More About My One Major Erroneous Post- Important

[David Sklansky]

I am still haunted by the one time I made a serious error about a non trivial subject in a post that was not merely expressing my opinion. Utah caught it and I acknowledged it. But no one else seemed to pay much attention to it. in spite of its importance.

I posted that if John and Mary are arguing about whether A or B is more likely to be true, you must bet on A, if that is John's side, and the following three things are all the case.

1. John is clearly smarter than Mary as far as anlytical thinking ability is concerned.

2. John is clearly more knowledgeable about the A vs B subject than Mary.

3. John is biased in that he personally would prefer B to be true.

Seems like a slam dunk right? I thought so too. Until Utah pointed out that it still might be right to bet on B if MARY IS WILLING TO LAY MUCH HIGHER ODDS ON B THAN JOHN IS WILLING TO LAY ON A. Assuming of course that they have the same amount of gamble in them. In other words their degree of certainty is a fourth factor. Thus If John is only a tad smarter, a tad more knowledgeable and only slightly biased against A (in that he would personally prefer slightly that B be true) and he makes A a 60% shot, you should still bet on B if Mary makes it a 95% shot.

The above may seem wrong to you. You may argue that it doesn't matter that John only makes A a slight favorite if he is a better linemaker. Who cares what Mary makes the line. But you would be wrong. Here is a concrete example.

The Yankees are playing the Dodgers. John knows these two teams better than Mary. He also is a better baseball bettor. He finds 100 bets a year and earns 9% on them. Mary makes 50 bets and earns 7%. John says the Yankees are 53% to win even though he is a Dodger fan. Mary makes the Dodgers 65%. And the reason she does is that she has uncovered the fact that in the last 50 years when a team scores more than 15 runs two games in a row, they go on to lose the third game 71% of the time. And this is the situation here. She know the Yankees are the better team and she understands regression to the mean, so she shades it down to 65%

Notice that this scenario does not violate the stated premises. Mary is still the less knowledgeble, and less intelligent handicapper. This situation arises so rarely that her knowing it, and John not knowing it, doesn't change that. But when it does arise, Mary will be favored over John. She may not be the 65% she proclaims and bets she is. But she will almost certainly be above 50% even though John is fairly sure she isn't.

This stuff comes up all the time in real life so don't ignore it. And thank Utah, not me.

[pvn]

Thanks, David.

[ALLEN CONRAD]

Let's say I believe their is a 65% chance that god does not exist. But my gf is 95% sure that god does exist. This means that there is a better chance that god exists than does not.

And the 5th factor would be to what degree person A is smarter than person B

And the 6th factor maybe the emotional state of person b, Maybe they will be more certain due to a confrontational mood?

[Alex/Mugaaz]

I spent some time thinking about what the exception could be before reading your answer. The only one I could think of is if there was some information that Mary knows that John doesn't, and that this info trumps everything else.

I think this example doesn't work very well, because even if Mary was a complete moron she should be able to draw the same conclusion as long as she had that info. It seems to me that the if John is more knowledgeable than Mary you can't give Mary the only crucial piece of info.

Is it possible to provide an example where John knows everything Mary does (and then some), yet can still be trumped because Mary has a higher degree of certainty? I can't think of one.

[josh_x]

I think this is kind of intuitive/obvious when you think of it more simply without all the percentages and specific conditions. You would you trust: me who thinks probably x or my slightly dumber friend who is very sure y?

Q: If john and mary have the same information and mary thinks 99% A and john thinks 51% B, who do you bet with?

[Paul Levy]

This is an interesting concept that would be worth expanding on. What would the break-even points and the partial derivatives to each factor be?

[ALawPoker]

I agree with everything you're saying, but I think your original error is one of semantics. It just depends what exactly you mean by "more knowledgeable." In the example you give, John is more knowledgeable about baseball betting in general. But Mary is more knowledgeable about baseball betting when one of the teams has scored 15 runs in their last two games.

The error is just in generalizing what constitutes knowledge in a subject. But whether it's ever possible to recognize it from the outside, Mary truly "knows" more about the situation at hand than John.

[ALawPoker]

^^^ EDIT: In other words, if you knew Mary had this insight, you'd consider her the more knowledgeable of the specific subject at hand.


The degree to which they are sure, of course matters. But if someone (of equal or lesser thinking ability) is able be more sure, it is just because they have a more specialized knowledge. Their level of sureness is basically just a measure of this underlying specific knowledge.

[Shandrax]

[ QUOTE ]
I posted that if John and Mary are arguing about whether A or B is more likely to be true, you must bet on A, if that is John's side, and the following three things are all the case.

1. John is clearly smarter than Mary as far as anlytical thinking ability is concerned.

2. John is clearly more knowledgeable about the A vs B subject than Mary.

3. John is biased in that he personally would prefer B to be true.

Seems like a slam dunk right? I thought so too. Until Utah pointed out that it still might be right to bet on B if MARY IS WILLING TO LAY MUCH HIGHER ODDS ON B THAN JOHN IS WILLING TO LAY ON A. Assuming of course that they have the same amount of gamble in them. In other words their degree of certainty is a fourth factor. Thus If John is only a tad smarter, a tad more knowledgeable and only slightly biased against A (in that he would personally prefer slightly that B be true) and he makes A a 60% shot, you should still bet on B if Mary makes it a 95% shot.

The above may seem wrong to you. You may argue that it doesn't matter that John only makes A a slight favorite if he is a better linemaker. Who cares what Mary makes the line. But you would be wrong. Here is a concrete example.
.
.
And the reason she does is that she has uncovered the fact that in the last 50 years when a team scores more than 15 runs two games in a row, they go on to lose the third game 71% of the time. And this is the situation here.

[/ QUOTE ]

You are contradicting yourself. In your example, Mary knows a specific fact, that John doesn't know, which makes statement 2 false.

[Shandrax]

[ QUOTE ]
I am still haunted by the one time I made a serious error about a non trivial subject in a post that was not merely expressing my opinion.

[/ QUOTE ]

Btw, this statement may very well be your third or even fourth error.