I didn't respond before because I was skimming... and I had no idea what you were saying. So I just reread this more carefully, then followed the conversation. Maybe people are not responding because it's phrased in a way they can't easily understand.
Funny, it made perfect sense to me.
To put it in English: What percentage of a group's members have to belong the subgroup for you to accept personally that the next member of the group you run across would ALSO fall within the subgroup?
An interesting idea, English
Or, to borrow from an old maxim and put flesh on the example, what percentage of Cretians would have to be known to be liars for you to accept that the NEXT Cretian you met is also a liar?
- What would the percentage need to be?
- What argument(s) or situation(s) would make you rethink your idea that perhaps your percentage is too high, or even that Cretians are not really liars at all?
- What would the percentage have to be so that you'd draw closure on the idea -- never willing to question again the proposition that a certain % of Cretians are liars?
To highlight the fallacy of the accident in particular, we can take an example from
Wikipedia:
1. Cutting people with a knife is a crime.
2. Surgeons cut people with knives.
[---------------------------------------]
3. Surgeons are criminals.
* * * *
Actually, I think it's a wonderful topic simply because of the practical nature of it. We all makes decisions like this every day, we just normally don't realize we're making the calculations.
Every time we judge someone or evaluate them without knowing all the information, we are making "hunches" based on how much proof we need that our hunch is probably true.
- The guy selling things out of the booth -- based on my knowledge of booth vendors, his appearance, the things he's selling, and other characteristics I can observe, what are the odds that he is ripping me off.... and probably by how much?
- The guy taking me out for a date -- based on my knowledge of his appearance, articulateness, occupation, background, topics of conversation, etc, what's the odds he's just out to score and not good LTR material?
- The woman running for office -- based on my knowledge of elections and politicians, her personality, her presentation, the groups she affiliates with etc., what's the odd's she'll be a good leader?
I mean, this is what comes up in religious and political discussions ALL the time (usually to support cynicism) -- "Oh, they're a <religion or party affiliation", they're just out to <some nefarious deed>, you can't trust them!"
What percentage of experiences have to be negative, etc., to result in this sort of blanket judgment, and what sort of proof is needed to change it (if it can be)?
The thing about this juegement from probability is that most people do it rather poorly. There are whole research programs based on the way most people assign probabilities to events in inconsistent and/or illogical ways.
Well, I am neither a Bayesian nor a Frequentist, nor do I care about what theories, ideas or statements are probably true. Talk of probability, especially in regard to rational decision-making, is mostly a load of rubbish.
In a way, I agree with you. If I have to rely on an argument like the above, it would be because I had no other line of reasoning.
P:Consider, it rains most of the time in Seattle (assume this is true for now)
C:Therefore it is likely raining now in Seattle.
C may or may not be ture. In a sense, the statement is a good conclusion. However, it is immediately overturned by going outside and not finding it to be raining (assuming it is not raining in Seatle at the moment).
Every branch of science uses statistics to form their conclusions. However, no matter what the statistics of medical symptoms may say, something fundamental about the mechanisms of a particular human is what determines whether or not the diagnosis is correct.
I am not much of a card player. But, I know, that even if you play by the "odds," you can loose. There is a reason they call it gambling.
Ther is even a claim that, if you play by the "odds," over the long term, you come out ahead. Again, there is no gaurantee of this either, just an increasing likelyhood that the numbers come out as expected. This is assuming a lot of things about fair play (and sometimes even assumptions about sane play from other players).
The financial markets are a still more complicated version of the same thing.