Statistics

# Curse of The MINIMAX!

Make a list of things that might happen. Label this list X_1, X_2, X_3, …, X_p, where “p” is for possibility. Each of these X_i is a thing that can or might happen—and happen in a certain period of time you designate. The X_i and time period or time limit both must be picked, and picked by you.

Here’s an example. Tomorrow might bring us these events: X_1 = a micrometeorite crashes to earth intact, impinging on your skull; or X_2 = It does’t and it’s a lovely sunny day. The time period is plain.

Considering X_1, you have the option to buy a Mighty Mini Meteor Shield 3000™, a helmet guaranteed to protect against all spaceborne objects under 3 inches in diameter. Retails for \$348,000. Comes in your color of choice, tinfoil silver or crazy pink. Or you go out with your pate exposed.

Under X_2, you have the chance of developing a treatable skin cancer that might show twenty years down the line. Or you could wear a fetching straw hat.

The range of what you consider will happen to you, the various scenarios X_i, is up to you to lay out. You must decide what the consequences of each X_i are, and what you would do to prevents or lessen, or even welcome or enhance, the outcomes.

What’s the worst that could happen here? Under X_1, an amusing death. Under X_2, mild discomfort, sometime well after Medicare kicks in.

Death is the maximum worst thing that could happen. You’d like the minimize the risk of the maximum worst thing. Under X_1, which is the scenario with the maximum worst thing, you could either buy the helmet or go bareheaded.

To minimize the maximum risk, you decide shell out the big bucks for the shell.

This is the minimax decision rule.

Minimix, however useful it is in adversarial games, when the other side is actively out to destroy you, has some curious side effects when used as a general decision rule. It works like this: (a) discover in your list the scenario that contains the worst possible risk, (b) take the action that minimizes that risk, and (c) ignore everything else.

There is no mathematical justification for minimax: it is not derived from universal moral principles. It is instead a mathematical encapsulation of how some people make decisions under uncertainty. What does it say about someone who wants to minimize the maximum risk, forgetting all other risks, and even the likelihood of these risks (about which more in a moment)?

It is not a manly attitude for most mortal concerns. For immortal ones, like the status of your eternal soul, sure. Be like Pascal and minimize the maximum risk of Hell. But for deciding whether to drive down to the store for a case of wine, where you might of course be t-boned into a bloody pile of fillets, maybe it’s a tad effeminate.

More than a tad. For you would be frozen into inaction always—if you had a good enough imagination to conjure worst case scenarios lurking everywhere. You couldn’t even sit still sheltering in place in a dark room, the windows slammed shut, sealing in the fetid air, because that meteorite might plunge through roof!

Minimax is effeminate because it is a decision rule based on fear. Sometimes fear is justified! Not usually, though. Minimax tends to be used by the effeminate, because these are the people who enjoy conjuring worst case scenarios.

Again: Minimax operates on the assumptions you bring to it. It is a decision rule, not an assumption generator. It was I that decided on the scenarios, the actions I could take, and the costs associated with them. Minimax is silent on these important topics. Once they are specified, however, minimax springs into action and tells you what to do.

Minimax insists I buy the helmet. Mimimax didn’t tell me that the helmet was an option.

Now when I hop into the car (which I do not own, so I’d have to steal one) to head to the liquor store, I do not consider being t-boned a possibility. Nor do I fret the brakes will fail. Or that a semi driver will spill coffee on this crotch, causing him to steer wildly through my front window. Nor do I ponder any of an infinite number of ways I can be killed. It is I that must bring the scenarios to the minimax decision rule. If I don’t bring weird and wild ones, then the rule can’t see them and won’t select for them.

Let’s try another example. X_1 is millions and millions and millions of deaths from a dread disease, which can be protected against by putting millions out of work (not the same who are killed, of course), enriching the rich, and further strengthening central government by giving it more power, and also weakening it by increasing its debt magnificently.

Our X_2 is a normal course of events, which we treat like the flu, where some die and most don’t, and we do nothing extraordinary like martial law lite.

Minimax says protect against the deaths. Not just now, but forever. Yes, forever, because this Fauci fellow says the disease could become seasonal (as flu now is). So we have to lock down three out of every twelve months in perpetuity. Minimax says saving just one life by these actions will be worth it.

The real problem, as is by now clear, is twofold: (1) using minimax as the decision rule, (2) generating the scenarios.

Minimax is Talebism; minimax is the precautionary principle; minimax is fear. Minimax says quantity of life is superior to quality.

What if not minimax? Far better to accord proper weight to the evidence, and use likelihood to decide. Now this is not so easy, and there is no space here to show how this maneuver can be gamed, too. But this is the direction to go.

Why these scenarios, and why not others? Why these solutions, and why not others? Why are we still trusting models that have already made busted forecasts four months into this thing?

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Categories: Statistics

### 22 replies »

1. Harry Goff says:

Well said Briggs – unfortunately mob hysteria has set in especially in our political class (and that includes the media) and consequently no one is listening except me and thee.

2. Ed says:

The Precautionary Principle is one of those motte-and-baley types of disputation (the late Zippy Catholic was a master exploding those types when combating Liberalism). Sure, how can anyone be against precaution? (Motte). But then comes: Sure, how can anyone be against micrometeorites shields?(Baley).
And finally: Did you see what that guy Briggs said? He is against precaution!!
Taleb is certainly right when attacking false equivocations of multiplicative processes with additive ones but without a clear criterion to show this panic isn’t also a multiplicative social disaster in the making what claim does he have to demand such extreme measures?
I’ll wait till he start getting margin calls to hear from him. Talk about skin in the game!!

3. Michael Dowd says:

Cuomo’s “solution” will save a few from death due to Corvid-19 but also guarantee that many more will die as a result, such as suicide, murder, madness, inability to get needed medical attention, etc. He will also assure that millions will live in misery because of his actions. I conclude Cuomo’s “solution” is not only sub optimal but clearly insane for the purpose he proclaims. However, it is optimal for the purpose of overthrowing our current form of government.

4. Harry Goff says:

Re Covid 19
In Australia up to 3.00PM 26 March 2020

178,000 people have been tested (note:: we are only testing those who may have been exposed – i.e. the testing cohort will have a larger number of positive reports than if we tested the general population)

Thus far::
2799 have tested positive
11 have died (all had serious underlying medical conditions before contracting the virus)
Infection rate of those tested is 1.57%
Death rate of those tested positive is 0.393%
Fatality rate per 100,000 of Aussie population .0477

These numbers do not indicate to me support for the current economic destruction that we are currently embarking upon.

For reference
Road deaths in Australia for last month (Feb 2020) 92
Road deaths in past 12 months 1163
Annual fatality rate for road deaths in 2019 was 4.6 per 100,000 of population. (compare to 0.0477 above)

2017 flu death rate in Australia 3.9 per 100,000 persons . (compare to 0.0477 above)

2019 flu death rate in Australia 3.0 per 100,000 persons. . (compare to 0.0477 above)

Although it is estimated that the actual rate is much higher, as one source suggests a death rate from flu annually to be about 12 per 100,000 in the over 50 age group.

Italy is currently Covid-19 central with lots of deaths which is sad.
BUT Lets be cautious and not claim that everyone who tests positively for COVID-19 after death died FROM the disease. They may very well have died WITH the disease. There is a difference and it matters.

5. Spetzer86 says:

I’m assuming everyone worried about saving “just one life” is now no longer pro-abortion. I haven’t heard when Planned Parenthood is being closed, but please keep an eye out.

6. Sheri says:

There is a chance of being electrocuted by your laptop or PC. This is likely to be fatal, especially if liquid is involved and you have the laptop plugged in at the time. A paper book at best will fall and injure your big toe. So, under the general line of thinking, you take a sledgehammer to the computer, go off-grid with only DC power at best (preferably no power) and read paper books. How many Precautionary Principle people just smashed their computers and ran for the hills for safety??? Exactly NONE. Why? Because no one really believes the PP, they just use it to smack people who disagree with their choices and to create tyrannical governments and to take all the money they can from producers based on shoddy science. It’s all a lie and they know it. Fall for it, and you’re a fool.

Washington DC CLAIMS to believe the Covid threat, but just shut down completely now, WEEKS after everyone else, and will reopen just in time for Ramadan, but close over Easter (right after POTUS announced he wanted things open for Easter, of course–can these idiots be more transparent?). If you can’t see what lying scum these people are, smash your computer and leave the modern world quickly and forever. Get a shaman, take up herbal meds, starve on a regular basis, die of curable diseases so you will be “safe”. Remember, only death is totally safe.

7. Dave says:

Minimax makes sense for two (or even three) player adversarial zero-sum (or more aptly named, fixed-sum) games. Not so much otherwise. Bayesian decision theory will do better in most other circumstances, assuming you can find accurate premises, define a reasonable utility function to handle trade-offs, etc.

I still claim there is option value with the current outbreak in being cautious at first to give more time to learn about the virus, how to treat it, best methods for prevention in daily life (e.g, how much would it slow the spread for everyone to wear masks?), prepare health care capacity, see how warm weather affects it, etc, before rushing back to normal daily life. There is value in more information here. You can always return to normal later. Harder to undo deaths. Some production will be lost forever, but some of it will have just been delayed.

8. Ken says:

“There is no mathematical justification for Minimax: It is not derived from universal moral principles.”

What mathematical justifications are based on universal moral principles?

“Mimimax is effeminate because…based on fear … sometimes that fear is justified.”

If a feared outcome is justified in being feared, how is that “effeminate” rather than rational?
Seems there’s a Sweeping Generalization fallacy intruding into the arguments made here – “is effeminate” rather than ‘sometimes effeminate.’
And so what? Name calling to dissuade use of a decision technique seems pretty lame.

9. Kalif says:

Why talk about the precautionary principle, which applies to future? Let’s take a look at what has happened so far. In many places, medical capacities were overwhelmed, which was not the case last year during the seasonal flu.

COVID doesn’t need to have higher mortality rate than the flu (and it may as well be the case) to be more dangerous. We can’t put seasonal flu on hold, so we can brag how this new virus is less of a problem, in terms of mortality. Combined with flu though, it can overwhelm the system. There’s little comfort in arguing that, BY ITSELF, it’s not a big deal, etc. It does not come by itself.

Second, even with lower mortality, if people are more likely to end up needing a ventilator than in case of flu, overall mortality is irrelevant. The system will be overwhelmed.

In epidemiology, very deadly diseases are not perceived as the worst. They eliminate everyone within a small perimeter and don’t spread. It’s the ones with long incubation, or the ones that are hard to detect, and have difficult but not deadly symptoms that are the issue.

Again, scintillating comparisons with seasonal flu are useless, as we don’t have the luxury to assess COVID on its own. Bayesian models do what it says on the tin. As more info comes in, they are refined, and that’s all.

10. RDittmar says:

I don’t know if you’ve seen this yet, but the scary projections for the course of the coronavirus that had Taleb running around with his hair on fire calling people psychopaths is the output of a 13-year old thousand-lines long piece of undocumented computer code that the author is unwilling to share with anyone else. Now Taleb’s on Twitter pretending to be the level-headed adult in the room:

11. Fredo says:

What I’d like to see is some sort of psychological analysis of what impact
that awful image of the bat perched on the edge of a soup bowl had on
the mass hysteria that has now dragged the world off to an open grave .
Don’t laugh it off, this is visceral atavistic iconography we know
very little about that I suspect was skillfully and deliberately planted early
on to kick this whole thing off. The image was not even from China so
someone had to dig it up and have it ready to go as it was one of the
first widely circulated images, and purportedly the cause of the
outbreak in Wuhan.

12. Guges says:

@Kalif

Kalif, the 2017/18 flu overwhelmed medical facilities across the US. Where was the panic? Where were the complete shutdowns of states with hot spots, tanking their businesses/companies.

We didn’t shut everything down, we took measured responses. And this happens all the time with the flu AND the flu has a vaccine/treatments….think about that for a second…we take the flu on a scale of 1-100 at a 10 and we’re taking this at a 95. We need to be at a 40 for a flu and about a 60 for this till we know more.

https://time.com/5107984/hospitals-handling-burden-flu-patients/

https://time.com/5107964/flu-2018-epidemic/

@Fredo This I believe was calculated to tank the economy & also hurt the re-election chances of someone. Notice only at the moment DEM governors are doing this (2 of the biggest states with overwhelmed entitlements are looking for bailouts)

13. Fredo says:

@Guges
Yea it’s that enlightened insane cabal that’s so concerned with sustainability
and saving the planet for themselves.

14. Kalif says:

@Guges
I am very familiar with what you cite and get first-hand info from the front lines and talk to people who worked during 17/18. You need to put it in the context, to compare it, though. There was no some exotic monkey/bat/etc. virus, ON TOP of all that misery then. There were no other countries that shut down and reported multiple fatalities all at once in 17/18, prior to the flu epidemic, were there? That’s what created momentum, not us.

We didn’t really start shutting down, until recently. Look at reuters pages from January; China in a lock-down, news everywhere, but our stock market never higher. Next came Italy, but we were still business as usual.

I don’t subscribe to any of the ‘manufactured crisis’ conspiracy theories. I just think people in charge knew we are not prepared and have no tests, vaccine, ventilators, masks, common sense, etc. , so they decided to shut down the country.
Having said that, I do believe all this will be used as an opportunity for a big wealth transfer from the bottom up in some form or the other, as it was the case in 2008/9.

15. Uncle Mike says:

Kalif,

The “people in charge” are the danger to society. They did not (probably didn’t) manufacture the virus, but they sure as heck manufactured the insane draconian authoritarian over-response.

~10,000 people died today in the US. That’s the standard death rate everyday number. Most of them died in a hospital, nursing home, hospice, abortion clinic or other medical facility.

~250 people died of complications from the WuFlu. That represents 2.5% of the deaths. Abortion, on the other hand, represents 22% of the deaths. Guess which one the “people in charge” allegedly care about?

Has even one of the “people in charge” suggested that we convert abortion clinics into hospitals to treat the WuFlu victims? So there’s your answer.

16. Fredo says:

Well all we really have to do is follow the breadcrumbs of the emergency
legislation being proposed across the globe to of course, keep everyone
‘safe’. Once all that’s enacted we can all come out of our holes take a look
around and see where we’ve landed. Funny it’s always about keeping
everyone ‘safe’ all tucked up in their beds.

17. DAV says:

Funny it’s always about keeping everyone ‘safe’ all tucked up in their beds.

Yup. It’s the Nanny State saying, “There! There! Mommy is here!”

18. Becky says:

I would posit that those crying about hurt feelings from the non use of their personal pronouns are crying loudest about the possibility of getting sick and dying. That possibility exists everyday and the risks are too numerous to think about every day.

I predict some backtracking and amnesia by those predicting massive death.

Hunches, especially experienced ones, can be pretty darn close.
My hunch says this thing left China on the first day.

19. The disease may well be seasonal but the good news is within a few months it is probable we will have both a cure AND a vaccine, so everyone will ignore it.