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Arguments from Authority

RoyLatham
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8/16/2010 4:05:31 PM
Posted: 6 years ago
This is another in the series of lessons on critical thinking initiated by Freeman.

Should you believe your doctor when he tells you how to treat your sprained ankle? You should, because she's an authority. The doc knows more about treating sprained ankles than even your grandpa, unless Gramps happens to be a trained specialist in sports medicine..

Should you cite Al Gore as an expert in global warming? How about citing a Nobel Prize winner in economics on whether to extend unemployment benefits?

An "authority" is a person claimed to be an expert on a subject relevant to a topic. A physician would be a likely authority on treatment of disease, and a plumber on how to cure a leaky pipe. Authorities are established by their credentials, such as long experience, academic degrees, publications in scientific journals, or acknowledgement of their expertise by other established experts.

Arguments from authority are sometimes valid and sometimes not. Here are some of the tests to see if such an argument is valid.

1.Does the claimed authority have the basic credentials?

For example, Al Gore is not an authority on climate science, because he has no training in climatology, relevant scientific publications, or a demonstrated track record of success in the field. As a citizen, he has every right to voice his opinion and present arguments, but he does so only on a par with anyone else interested in the subject.

2.Is the claimed authority providing an opinion on a subject relevant to his or her specialty?

A group of Nobel Prize physicists signed a statement that a Star Wars missile defense system could not be built successfully. Nobel Prize winning physicists certainly have great credentials, but their expertise is in physics, and the question of whether a Star Wars defense can be made to work is not a scientific problem, it is an engineering problem. No claim was ever made that a law of physics would be violated, it was purely a question of the state of technology.

3.Is the specific subject a specialty in which the person has expertise?

Economics has microeconomic problems and macroeconomic problems. A person who won a Nobel Prize on how a microeconomic topic may not be an authority on how a national economy is likely to behave. Being an economist, he may have a better idea than the average person, but his opinion is not authoritative. As the world becomes more specialized, experts are becoming more narrowly focused, so the situation is more common.

4.Is the question at issue a technical question or a question of values?

An authority on crime and punishment can be rightly expected to have something relevant to say about the effect the death penalty has on deterring murder. But he is not an authority on whether it is more important for a thousand guilty murders to be set free than to have one innocent person convicted. Your opinion on that is as good as the expert's. Economists often agree on economic effects, buts disagree on policy goals. When is comes to deciding the morality of redistributing wealth, for example, they have no special expertise.

5.Is the expert's opinion agreed to by other experts?

If the expert is a minority of one in his field, he still may be right, but the claim to authority is diminished. There are fully qualified earth and life scientists who do not believe the theory of evolution is correct. However, a poll shows that 99.86% of earth and life scientists believe that the theory of evolution is correct. Of course, the 99.86% might still be wrong, but the claim to authority is on the pro-evolution side and opponents must argue the facts independent of authority.

One of the popular arguments against authoritative opinion is to argue that anyone with the credentials needed to establish authority is disqualified because they have been co-opted by the system. Thus physicians are not qualified to talk about alternative medicine because their livelihood depends upon dispensing traditional medicine. Nuclear engineers are not qualified to opine about nuclear safety because their livelihood depends upon the nuclear industry continuing. In short, the argument is that anyone qualified to be an authority ought to be disqualified in favor of someone with no credentials.

The error in that argument is that professional ethics apply equally. There is no reason to believe that an opponent of established knowledge is more ethical than a proponent. The opponent may have a strong monetary incentive to cash in on his alternative theory or he may have an ideological incentive in his radical theory being validated. In fact, it is unlikely that more than a few scientists or engineers would be swayed by financial incentives of a profession. Experts are intelligent people who are unlikely to be able to make a living if a single issue turns out against their interests.

If credentialed authority is posed again uncredentialed claims, then the battle of authorities goes to the credentials. If both sides have respectable qualifications, then it's a battle of the facts. Either side may win an argument based upon citing facts, but the factual argument must be a sound one.

Finally, authorities sometimes make flat out mistakes. There is a problem of proabability theory called "The Monty Hall Problem," named after the host of a television game show. Contestants had to guess which of three doors had a prize behind it. After guessing, Monty would open one of the other doors, one that did not have the prize. The contestant was then asked if he wanted to switch doors. The correct answer to the problem is that switching doors doubles the chances of winning. However, even when the proof was given mathematically, there were several learned professors of mathematics who refused to believe that there was an advantage in switching. Only computer simulations finally convinced them. I wrote up the problem in a blog post http://factspluslogic.com...

There is a traditional Japanese saying about the failure of experts: "Even monkeys fall from trees."
mattrodstrom
Posts: 12,028
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8/18/2010 10:33:04 PM
Posted: 6 years ago
At 8/16/2010 4:05:31 PM, RoyLatham wrote:
However, even when the proof was given mathematically, there were several learned professors of mathematics who refused to believe that there was an advantage in switching.

I was pretty sure too..

and I don't see abstract mathematical proof convincing me...

what did was thinking that initially there's a 2/3 chance that the prize is in the 2 NON picked doors.

THEN after opening up one, NON-prize, door of the 2 NON-picked....

there's still the 2/3 chance on the 1 remaining Non-picked door.

BUT it stumped me good enough that I wouldn't have thought about it had you not said so.
"He who does not know how to put his will into things at least puts a meaning into them: that is, he believes there is a will in them already."

Metaphysics:
"The science.. which deals with the fundamental errors of mankind - but as if they were the fundamental truths."
belle
Posts: 4,113
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8/18/2010 10:39:44 PM
Posted: 6 years ago
it makes perfect sense to me now. the two non-picked doors can be thought of as a single unit. but for some reason i had a terrible time wrapping my head around it at first...
evidently i only come to ddo to avoid doing homework...
lovelife
Posts: 14,629
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8/18/2010 11:10:51 PM
Posted: 6 years ago
I don't actually understand, can someone explain why it would be more likely behind door #3 then door #2?
Without Royal there is a hole inside of me, I have no choice but to leave
mattrodstrom
Posts: 12,028
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8/18/2010 11:19:37 PM
Posted: 6 years ago
At 8/18/2010 11:10:51 PM, lovelife wrote:
I don't actually understand, can someone explain why it would be more likely behind door #3 then door #2?

3 doors.

You pick door #2

Door #2 has a 1/3 chance of being Prize

The Unpicked Doors 1&3 have a 2/3 chance of being prize

when Door 1 is Opened REVEALING NO prize...

Unpicked Doors 1&3 Retain their 2/3 chance of being prize... the opening of door 1 doesn't affect this...

HOWEVER... being that door 1 is NOT prize....

the 2/3 chance of being prize is all on door 3.
"He who does not know how to put his will into things at least puts a meaning into them: that is, he believes there is a will in them already."

Metaphysics:
"The science.. which deals with the fundamental errors of mankind - but as if they were the fundamental truths."
J.Kenyon
Posts: 4,194
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8/18/2010 11:23:17 PM
Posted: 6 years ago
At 8/18/2010 11:10:51 PM, lovelife wrote:
I don't actually understand, can someone explain why it would be more likely behind door #3 then door #2?

Take three opaque cups and use them to cover up a coin. Model out the problem on a table or desk. You'll get it, I guarantee it.
Freeman
Posts: 1,239
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8/18/2010 11:34:56 PM
Posted: 6 years ago
At 8/16/2010 4:05:31 PM, RoyLatham wrote:
This is another in the series of lessons on critical thinking initiated by Freeman.

Should you believe your doctor when he tells you how to treat your sprained ankle? You should, because she's an authority. The doc knows more about treating sprained ankles than even your grandpa, unless Gramps happens to be a trained specialist in sports medicine..

Should you cite Al Gore as an expert in global warming? How about citing a Nobel Prize winner in economics on whether to extend unemployment benefits?

An "authority" is a person claimed to be an expert on a subject relevant to a topic. A physician would be a likely authority on treatment of disease, and a plumber on how to cure a leaky pipe. Authorities are established by their credentials, such as long experience, academic degrees, publications in scientific journals, or acknowledgement of their expertise by other established experts.

Arguments from authority are sometimes valid and sometimes not. Here are some of the tests to see if such an argument is valid.

1.Does the claimed authority have the basic credentials?

For example, Al Gore is not an authority on climate science, because he has no training in climatology, relevant scientific publications, or a demonstrated track record of success in the field. As a citizen, he has every right to voice his opinion and present arguments, but he does so only on a par with anyone else interested in the subject.

2.Is the claimed authority providing an opinion on a subject relevant to his or her specialty?

A group of Nobel Prize physicists signed a statement that a Star Wars missile defense system could not be built successfully. Nobel Prize winning physicists certainly have great credentials, but their expertise is in physics, and the question of whether a Star Wars defense can be made to work is not a scientific problem, it is an engineering problem. No claim was ever made that a law of physics would be violated, it was purely a question of the state of technology.

3.Is the specific subject a specialty in which the person has expertise?

Economics has microeconomic problems and macroeconomic problems. A person who won a Nobel Prize on how a microeconomic topic may not be an authority on how a national economy is likely to behave. Being an economist, he may have a better idea than the average person, but his opinion is not authoritative. As the world becomes more specialized, experts are becoming more narrowly focused, so the situation is more common.

4.Is the question at issue a technical question or a question of values?

An authority on crime and punishment can be rightly expected to have something relevant to say about the effect the death penalty has on deterring murder. But he is not an authority on whether it is more important for a thousand guilty murders to be set free than to have one innocent person convicted. Your opinion on that is as good as the expert's. Economists often agree on economic effects, buts disagree on policy goals. When is comes to deciding the morality of redistributing wealth, for example, they have no special expertise.

5.Is the expert's opinion agreed to by other experts?

If the expert is a minority of one in his field, he still may be right, but the claim to authority is diminished. There are fully qualified earth and life scientists who do not believe the theory of evolution is correct. However, a poll shows that 99.86% of earth and life scientists believe that the theory of evolution is correct. Of course, the 99.86% might still be wrong, but the claim to authority is on the pro-evolution side and opponents must argue the facts independent of authority.

One of the popular arguments against authoritative opinion is to argue that anyone with the credentials needed to establish authority is disqualified because they have been co-opted by the system. Thus physicians are not qualified to talk about alternative medicine because their livelihood depends upon dispensing traditional medicine. Nuclear engineers are not qualified to opine about nuclear safety because their livelihood depends upon the nuclear industry continuing. In short, the argument is that anyone qualified to be an authority ought to be disqualified in favor of someone with no credentials.

The error in that argument is that professional ethics apply equally. There is no reason to believe that an opponent of established knowledge is more ethical than a proponent. The opponent may have a strong monetary incentive to cash in on his alternative theory or he may have an ideological incentive in his radical theory being validated. In fact, it is unlikely that more than a few scientists or engineers would be swayed by financial incentives of a profession. Experts are intelligent people who are unlikely to be able to make a living if a single issue turns out against their interests.

If credentialed authority is posed again uncredentialed claims, then the battle of authorities goes to the credentials. If both sides have respectable qualifications, then it's a battle of the facts. Either side may win an argument based upon citing facts, but the factual argument must be a sound one.

Finally, authorities sometimes make flat out mistakes. There is a problem of proabability theory called "The Monty Hall Problem," named after the host of a television game show. Contestants had to guess which of three doors had a prize behind it. After guessing, Monty would open one of the other doors, one that did not have the prize. The contestant was then asked if he wanted to switch doors. The correct answer to the problem is that switching doors doubles the chances of winning. However, even when the proof was given mathematically, there were several learned professors of mathematics who refused to believe that there was an advantage in switching. Only computer simulations finally convinced them. I wrote up the problem in a blog post http://factspluslogic.com...

There is a traditional Japanese saying about the failure of experts: "Even monkeys fall from trees."

Ahh... yes... excellent post Roy. This is also related to another similar topic; namely, the value of various of various forms of "evidence". As you go about creating arguments, it's important to realize that there is a hierarchy of credible evidence. http://www.google.com...

For instance, you could probably find at least one well known, respected, and credible anthropologist that believes humans and Neanderthals had children. However, this researcher's opinion must also be weighed against the expert opinions of other members of the scientific community. If, for example, the American Anthropological Association holds to the view that humans probably didn't have children with Neanderthals, then their opinion must necessarily be weighed higher than that of a single anthropologist.

It's possible to justify any argument, no matter how wacky, with the opinion of "experts". However, it's important to realize where the opinions of these "experts" fit in with the rest of organisations and individuals who are also experts on any given topic.
Chancellor of Propaganda and Foreign Relations in the Franklin administration.

"I intend to live forever. So far, so good." -- Steven Wright
mattrodstrom
Posts: 12,028
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8/18/2010 11:37:02 PM
Posted: 6 years ago
At 8/18/2010 11:34:56 PM, Freeman wrote:
For instance, you could probably find at least one well known, respected, and credible anthropologist that believes humans and Neanderthals had children.

Just FYI... I'm pretty sure that's the consensus now...

in fact if you're a stripe of Eurasian... You're prolly between 1-4% Neanderthal
"He who does not know how to put his will into things at least puts a meaning into them: that is, he believes there is a will in them already."

Metaphysics:
"The science.. which deals with the fundamental errors of mankind - but as if they were the fundamental truths."
lovelife
Posts: 14,629
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8/18/2010 11:38:30 PM
Posted: 6 years ago
Wouldn't the chance be exactly the same tho? I fail to see how dorr #1 affects door 2's chance of having it, unless door #1 had it.
Without Royal there is a hole inside of me, I have no choice but to leave
J.Kenyon
Posts: 4,194
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8/18/2010 11:39:24 PM
Posted: 6 years ago
At 8/18/2010 11:38:30 PM, lovelife wrote:
Wouldn't the chance be exactly the same tho? I fail to see how dorr #1 affects door 2's chance of having it, unless door #1 had it.

Just model it out and it will come to you. Shut up and do it.
lovelife
Posts: 14,629
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8/18/2010 11:41:33 PM
Posted: 6 years ago
At 8/18/2010 11:39:24 PM, J.Kenyon wrote:
At 8/18/2010 11:38:30 PM, lovelife wrote:
Wouldn't the chance be exactly the same tho? I fail to see how dorr #1 affects door 2's chance of having it, unless door #1 had it.

Just model it out and it will come to you. Shut up and do it.

I fail. The coin somehow escaped all three cups. By the logic that trying to do it will give me the answer I can say that there is a 0% chance its cup #3
Without Royal there is a hole inside of me, I have no choice but to leave
lovelife
Posts: 14,629
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8/18/2010 11:41:59 PM
Posted: 6 years ago
At 8/18/2010 11:41:33 PM, Nags wrote:
At 8/18/2010 11:39:24 PM, J.Kenyon wrote:
Shut up and do it.

A creed to live by, lovelife.

>.<
Without Royal there is a hole inside of me, I have no choice but to leave
Xer
Posts: 7,776
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8/18/2010 11:42:14 PM
Posted: 6 years ago
At 8/18/2010 11:41:33 PM, lovelife wrote:
I fail. The coin somehow escaped all three cups. By the logic that trying to do it will give me the answer I can say that there is a 0% chance its cup #3

Can someone translate this to English?
Freeman
Posts: 1,239
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8/18/2010 11:43:04 PM
Posted: 6 years ago
At 8/18/2010 11:37:02 PM, mattrodstrom wrote:
At 8/18/2010 11:34:56 PM, Freeman wrote:
For instance, you could probably find at least one well known, respected, and credible anthropologist that believes humans and Neanderthals had children.

Just FYI... I'm pretty sure that's the consensus now...

As someone who has studied this issue in some depth, I don't think so. There may have been a few children like that, but it wasn't common. Moreover, our respective genomes are too dissimilar for there to have been any significant interbreeding between Neanderthals and H. Sapiens.

If you disagree, then prove me wrong with evidence.

in fact if you're a stripe of Eurasian... You're prolly between 1-4% Neanderthal
Chancellor of Propaganda and Foreign Relations in the Franklin administration.

"I intend to live forever. So far, so good." -- Steven Wright
mattrodstrom
Posts: 12,028
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8/18/2010 11:43:15 PM
Posted: 6 years ago
At 8/18/2010 11:38:30 PM, lovelife wrote:
Wouldn't the chance be exactly the same tho? I fail to see how dorr #1 affects door 2's chance of having it, unless door #1 had it.

A) Door #1 DOESN'T Affect 2's chances.

B) from the top... Your pick #2 has a 1/3 chance.

C) the NON-Picked Doors 1&3 have a 2/3 chance.

D) Door 1 is revealed Empty... door 1 has no chance

BUT C STILL HOLDS TRUE... the NON Picked doors (1&3) STILL have a 2/3 chance.... NOTHING happened that changes this.... you've just found out that door 1 has no chance.

so.... if (1&3) still have 2/3 chance... and 1 has no chance...

then (3) has 2/3 chance!
"He who does not know how to put his will into things at least puts a meaning into them: that is, he believes there is a will in them already."

Metaphysics:
"The science.. which deals with the fundamental errors of mankind - but as if they were the fundamental truths."
lovelife
Posts: 14,629
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8/18/2010 11:43:51 PM
Posted: 6 years ago
At 8/18/2010 11:42:14 PM, Nags wrote:
At 8/18/2010 11:41:33 PM, lovelife wrote:
I fail. The coin somehow escaped all three cups. By the logic that trying to do it will give me the answer I can say that there is a 0% chance its cup #3

Can someone translate this to English?

I am not meant to learn.
Without Royal there is a hole inside of me, I have no choice but to leave
mattrodstrom
Posts: 12,028
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8/18/2010 11:45:22 PM
Posted: 6 years ago
At 8/18/2010 11:43:04 PM, Freeman wrote:
At 8/18/2010 11:37:02 PM, mattrodstrom wrote:
At 8/18/2010 11:34:56 PM, Freeman wrote:
For instance, you could probably find at least one well known, respected, and credible anthropologist that believes humans and Neanderthals had children.

Just FYI... I'm pretty sure that's the consensus now...

As someone who has studied this issue in some depth, I don't think so.

before I go looking for the article...

have you been under a rock since May??? or have you heard the same news I've been hearing?
"He who does not know how to put his will into things at least puts a meaning into them: that is, he believes there is a will in them already."

Metaphysics:
"The science.. which deals with the fundamental errors of mankind - but as if they were the fundamental truths."
lovelife
Posts: 14,629
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8/18/2010 11:45:30 PM
Posted: 6 years ago
At 8/18/2010 11:43:15 PM, mattrodstrom wrote:
At 8/18/2010 11:38:30 PM, lovelife wrote:
Wouldn't the chance be exactly the same tho? I fail to see how dorr #1 affects door 2's chance of having it, unless door #1 had it.

A) Door #1 DOESN'T Affect 2's chances.

B) from the top... Your pick #2 has a 1/3 chance.

C) the NON-Picked Doors 1&3 have a 2/3 chance.

D) Door 1 is revealed Empty... door 1 has no chance

BUT C STILL HOLDS TRUE... the NON Picked doors (1&3) STILL have a 2/3 chance.... NOTHING happened that changes this.... you've just found out that door 1 has no chance.

so.... if (1&3) still have 2/3 chance... and 1 has no chance...

then (3) has 2/3 chance!

So does 2....? Out of those remaining 2 and 3 each have a 1/2 chance. You shouldn't have to change your guess because the odds will be better if you do. The odds do not change, unless someone is cheating.
Without Royal there is a hole inside of me, I have no choice but to leave
Xer
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8/18/2010 11:47:17 PM
Posted: 6 years ago
At 8/18/2010 11:43:15 PM, mattrodstrom wrote:
BUT C STILL HOLDS TRUE... the NON Picked doors (1&3) STILL have a 2/3 chance.... NOTHING happened that changes this.... you've just found out that door 1 has no chance.

so.... if (1&3) still have 2/3 chance... and 1 has no chance...

Door 1 (1/3) + Door 3 (1/3) = 2/3
subtract Door 1 (1/3) from 2/3 [because the host revealed Door 1 was wrong]
= 1/3
Thus, Door 3 still only has a 1/3 chance of being the correct door.

Where am I going wrong here.
lovelife
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8/18/2010 11:49:22 PM
Posted: 6 years ago
At 8/18/2010 11:47:17 PM, Nags wrote:
At 8/18/2010 11:43:15 PM, mattrodstrom wrote:
BUT C STILL HOLDS TRUE... the NON Picked doors (1&3) STILL have a 2/3 chance.... NOTHING happened that changes this.... you've just found out that door 1 has no chance.

so.... if (1&3) still have 2/3 chance... and 1 has no chance...

Door 1 (1/3) + Door 3 (1/3) = 2/3
subtract Door 1 (1/3) from 2/3 [because the host revealed Door 1 was wrong]
= 1/3
Thus, Door 3 still only has a 1/3 chance of being the correct door.

Where am I going wrong here.

Thats what I was thinking.
Without Royal there is a hole inside of me, I have no choice but to leave
Puck
Posts: 6,457
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8/18/2010 11:50:17 PM
Posted: 6 years ago
At 8/18/2010 11:47:17 PM, Nags wrote:
At 8/18/2010 11:43:15 PM, mattrodstrom wrote:
BUT C STILL HOLDS TRUE... the NON Picked doors (1&3) STILL have a 2/3 chance.... NOTHING happened that changes this.... you've just found out that door 1 has no chance.

so.... if (1&3) still have 2/3 chance... and 1 has no chance...

Door 1 (1/3) + Door 3 (1/3) = 2/3
subtract Door 1 (1/3) from 2/3 [because the host revealed Door 1 was wrong]
= 1/3
Thus, Door 3 still only has a 1/3 chance of being the correct door.

Where am I going wrong here.

The initial setup is a 2/3 ratio in favour of the game (a loss). Since the host is forced to reveal a door where the prize is not located, swapping which door you chose leads to the improved odds.
Freeman
Posts: 1,239
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8/18/2010 11:51:05 PM
Posted: 6 years ago
At 8/18/2010 11:45:22 PM, mattrodstrom wrote:
At 8/18/2010 11:43:04 PM, Freeman wrote:
At 8/18/2010 11:37:02 PM, mattrodstrom wrote:
At 8/18/2010 11:34:56 PM, Freeman wrote:
For instance, you could probably find at least one well known, respected, and credible anthropologist that believes humans and Neanderthals had children.

Just FYI... I'm pretty sure that's the consensus now...

As someone who has studied this issue in some depth, I don't think so.

before I go looking for the article...

have you been under a rock since May??? or have you heard the same news I've been hearing?

What have you been hearing?

*Begins reading* http://www.nytimes.com...
Chancellor of Propaganda and Foreign Relations in the Franklin administration.

"I intend to live forever. So far, so good." -- Steven Wright
Freeman
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8/18/2010 11:54:40 PM
Posted: 6 years ago
At 8/18/2010 11:51:05 PM, Freeman wrote:
At 8/18/2010 11:45:22 PM, mattrodstrom wrote:
At 8/18/2010 11:43:04 PM, Freeman wrote:
At 8/18/2010 11:37:02 PM, mattrodstrom wrote:
At 8/18/2010 11:34:56 PM, Freeman wrote:
For instance, you could probably find at least one well known, respected, and credible anthropologist that believes humans and Neanderthals had children.

Just FYI... I'm pretty sure that's the consensus now...

As someone who has studied this issue in some depth, I don't think so.

before I go looking for the article...

have you been under a rock since May??? or have you heard the same news I've been hearing?

What have you been hearing?


*Begins reading* http://www.nytimes.com...

Hmm... http://www.usatoday.com...

This is most peculiar indeed. Most of what I know on this subject comes from textbooks that are at least one year old at this point.
Chancellor of Propaganda and Foreign Relations in the Franklin administration.

"I intend to live forever. So far, so good." -- Steven Wright
mattrodstrom
Posts: 12,028
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8/18/2010 11:55:41 PM
Posted: 6 years ago
At 8/18/2010 11:51:05 PM, Freeman wrote:
At 8/18/2010 11:45:22 PM, mattrodstrom wrote:
At 8/18/2010 11:43:04 PM, Freeman wrote:
At 8/18/2010 11:37:02 PM, mattrodstrom wrote:
At 8/18/2010 11:34:56 PM, Freeman wrote:
For instance, you could probably find at least one well known, respected, and credible anthropologist that believes humans and Neanderthals had children.

Just FYI... I'm pretty sure that's the consensus now...

As someone who has studied this issue in some depth, I don't think so.

before I go looking for the article...

have you been under a rock since May??? or have you heard the same news I've been hearing?

What have you been hearing?


*Begins reading* http://www.nytimes.com...

yep
"He who does not know how to put his will into things at least puts a meaning into them: that is, he believes there is a will in them already."

Metaphysics:
"The science.. which deals with the fundamental errors of mankind - but as if they were the fundamental truths."
lovelife
Posts: 14,629
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8/18/2010 11:56:37 PM
Posted: 6 years ago
At 8/18/2010 11:50:17 PM, Puck wrote:
At 8/18/2010 11:47:17 PM, Nags wrote:
At 8/18/2010 11:43:15 PM, mattrodstrom wrote:
BUT C STILL HOLDS TRUE... the NON Picked doors (1&3) STILL have a 2/3 chance.... NOTHING happened that changes this.... you've just found out that door 1 has no chance.

so.... if (1&3) still have 2/3 chance... and 1 has no chance...

Door 1 (1/3) + Door 3 (1/3) = 2/3
subtract Door 1 (1/3) from 2/3 [because the host revealed Door 1 was wrong]
= 1/3
Thus, Door 3 still only has a 1/3 chance of being the correct door.

Where am I going wrong here.

The initial setup is a 2/3 ratio in favour of the game (a loss). Since the host is forced to reveal a door where the prize is not located, swapping which door you chose leads to the improved odds.

What is it with males and trying to make people lose the game. It only works on me when people say something about losing it too. Never had that problem with females...

Anyway if he revealed a fake how exactly does that make the odds any higher...?
Without Royal there is a hole inside of me, I have no choice but to leave
J.Kenyon
Posts: 4,194
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8/18/2010 11:57:05 PM
Posted: 6 years ago
Ok, here we go.

Since you're too lazy to do it yourself, I'll model it out for you.

( ) ( ) ($)

As you can see, door 3 contains the prize. You can pick any one of the three. Let's play out each possibilty.

You pick door 1. The game show host opens up door 2, revealing that the prize is not there. If you switch, you will pick door 3 and win the prize.

OR

You pick door 2. The game show host opens up door 1, revealing that the prize is not there. If you switch, you will pick door 3 and win the prize.

OR

You pick door 3. The game show host opens up either door 1 or door 2, revealing that the prize is not there. If you switch, you will pick either door 1 or door 2 and WILL NOT win the prize.

CONCLUSION:
As you can see, out of the three possible scenarios, switching will win you the prize twice. Not switching will only win you the prize once. Simple, no?