A Short Lesson in Bad Decision-Making

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21

I'm calling shenanigans on Wendy Delmater… to wit, she writes
The kids had eight flashlight batteries in a basket, and an empty flashlight. Two were fully charged, six of the batteries were dead: emptier than a politician's promises. The person viewing the exhibit was asked to guess the odds of getting the two charged batteries into the flashlight. Upon lifting a flap, the actual odds were revealed. Everone was shocked that the odds were 36 to 1. It was not intuitive, even for the science fair judges, who should have known better.

 

First, she sats the odds were 36 to 1, which would imply the PROBABILITY to be 1/37 (see for example http://www.problemgambling.ca/en/resourcesforprofessionals/pages/probabilityoddsandrandomchance.aspx).

Next-I don't even see the probability to be 1/36 or even 1/37.

8 choose 2 = 28. there is 1 combination that works, so the probability is 1/28

> combn(c("G","G","B","B","B","B","B","B"),2)
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,] "G"  "G"  "G"  "G"  "G"  "G"  "G"  "G"  "G"  "G"   "G"   "G"   "G"   "B"  
[2,] "G"  "B"  "B"  "B"  "B"  "B"  "B"  "B"  "B"  "B"   "B"   "B"   "B"   "B"  
     [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
[1,] "B"   "B"   "B"   "B"   "B"   "B"   "B"   "B"   "B"   "B"   "B"   "B"  
[2,] "B"   "B"   "B"   "B"   "B"   "B"   "B"   "B"   "B"   "B"   "B"   "B"  
     [,27] [,28]
[1,] "B"   "B"  
[2,] "B"   "B"  
 

22

sorry-double posting-didn't realize i could respond directly.I'm calling shenanigans:
The kids had eight flashlight batteries in a basket, and an empty flashlight. Two were fully charged, six of the batteries were dead: emptier than a politician's promises. The person viewing the exhibit was asked to guess the odds of getting the two charged batteries into the flashlight. Upon lifting a flap, the actual odds were revealed. Everone was shocked that the odds were 36 to 1. It was not intuitive, even for the science fair judges, who should have known better.

First, you say the odds were 36 to 1, which would imply the PROBABILITY to be 1/37 (see for example http://www.problemgambling.ca/en/resourcesforprofessionals/pages/probabi…).
Next-I don't even see the probability to be 1/36 or even 1/37.
8 choose 2 = 28. there is 1 combination that works, so the probability is 1/28
bn(c("G1","G2","B1","B2","B3","B4","B5","B6"),2)
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,] "G1" "G1" "G1" "G1" "G1" "G1" "G1" "G2" "G2" "G2"  "G2"  "G2"  "G2"  "B1"
[2,] "G2" "B1" "B2" "B3" "B4" "B5" "B6" "B1" "B2" "B3"  "B4"  "B5"  "B6"  "B2"
     [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
[1,] "B1"  "B1"  "B1"  "B1"  "B2"  "B2"  "B2"  "B2"  "B3"  "B3"  "B3"  "B4"
[2,] "B3"  "B4"  "B5"  "B6"  "B3"  "B4"  "B5"  "B6"  "B4"  "B5"  "B6"  "B5"
     [,27] [,28]
[1,] "B4"  "B5"
[2,] "B6"  "B6"

23

I think that birthday trick has something to do with the popular birthdays of late September and mid November.  Which of course correspond to the popular conception days of late December and mid February.  It isn't just math that wins bets. 

24

I think the batteries answer is 1/28.  2/8 times 1/7.

25

Paul Hawken goes after this optimism pessimism thing pretty well.  He articulates this better than I could.  The intiuitive mind can see the new dawn, while the rational mind drowns in darkness.  We are the ones we have been waiting for.
http://www.youtube.com/watch?v=v-xb-sdrmOQ

26

 Thanks Grover. Tweeker . You live and learn. Well, maybe some do.
I have yet to come up with a plausible reason why the need for sleep has not been at least minimised by evolution. The need for sleep is so obvious that it is neigh on impossible to ask the question, why do sentient beings all do this pathological behaviour? Even sharks do it. It seems to be a fundamental price for sentience. I would even go so far as to say that we will know that Robots are truly sentient when they need to sleep.
The true mystery seems to be hiding in plain sight.
 
I use this line of reasoning to conclude that I must be magnificently sentient.

27

Arthur,
Robots do need sleep. Have you ever left your computer on for 2 weeks strait?  Things start getting weird, as they do for a person who's been awake too long.  Just because it makes evolutionary sense doesn't mean it makes practical sense. By your thinking, we should have all developed super speed and skin that can stop bullets. Entropy affects everything, we just need to sleep every once in a while. 

I guess if you really want to go into it, you could argue that if we never needed to sleep then we wouldn't have been driven to learn to create a safe shelter, which is necessary for a family and other complex social developments. If we didn't need to sleep we wouldn't need to stop moving around, and we wouldn't have built villages and towns.  

But I like to think that it isn't that complicated, and we just need to cool off the wiring. 

 

 

28

It's also worth mentioning that yawning may be one of first forms of evolutionary communication. Many animals that need to hunt together in a pack or community have yawns that seem contagious.  Have you ever made someone else yawn just by yawning yourself?  Some scientists say that yawning was a crucial tool used by communities to keep the group on the same schedule, sleeping at the same time in order to hunt together.

29

RJE: The most fascinating thing I find about my sparse body hair is that I get goose bumps when cold, an evolutionary adaptive response to increase the protective layer of warm air adjacent to my skin that is clearly redundant.
I also get 1/28 for the chance of getting both live batteries but my algebraic method is conditioned by my genetics background. There is a 2/8 chance of getting the first battery and a 1/7 chance of the second. 2/8 multiplied by 1/7 is 1/28. Maybe also influenced by playing poker, which fundamentally is an exploitation of one's probability and bluffing skills. 

Interesting comment about the sabre tooth tiger Adam. As a geneticist I'd say we are wired for those traits that have a selective advantage, i.e. allow reproduction. Immediate death from food precludes offspring whereas a slow death from a bad diet occurs in the post-reproductive years.

30

1/28 or 1/36 - still worse odds than people intuitively think.And I had a math PhD help the kids 'cause I ain't a math wiz. Feel free to corrrect any mistakes and no hard feelings.

31

…
"Lottery: A Tax on People Who Are Bad at Math"

Amusingly enough, I found that bumper sticker in a Las Vegas convenience store laugh

32

Okay, I decided to test my BS meter against Adam’s article. The mental trick is that one starts by thinking of the likelihood of someone else having one’s own birthday. That’s the defect that sets us up for the kill, all the prof has to do is find a match, not a particular match. Perhaps more importantly, the prof does not have to find the match, he gets the pool to self-declare its match. I find the How and Why of our self-deceptions more interesting than the actual statistics–and that itself is a gateway to self-deception.
That said, I tried to grok the wikipedia link, though I dare not try to work it with pencil and paper. In defense of Wendy, I think 1 in 37 is grossly low, but I won’t try to defend that with calculations. Adam’s problem was the probability of a match in a given pool, and as shown, the probability of a match was very high. But in the case of the batteries, we know there is a match. The challenge is to pick the two good batteries out of a group of eight. Can you imagine Adam’s professor picking a birthday pair out of his class (without looking at the class roster)? The probability of that is exceedingly slim,a fraction of a percent. What if he had to pick out the four pairs WITHOUT KNOWING that with any of the pairs he picked he had reduced the overall number to choose from? The probability of there being a birthday match in a given group, and the probability of your being able to select it at random are two very different things (it seems to me).
Now, Wendy’s brief statement of the problem didn’t say how we know we’ve picked a good battery. Without a battery tester, in the real world we can’t know until we put them in the flashlight–and by then it’s too late. Two dead batteries, no problem. One good and one dead, you’ve just killed your chances of ever picking two good batteries, although you now have two half-good batteries. But with every bad battery you test with one of them, you’ve cut that remaining battery power in half.
So in Wendy’s problem, you must guess correctly the first time, and the first time only. Finding a pair of bad batteries with your first guess actually helps, because at least with a complete failure you can eliminate 2/8 of the choices. But at the same time, your odds of choosing a mismatched battery pair increase have also increased proportionally.
In fact, numbers force us into bad decisions more often than not. I work in the realm of risk and threat, neither of which are mathematically calculable (risk is to an extent, but not threat), but which my overlords demand I squeeze into a mathematical likelihood (the threat is 60% likely). Hogwash, there are so many variables in what that threat can choose (the enemy always has a choice) and more introduced by our countermeasures, that there is no way of actually reducing a real life threat to a probability.
So, yes, knowing some statistics and probability is worth while, but it can’t solve a lot of problems, and it doesn’t even always provide good guidance on how to solve a lot of them.

33

In fact, I would say that in the professor’s wager there was no threat, just a gamble; and the risk was only $5.
But if one needed the flashlight to fix the generator as the house sunk into a deep freeze, the risk is substantial–one could lose everything, even one’s life. At which point the threat of picking anything but the two good batteries becomes incredibly important, even lethal. Wisdom would have been to toss the dead batteries ages ago, or at least not to have mixed them with good batteries. I don’t see statistics providing much guidance to help if one is stupid enough to get stuck having to guess at good batteries.
On the other hand, if someone offered you a bargain on a bag of batteries, say 20, with the caveat that maybe one or two of the batteries were dead, these statistical exercises today should be enough to warn you off of that “bargain.”

34

“The true mystery seems to be hiding in plain sight.”
I have given this some thought and all I could come up with is TIME. Why? We have just come out of our fear as a species with regards to the night during the age of light. Before then Fear ruled the night and in response we slept, we still sleep, as not enough evolutionary time has passed to have changed the need for sleep. That and a host of quick answers but I think “evolutionary time” is the reason we still require sleep from sun down to sun up.
My habits today are different than when I was younger (less sleep needed) but is probably more choice than anything.
Happy Sailing and I’m going back to bed!
BOB

35

Don't you guys dream? lol C.G. Jung and Joseph Campbell say it best…
https://www.youtube.com/watch?v=lDEeQegYOz4

Peace! (ful) dreams

36

And what worries me – scares me, is more accurate – is that I don't observe this same caution in the actions of the people making the truly big decisions.
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In her book "Quiet", Susan Cain talks about how the west has gone from a Culture of Character to a Culture of Personality.  I think she is right, our culture rewards people for making snap decesions and moving on.  What is valued is salesmanship, being right about something is not as important as being willing and able to promote your own view.  Caution is seen as a weekness and the trick is to not  be around when the bill comes due for poor decisions.

What worries me is the amount of pain a nation must feel before considering that there is something wrong with the status quo.

 

37

you said:
"Baseball is a great analogy for what's going on in the world."

You have in this statement said the truth.

Baseball is seen through a prism of spoiled Rich dudes who have the world by the tail. The reality is these are our youths playing a game that frankly they would do for far less but will gladly take whatever they are offered.

Baseball is NO different than the world society at large, These kids are for the most part underprivileged and in many cases just third world boys who play a game well. They have their temptations as we all do, are competitive as we all are, and frankly are unprepared for what comes their way as most are.

The drugs or performance enhancing ones are pushed on them well before they get to the Bigs. Imagine if you would the temptation for a boy, 18, 19 years old who can hit the cover off the ball but needs to only hit that little white thing 10 more feet to hit the ball out or just hard enough to get it through the infield to make it to the Bigs, Taking something that is pressure pushed on them by agents or subtly through the organization they play for is powerful when winning and making it to the show is all encompassing. We are talking millions here as that is the average these kids, again, I say kids, will earn. 

Anyways, like I said and you referenced in your quote above, and that is baseball is very much a window pane into everything we see in the world today. I actually believe it's the influence of society that influence the game and, not the other way around. These kids are learning from the intellectuals and the lawless what is expected of them to succeed. As with everything blame must be assessed and ballplayers are an easier mark than having Congress go before the public and be paraded out in front of the world, and I dare say that every Congressman would plead the 5Th with every question asked of them. It's a double standard. Plus we are all guilty of playing the game, would do just about anything to feed and cloth our kids. Taking steroids so that we can get back to work sooner or taking alcohol and drugs for the lift it gives us as we sing and dance at times don't seem so bad. Moderation right, so these kids learn all this shit from us. Yet, they are to be perfect role models when they have learned, and have had reinforced on them all that we show as acceptable behavior. It really comes down to their mental and physical toughness, and that will change with every injury and responsability accumulated on the field and at home.

I just don't judge (severily) personally anyone myself. I am not walking in their shoes, and I know what I would do to take care of my family. Everything and anything short of taking another persons life or stealing to get what I wanted. I will work however and hard but I will work. 

These kids are doing what their families, coaches and owners of their contracts are asking of them, and then thrown under the bus when they get caught. That's just the truth, and it's on all of us for expecting more from them and not from ourselves.

The ones that actually get involved with enhancing are the older ball players that have lost a step, been hurt and don't hit it quite as far or hard, and are having to do something. Their life styles and families are more entrenched in the dream and finances as never before, and staying in the Bigs is the whole deal going bad or staying as is. That's a tough, tough decision, and one that every single one of us would have to make to stay in our positions in life. Risk/Reward.

Regards

BOB

38

[quote=cowpoke]In her book "Quiet", Susan Cain talks about how the west has gone from a Culture of Character to a Culture of Personality. 
[/quote]
Cowpoke
Thanks for sharing this insight.  It helps clarify a feeling I’ve had for a long time, but couldn’t express well.  The rest of your post shows how dangerous this trend is.
Travlin 

39

Selection takes place over long time frames. People have only been able to conceive of numbers large than a few dozen for a relatively short time - certainly not long enough for selection to make a difference, even if ability with sets large enough to be statistically significant made a difference in passing on your genes.There is a good chance that the species will never evolve along those lines. That is, that those skills will never be a factor in selection.
That does not mean that the cultural trait of using statistics could not become a factor in the survival of the culture - that a culture that values statistical inference (in particular, and science in general) may not come to dominate those that do not.
Do we have time before those who go with their gut drive us over the edge?
Not looking so good from here.

40

The article discusses statistics then asks a question.
I think it is important to know there are two kinds of statistical analysis. The first kind treats problems like the birthday problem. Or talks about taking colored balls out of urns. Here there is no history, just the present - the urn full of balls - and the future, possible selections.

The second kind talks about what happens when you know a bunch of stuff has already happened. The results here are even more startling. It is called Bayesian statistics.

The relevance?

If we ask - should the government simply print money to pay its bills? - the answer is No.

If we state

 - the government has created programs for which it must pay and

 - has set tax rates that are supposed to pay for those programs but cannot

then say

 - should the government print money to pay its bills?

we come to a different conclusion.

What am I saying? I am saying that the analogy drawn in the article can lead to false conclusions, so is a bad analogy.

A better analogy takes history into account, does not treat the problem in isolation.

An interesting example is the Price is Right example. When offered three doors, you pick one. The host then opens a different door and shows you it is not the best door. Should you change your pick?

Going back to the questions at the end of the article - should the government print money to pay its bills?

These bills are a problem because the Congress put programs in place for which there was no revenue - wars, other programs. Revenue was never there to pay for these programs. Taxes were not raised. Revenue now is insufficient to pay for those programs.

Revenus is also down because the economy has shrunk over the last 5 years.

What to do?

In the government case, it can print the money. In this case, I believe it should.

My point? Decisions in real life need to be made in the context in which the implications of those decisions will happen. Not in a statistical distribution in which context is not a factor.