First sidenote that dont assume that if something is a heuristic it is automatically a wrong way of thinking.(sorry if i misinterpret this, because you dont explicitly say this at all :) In some situations simple heuristics will outperform regression analysis for example.
But about your mainpoint. If I understood right this is actually a problem of violating so called “ratio rule”.
(1) The degree to which c is representative of S is indicated by the conditional propability p (c | S)- that is, the propability of members of S have characterestic c.
(2) The propability that the characteristic c implies membership S is given by p (S | c). (Like you write)
(3) p (c | S) / p (S | c) = p(c) / p(S)
This is the Ratio Rule= Ratio of inverse propabilities equals the ratio of simple propabilities. So to equate these two propabilities p(c|S) and p(S|c) in the absence of equating ALSO the simple propabilitis is just wrong and bad thinking.
Representative thinking does not reflect these differences between p(c|S) and p(S|c) and introduces a symmetry in the map (thought) that does not exist in the world.
For example: “Home is the most dangerous place in the world because most accidents happen in home. So stay away from home!!!”
--> This is confusion about the propability of accident given being home with propability being home given accident.
Thank you. English isn’t my first language, so for me feedback means a lot. Especially positive :)
My point was that representative heuristic made two errors: firstly, it violates “ratio rule” (= equates P(S|c) and P(c|S)), and secondly, sometimes it replaces P(c|S) with something else. That means that the popular idea “well, just treat it as P(c|S) instead of P(S|c); if you add P(c|~S) and P(S), then everything will be OK ” doesn’t always work.
The main point of our disagreement seem to be this:
(1) The degree to which c is representative of S is indicated by the conditional propability p (c | S)- that is, the propability of members of S have characterestic c.
1) Think about stereotypes. They are “represent” their classes well, yet it’s extremely unlikely to actually meet the Platonic Ideal of Jew.
(also, sometimes there is some incentive for members of ethnic group to hide their lineage; if so, then P(stereotypical characteristics|member of group) is extremely low, yet the degree of resemblance is very high)
(this is somewhat reminds me of the section about Planning Fallacy in my earlier post).
2) I think that it can be argued that the degree of resemblance should involve P(c|~S) in some way. If it’s very low, then c is very representative of S, even if P(c|S) isn’t high.
Overall, inferential distances got me this time; I’m probably going to rewrite this post. If you have some ideas about how this text could be improved, I will be glad to hear them.
Thanks for the post. I love it.
My comments:
First sidenote that dont assume that if something is a heuristic it is automatically a wrong way of thinking.(sorry if i misinterpret this, because you dont explicitly say this at all :) In some situations simple heuristics will outperform regression analysis for example.
But about your mainpoint. If I understood right this is actually a problem of violating so called “ratio rule”.
(1) The degree to which c is representative of S is indicated by the conditional propability p (c | S)- that is, the propability of members of S have characterestic c.
(2) The propability that the characteristic c implies membership S is given by p (S | c). (Like you write)
(3) p (c | S) / p (S | c) = p(c) / p(S)
This is the Ratio Rule= Ratio of inverse propabilities equals the ratio of simple propabilities. So to equate these two propabilities p(c|S) and p(S|c) in the absence of equating ALSO the simple propabilitis is just wrong and bad thinking.
Representative thinking does not reflect these differences between p(c|S) and p(S|c) and introduces a symmetry in the map (thought) that does not exist in the world.
For example: “Home is the most dangerous place in the world because most accidents happen in home. So stay away from home!!!” --> This is confusion about the propability of accident given being home with propability being home given accident.
Thank you. English isn’t my first language, so for me feedback means a lot. Especially positive :)
My point was that representative heuristic made two errors: firstly, it violates “ratio rule” (= equates P(S|c) and P(c|S)), and secondly, sometimes it replaces P(c|S) with something else. That means that the popular idea “well, just treat it as P(c|S) instead of P(S|c); if you add P(c|~S) and P(S), then everything will be OK ” doesn’t always work.
The main point of our disagreement seem to be this:
1) Think about stereotypes. They are “represent” their classes well, yet it’s extremely unlikely to actually meet the Platonic Ideal of Jew.
(also, sometimes there is some incentive for members of ethnic group to hide their lineage; if so, then P(stereotypical characteristics|member of group) is extremely low, yet the degree of resemblance is very high)
(this is somewhat reminds me of the section about Planning Fallacy in my earlier post).
2) I think that it can be argued that the degree of resemblance should involve P(c|~S) in some way. If it’s very low, then c is very representative of S, even if P(c|S) isn’t high.
Overall, inferential distances got me this time; I’m probably going to rewrite this post. If you have some ideas about how this text could be improved, I will be glad to hear them.