Common sayings expressed in Mathematical notation

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naturalplastic
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10 Oct 2017, 7:38 pm

Try:
"Fool me once, shame on you. Fool me twice, shame on me."

And

"You can fool some of the people all of the time, and all of the people some of the time. But you can't fool all of the people all of the time."

And..

"There must be fifty ways to leave your lover. "

and

"the early bird catches the worm."



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12 Oct 2017, 1:31 pm

f∈Evil f(love of money)=0



naturalplastic
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12 Oct 2017, 5:26 pm

love of money = [square root sign] over "evil"

(All ya' need) minus :heart: = zero



jrjones9933
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13 Oct 2017, 10:08 am

naturalplastic wrote:
Try:
"Fool me once, shame on you. Fool me twice, shame on me."


The underlying concept expressed in probabilities seems to include the idea of making predictions in the face of deception. Game theory demonstrates the Best Response Functions for these kinds of situations in simpler terms.

To boil it down, if you get information from another party to inform your decision, you have to consider the alignment of your goals and the other party's goals. If you both benefit from the same outcome, the BRF of the other party is to give you accurate information, and your BRF is to trust them. If you benefit from completely different outcomes, then they have no incentive to give you accurate information and you have no reason to make your decision based on the information they give you.

The cases in between, where there is some overlap between goals, where both you and your informer both benefit to some degree from the same outcomes, give you a BRF that uses the similarity between your goals to decide how much to utilize the information.

The saying, "fool me once, shame on you; fool me twice, shame on me," oversimplifies this dynamic by reducing the choices to two, eliminating the in-between cases. The first instance of making a detrimental or at least non-beneficial decision proves that you benefit from different outcomes, in this conception. The saying seems like an expression of Black & White thinking.

I don't think it has mathematical validity, so it's a really interesting case. Let's say that I'm the decider trying to choose a number as close as possible to some unknown target, and I benefit in direct proportion to how close the number is to that target up to a range of eight units. My informant also benefits from my choice in the same way, but they have a different target number that is four lower than my target. They know my target number, but they can tell me whatever they want about what that number is. From there, you can specify the benefits in equations, and actually find the best number for the informant to tell the decider (lower than the decider's target, but not too much lower), and the best number for the decider to choose (higher than what they're told by some specific amount). However, in the simplified mathematical conception, the mathematician knows all of the underlying functions exactly, and that's not often the case in reality; we have to wing it on our best-informed best guesses.

The saying indicates that the decider and the informer are playing a repeated game. In the standard Game Theory conception, the decider uses the outcomes to figure out those underlying functions, and can make better decisions as they play more rounds of the same game. In the conception given by the saying, one bad decision or bad guess by the decider about the motivations of the informer indicates that the decider and informer don't have any overlapping areas of interest, and that the decider should stop playing that game altogether.

If you consider the Cognitive Miser hypothesis as valid, and take into account all the costs of figuring out the motivations of an unreliable informant, and the likely availability of other informants and other games to play, the heuristic makes some sense. It may be more beneficial to only take information from people with whom you have completely shared interests. I'm skeptical, though.


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naturalplastic
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16 Oct 2017, 5:17 pm

^
You MUST be putting us all on.

Its pretty simple. And it IS a rather black and white situation.

IF X fools Y more than zero times but less than two times than X is culpable.

But if X fools Y two, or more, times then Y is culpable.

Sooo...

The culpability factor of X and Y are both determined by number of times X fools Y.

So the CF of X equals plus 1 if X F's over Y one time. But the CF of X is zero, and the CF of Y becomes plus one if the FF (fooling frequency) exceeds one.



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17 Oct 2017, 6:55 pm

GR8 thread!! !! ! :nerdy: :nerdy: :nerdy: :nerdy: :D :D :D :D



naturalplastic
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18 Oct 2017, 2:08 pm

A couple more for the mathletes to chew on.

"Don't count your chickens before they hatch".

"Don't buy a pig in a poke".



jrjones9933
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18 Oct 2017, 2:18 pm

Not putting you on :-(


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naturalplastic
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18 Oct 2017, 6:14 pm

Sorry.

Not even sure why I said that.

Ironically you are probably the first participant on this thread who is NOT being slightly tongue-in-cheek (including me). :)

Your post is prolly over my head. But I will try to digest it a second time! :lol:



jrjones9933
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20 Oct 2017, 6:35 pm

It's okay.

As much as possible, I want to tie these ideas into established economic ideas. They aren't easy to understand; it took me considerable effort. I tried to find an open source game theory textbook that would explain it better, but I couldn't find a good free chapter on Games of Incomplete Information.


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