain the big prize and 3) has the lowest number of boxes satisfying 1 and 2.
Now consider a case of the game. Contestant guesses box 2. The assistant opens box 1 showing that it contains a small prize ? The contestant is allowed to switch and guess that the prize is in box 3. Should the contestant switch ? Does it make any difference for the probability of winning ?"
*In this the chance of winning is the same (1/2) whether the contestant switches or not. Given rule 3 stated above, box 1 is opened whether the big prize is in 2 or in 3 so no information is revealed.*
"How about another case of the game. Contestant guesses box 2. The assistant opens box 3 showing that it contains a small prize ? The contestant is allowed to switch and guess that the prize is in box 1. Should the contestant switch ? Does it make any difference for the probability of winning ? "
*here given rule 3, opening box 3 means the big prize must be in box one so the contestant should switch. The point (if any) of the new puzzle is that it the other case which shows that it can sometimes be costless to switch (a knife edge result).*
Finally someone commented on this blog by writing to firstname.lastname@example.org.
OK OK so it was my mom commenting on "right plan wrong pills". My mom
Katharine Waldmann MD used to take care of people with HIV as her job. Now that she has retired she does it as a volunteer. She explains to me that the WHO proposes 3 drugs not including protease inhibitors for medical reasons not because they respect patent law (which they appear willing to ignore)
Katharine Waldmann writes
"I was told by a drug rep from the company that makes Viramune that the talk of a three drug pill(zerit, Epivir (lamivudine) and viramune) is based on the plan to buy from India where this is made--patent violation of course.
Protease inhibitors are very potent but besides expense they have problematic side effects--diabetes, lipodystrophy, high blood lipids. They are big capsules to take (not hydrophilic so large doses needed to get enough absorbed)and usually need to take many a day: Viracept ten a day (just started making tabs where one neede to take only two twice a day), Fortovase six or eight twice a day.
What helps is that ritonavir (Norvir) interferes with the metablism of most of the others, so 100 mg of ritonavir makes it possible to reduce the number of other capsules and has enabled shifting from three times a day dosing and meal restrictions. Kaletra is a capsule with ritonavir plus lopinavir in one capsule.
There has been a big push to avoid protease inhibitors as first line treatment. Trizivir has three NRT's but usually a fourth has to be added. Efavirenz (Sustiva) is very effective and a once a day program is possible--Sustiva 600 mg, Epivir 300 mg, and Viread 300 mg.
Capsules don't keep well in heat and humidity. So I don't think it is only or even mainly the cost of PI's, but some of these other issues.
Another locally realistic violation of Bell’s inequality ?
I am thinking about the EPR experiment. I am actually thinking about the experiment as proposed by E P and R, not the experiment as performed. There are four basic but very weird points to remember in order to understand the proposed experiment. One is that electrons spin around sort of like little globes but that the absolute value of the angular momentum is always hbar/2 no matter from which direction you look at them. This is not like, say, the earth which spins around the North-South axis so the angular momentum is less if you look down another axis. The second strange fact is that you can’t measure the angular momentum of one single electron around two different axis (one version of the Heisenberg principal). This can be understood as measuring around one axis changes the spin around another axis. This makes sense in terms of comprehensible things like macroscopic magnets because the way to measure spin is with a magnet and a magnet does change spin. The third strange fact is that sometimes you know that the spin of two electrons around any axis is opposite. This is true if the two electrons are in what is called a singlet state. This means that even if you can’t know which way (clockwise or counterclockwise) each electron is spinning around both the North South axis and the East West axis you can know that the two are spinning in opposite directions around each axis. The fourth strange fact is that, according to quantum mechanics the correlation between “spin is clockwise around the North South axis” and “Spin is clockwise around the North-East South-West axis” is greater than one !!! that is the probability both are clockwise is greater than the probability that the spin around the North South axis is clockwise and the spin around the other axis is whatever and unmeasured. I won’t be able to explain this so that it makes sense. It is clearly crazy. It is also an experimental result not just a theory. I am sure I will never understand this, so I can’t explain it. Trying to grasp this fact, and it appears to be a fact (see below) is like trying to pound a square peg into a round hole.
Now the point of EPR is that Heisenberg shmeizenberg you can use the singlet state fact to test the quantum mechanical correlation greater than one by measuring the spin around N-S of one of the electrons and the Spin NE-SW of the other. They were very sure that the experimental result would disprove quantum mechanics. After some decades the experiment was finally performed (with light not electrons) and quantum mechanics was confirmed. I gave up.
Then I heard about the work of Luigi Accardi and Massimo Regoli. They have an argument that you can reconcile the experimental result with a locally realistic theory (one that makes sense as correlations are less than or equal to one) if the singlet state is a statement about measuring spin around one magic axis (NS say). The quantum craziness comes from treating electron 2 is counterclockwise around NS as equivalent to electron 1 is clockwise around NS AND electron 2 is counterclockwise around NE-SW as equivalent to electron 1 is clockwise around NE-SW. What if the singlet state had to do only with the N-S axis ?
An objection is that the singlet state fact has been tested for many directions and always works.
I have a slightly modified version of the Accardi Regoli story (which is probably in one of their working papers which I haven’t read). Here the experiment is we have electrons that were in the signlet state flying out of a source each one through an electromagnet which can be oriented NS or NE-SW. If both electromagnets are oriented the same way, the spins are opposite. If the experimenter moves the electromagnets so they are not oriented the same way, the electrons see this and don’t act like singlet state electrons at all anymore. This means that the EPR experiment result is not equivalent to a correlation greater than one.
OK so the little electrons are spying on the experimenter. There are two things. Which way does he point the electromagnets and are both turned on (measuring) or not. If they are oriented on the same axis then the measurement of electrons going through magnet 1 does not depend on whether magnet two is turned on and the measurement of electrons going through magnet 2 is always opposite. If they are oriented in different directions, then the measurement of electrons going through magnet 1 depends on whether magnet two is turned on. This is an effect of an event which took place a long time ago (by flying electron terms) so there is nothing impossible about it.
Did the Republicans manage to overestimate what they could get away with ?
I was amazed to read in a Fox news poll (yes a Fox news poll) that slightly more polled registered voters (31%) think the Medicare bill will be bad for senior citizens than think it will be good for senior citizens (30%).
Now the general view in the blogosphere is that this was a bad bill compared, at least, to equally cheap bills with fewer favors for insurance companies. I assumed that it would be politically popular. So it seems did Paul Krugman and the Republicans on speaking terms with him.
"The prevailing theory among grown-up Republicans — yes, they still exist — seems to be that Mr. Bush is simply doing whatever it takes to win the next election."
If the medicare bill is unpopular, it would be part of whatever it takes to win the next election.
The Washington Post reports that Washington DC is going to distribute free condoms in public buildings. This seems to me to be an excellent idea. One of the explicit aims is to fight embarassment about condoms.
Of course the post has to follow the standard of balanced coverage. The HIV virus refused to comment, so the con position was taken by monomaniacal advocates of monogamy. I think the work monomaniacal is fair, since even the advocate did not claim that any marginal effect of condom distribution on promiscuity was relevant. Instead the argument was two false statements combined with a blatant fallacy.
"I'm not aware of any evidence that that sort of activity has a positive effect," said Robert E. Rector, a family-issues researcher at the conservative Heritage Foundation. "The number-one determinant of whether a person will catch a sexually transmitted disease is the number of lifetime sexual partners. We seem to go out of our way as a government and a nation to avoid telling people that, but we hand out a lot of free condoms."
Well I guess that Rector might not be aware of it, but their is strong evidence that AIDS prevention efforts stressing condoms have been succesful in Uganda and among gay men in the USA. I suppose it defendes on how you define "that sort of activity". It is hard to prove that condoms are the key to success because Rector's second claim is absurdly grossly false as he must know. He boldly asserts that the Bush administration goes out of his way to avoid telling people that abstinence or monogamy would reduce HIV transmission. Where do they find people like that ? The man is clearly out of touch with reality. Why didn't he criticize the DC government by contrasting it with the Bush administration which follows a policy closer to the views of people like him ?
The logical fallacy is the claim that the number one determinant of .... This is like saying the number one reason that people catch AIDS is the AIDS virus and it would be better to have no aids virus than to hand out condoms. The issue is what is the best public policy. Not what would be nice if you could magically convince all people (or HIV particles) to do what you think best. Saying number one, then acting as if you said only is a logical error so extreme as to be extremely rare.
Then we hear from the Bush administration
"Tom Coburn, a physician, co-chairman of a presidential AIDS panel and former Oklahoma congressman, called condom distribution misguided because, he said, condoms fail 20% of the time
"We used to think condoms were fairly effective," he said. "If used perfectly, they are probably 94 or 95 percent effective, but we're human, and we don't use them perfectly. . . . The city would be much better off spending its money getting people tested, treated and counseled not to give the virus to others."
Coburn deliberately confounds two issues. One is do condoms fail, the other is do couples who plan to rely on condoms actually use them. It is homicidally misleading to tell people that condoms are no good, because other people didn't put them on.
94 or 95% success seems to me shockingly low. I personally have never experienced a condom failure .In fact, itis indeed the low end of results from studies which show 1 to 5% failure.
Such true condom failure does not correspond, as asserted by Coburn, to using "them perfectly". In fact it is clear that some people have much more trouble with true condom failure than others which implies
This is clear because failure rates are significantly different for different couples. To avoid blaming the victims I should notel that this could be due to anatomy not behavior. It seems that a large penis could be a risk factor which might explain my 100% condom success rate reported above.
I think that, to be true to his Hypocratic oath, Dr Coburn should not be reporting misleading statistics on condom failure but rather should explain to people not to open condom packages with sharp objects, unroll them before putting them on or use oil based lubricants. In fact, I think that men who really care about fighting AIDS should be willing to be videotaped while putting on a condom according to proper procedure.
Finally, the true condom failure rate due to breaking or slipping overstates the AIDS blocking failure rate. The reason is that spermacide kills HIV. Thus in an actual experiment (ugh) it was shown that there was no then measurable HIV released from spermacide treated condoms filled with infected semen and pressed with e plunger even though the experimenters had pricked a hole in the condom with a pin. I forget the cite and this was detectable a long time ago before PCR was used.
Well it's decided. The US is willing to compromise with Ayatollah Ali Al-Sistani on little issues like separation of church and state so long as we get our way on one man one vote electoral democracy (which we oppose).
The alleged issues are the absence of a census of subjects of a totalitarian dictatorship where everyone had ration cards and the risk of tyranny of the majority. To me the first claim is patently absurd. It's not like the Ba'athist regime didn't keep track of people. It is true that separate lists are needed in the Kurdish mini states, but I would be surprised if they didn't keep track at all.
If one is planning on introducing democracy eventually (as the Bush administration still claims) one has to confront the risk of tyranny of the majority eventually. I have already written that this can be done with a not democratically written constitution to be approved or rejected by referendum.
Now I wonder about how to avoid tyranny of the Shi'ite Arab majority. This should not be hard as they are 60% of the population. I think that in a first past the post system electoral districts can be designed so a Shi'ite Arab sectarian nationalist party could not obtain a majority. I mean Bremer works for a Texan Republican, he should have access to good advice on gerrymandering.
This seems to me a blatent case of discriminating on the basis of religion. I am not at all thrilled that a ruling in Davey's favor will inevitably lead to law suits demanding equal funding for creation science and genuine evolutionary biology etc. However, the case seems clear to me.
I hasten to add that I am not moved by religious sentiment. I am an atheist and always have been one.
Still at the Washington Post. The WHO is trying to get 3000000 HIV infected people under anti-retroviral therapy by 2005. I guess this is partly a response to more money from Bush (first praise of Bush in this blog) and partly because it is clear that you can't get people to get tested for AIDS if diagnosis is just a death sentence. The thing that bothers me is
"An expert panel assembled by WHO recommends four drug combinations, out of about 35 available. The one likely to be most popular contains stavudine (d4T), lamivudine (3TC) and nevirapine in a single pill. None of the four combinations includes a protease inhibitor. Drugs in that class are generally more expensive. In many places, including rich countries, they are often held back and used only if first-line treatment fails. "
My impression was that protease inhibitors were necessary for multidrug therapy to work. Now why are they expensive ? Not, I think, because they cost that much to make, but because they are under patent. Now with some billions to work with couldn't the Bush administration buy in bulk at a huge discount. I don't mean a normal volume discount. I mean a discount negotiated by any means necessary. As in
"gee you like the medicare benefit plan but you know some people think we should have medicare bargain tough with you. However, I will veto that if you sell us protease inhibitors for 3 million people a year at cost. Oh they are under patent ? Hmm we haven't looked at patent law reform in years."
Not like Bush but I doubt anything like that would be necessary. It's not like pharamceutical companies are making money out of treating AIDS in the third world now anyway. The only risk is re-importation. I don't see why they can't make the pills a different color size and shape to hamper smuggling them back.
I really don't see why that hasn't been done some how.
The Washington Post reports
"The Bush administration has decided to repeal most of its 20-month-old tariffs on imported steel to head off a trade war that would have included foreign retaliation against products exported from politically crucial states,"
I thought they were at least supposed to pretend they cared about the public interest not just winning elections. The whole article with many quotes from administration sources contains no hint that they care about foreigners (no big surprise) or people who live in non-swing states. Now if the people in solidly pro Bush states were a bit more alert they would become swing states now that that is clear.
I'm not surprised, of course, but I am dismayed by the brazenness
hypocrisy is the tribute that vice pays to virtue - (I forget who said that).