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>> The conjunction of two events can’t be more likely than just one event by itself. > This is mathematically incorrect. If two events are mutually dependent o
by smadge 8y ago
>> The conjunction of two events can’t be more likely than just one event by itself.
> This is mathematically incorrect. If two events are mutually dependent on the other to occur then two events are more likely to occur together than either or independently.
The original statement is correct. You are talking about conditional probability: the probability that one event will occur given that another event has occurred. i.e. if A and B are two events P(A|B), read as the probability of A given B. This is equal to P(A and B)/P(B). Notice that, The conjunction of the two events, P(A and B), is divided by the probability of B, P(B). We have reduced the probability space to the smaller space of just B. The conjunction of two events is just their set intersection (at least in a probability system which defines events as sets of outcomes) and can never be larger than either event.
- s-shellfish 8y agoThat assumes events are sequentially occurring.
- tetromino_ 8y agoI think there's an issue of terminology. Please see https://en.wikipedia.org/wiki/Event_(probability_theory) https://en.wikipedia.org/wiki/Event_(probability_theory) and https://en.wikipedia.org/wiki/Probability_space https://en.wikipedia.org/wiki/Probability_space for what mathematical statistics means by the term "event". I suspect that what you are calling "events" are actually values of some function defined on the set of (mathematical) events. Such a function is called a random variable. The values of a random variable are a major object of study in statistics - but they are not events.
- s-shellfish 8y agoI'm trying to direct this conversation away from using logic and math to reason about interpersonal relationships. It's garbage. Math talks about math. Logic talks about logic. This article conflates it with how people think about one another. They are calling an event that occurs twice a singular event. My mind, your mind, the same statement, understood and accepted twice, possibly at different points in time (which is obvious given the fact that I have to literally hit send on this message) but you may be thinking the same thoughts as I at the same time, mutually dependent because we are all idiots that think it's fine to use logic and math to describe all minds. It's not an RV when it comes to thoughts you choose to think! The RV is the thoughts you don't want to think.
- deleted 8y ago[deleted]
- smadge 8y agoThe origin mask quote(“The conjunction of two events can’t be more likely than just one event by itself.”) was in the context of an experiment in which subjects were given a description of a person and they responded that it was more likely she was a “feminist bank-teller” than either just a feminist or just a bank-teller. Here the appeal to formal probability is justified because obviously there are more bank-tellers than feminist bank-tellers, and likewise more feminists than feminist bank tellers.
- s-shellfish 8y agoThat's not the point of the article. The greater context is about the relation between an individual mind and other minds. Paraconsistent logic allows contradicting statements to be held without implying one must be true or the other. Why would there obviously be more feminist bank tellers than female bank tellers? What if there's a cultural connection that guides both decisions to be made together? Don't people aggregate personality details in clusters by choice in order to be accepted via conformity? Isn't that the principle recommendation engines operate on fundamentally?
- losvedir 8y ago> Why would there obviously be more feminist bank tellers than female bank tellers? No! You still aren't paying attention and at this point I think you might be just trolling, but here's one more good faith response. To reiterate, the article brings up the interesting result that people think it's more likely that someone is a "feminist bank teller" than that she is a "bank teller". To be clear there are some number of bank tellers, and of them, some are feminist. There cannot be more people who are feminist and bank tellers than people who are simply bank tellers. The feminist ones are a subset of all bank tellers. So the probability that someone is both is less than or equal to the probability that someone is just a bank teller. If you know them well, and they go to marches and such and your ascertain that they are definitely feminist, then the probability that they are both is equal to (but not greater) than the probability that they're a bank teller.
- derangedHorse 8y agoCalculating the probability that A and a sequential event B will happen rather than inferring the probability of A given an a posteriori event B might be more intuitive to bring up in this argument. An easy way to explain how the conclusion was derived is just by considering that we have to multiply probabilities to calculate the probability of a conjunction of events, and since most probabilities are below 1, the number will always be less than or equal to a single event.
- s-shellfish 8y agoThis doesn't take people being able to choose how to think into account.
- derangedHorse 8y agoThe logic is sound so I'm not sure how "being able to choose how to think" changes anything
- s-shellfish 8y agoGo back to the original article. Now think about it being used to disprove everything you think about things instead of it being used to prove everything you think about things.