Ignoring "Background Probability" - The luckyme Syndrome

[David Sklansky]

Luckyme is a regular poster on these forums with a good mind, a very good heart, and a blindspot regarding Baye's Theorem. I'm guessing a lot of others have this same blindspot. So I would like to address it here. For now, not in detail. Others can elaborate.

The blindspot is evident when luckyme or others insist that all things can be evalusted properly on a "case by case basis" Was Jesus resurrected? (Look at the evidence) Should we hire this Hell's Angel? (Interview him) etc.etc.

I believe the blindspot derives partially from mathematical inexpertise and partially from the laudable desire not to discriminate. So luckyme wants to ignore the fact that miracles have never been verified or that Hell's Angels are (hypothetically) four times more likely to be chronically late.

But it is simply wrong to think this way in the vast number of cases. Background probability, if that is a real term, has an effect on overall probability whether we like it or not. A simple example occurs in sports betting. If the home team wins 60% of all games and you evaluate team A to be slightly better than team B you still must bet B if it is at home.

Here is a better example. Suppose you know that 50% of American, married, 25 year olds divorce by age 60. And that 90% of Swedish married 25 year olds do. You randomly select an American and a Swedish 25 year old couple to spend a day with. Both couples seem very happy. You now must make a line that they will get divorced. Luckyme would like to say that they are both, perhaps 20%. But he would almost certainly be wrong. (The exception would be if the 50-90 discrepancy was fully obvious at age 25. In other words, Swedish couples were vastly less likely to get along even at that young age. So finding a friendly young Swedish couple would be the whole ball of wax. Possible but highly unlikely). If the American couple was truly 20%, the Swedish couple is higher. Perhaps 35%. That's still a lot lower than the background probability of 90% but nowhere near the American's.

I completely understand why the above concept has a nasty underlining to it. And therefore in trivial cases shouldn't even be mentioned. But in important cases most would say it needs to be recognized. Regardless it needs to be understood if you are a card carrying two plus twoer which is frankly my only motivation for bringing it up.

[Brocktoon]

So this is just a creative way to start a racial profiling thread right?

[David Sklansky]

DEFINITELY NOT. The fact that arguments against racial profiling are usually flawed bothers me ONLY in the mathematical sense. Put another way if the government announced "in spite of the fact that this policy will likely cause more people to die, we are stopping profiling because we don't want minority children to feel bad" I would have no problem with it.

I've said many times that my subjects pick me. Because people are making flawed arguments about them. I don't pick subjects base on how important they are to me.

[luckyme]

Hmmmm...garshh, blush, I'm flattered, that's the second syndrome I've had named in my honor, the other was more threatening.

Your examples seem yawningly obvious, and I don't find them particularly nasty..the numbers are the numbers, so I think you've misfocused here.

Since I agree with the Hell's angel one, I'll deal with the Resurrection problem. Remember you're having an argument with a believer. if the strongest case you can make is "miracles haven't happened" you're just right back to the basic disagreement, you haven't argued anything.
His strongest argument on that line of thinking is to stick out his tongue and say "have so, have so".

Iow, he's not believing in them because of an misapplication of Bayes. He'd like to think he has evidence. If you're going to make a strong argument to him you need to kick out the planks he's standing on, not the ones you think he should be.
It's not an argument against Bayes' that's made in those cases, it's a claim that the Bayes argument isn't 'strong' in the sense of 'winning the point'.

I'm off to a family function, but wanted to get some response to you seeing I'm now in the Annals of Sklansk.

I'll be baaaack, luckyme

[elrudo]

David,

insurance companies charging higher prices for people with 'bad postal codes', even if what is insured has nothing to do with where people live, is that an example of the same thing in practice ?

[Bibigon]

[ QUOTE ]
David,

insurance companies charging higher prices for people with 'bad postal codes', even if what is insured has nothing to do with where people live, is that an example of the same thing in practice ?

[/ QUOTE ]

Not to speak for David, but yes, this is a pretty similar example. Insurance companies actually ignore some factors similar to this, in spite of the fact that they would be helpful, precisely because it is hard to sell the idea of background probability to some people in terms of an insurance premium. The belief is that the backlash against doing so would outweigh the mathematical benefits.

[mikechops]

[ QUOTE ]
So this is just a creative way to start a racial profiling thread right?


[/ QUOTE ]

I have to admit this was my thought on reading the OP [img]/images/graemlins/smile.gif[/img] DS is absolutely correct to state the mathmatics may justify taking a negative view on Hell's Angels, Swedish couples or away baseball teams, based upon their membership of a group.

The correct argument against racial profiling is not to say it is mathmatically unsound. The cost of alienating a whole group of mainly decent people and the unpleasantness for the rest of us of living in a society where people aren't treated equally, mean it's just not worth it.

[Bibigon]

[ QUOTE ]
The correct argument against racial profiling is not to say it is mathmatically unsound. The cost of alienating a whole group of mainly decent people and the unpleasantness for the rest of us of living in a society where people aren't treated equally, mean it's just not worth it. /quote]

Well, not so much so that it's not worth it as that those are real costs that must be considered in the cost/benefit analysis in the end - it's not clear from the reasoning in your post that it's not worth it.

[mikechops]

I'm not saying it is never worth it. You are right it is a cost/benifit decision. Driving while black? Ignore it. Flying while Saudi Arabian? hmmm.

[poker-penguin]

[ QUOTE ]
I'm not saying it is never worth it. You are right it is a cost/benifit decision. Driving while black? Ignore it. Flying while Saudi Arabian? hmmm.

[/ QUOTE ]

Arab is the new black.