/sci/ - Science & Math

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Anonymous Mon Aug 20 19:13:14 2018 No.9949249 [Reply] [Original]

can anyone solve the Sure Thing Paradox

I flip a coin. You can now bet £100 on whether it has landed on Heads or Tails.
If you don't bet anything -- I will give you £95.

If you know it landed on heads, you ought to make a bet.
If you know it landed on tails, you ought to make a bet.
You know it landed on heads or tail, therefore you ought to make a bet

>>	Anonymous Mon Aug 20 19:15:20 2018 No.9949252 Those two things can not be true at the same time.

>>	Anonymous Mon Aug 20 19:17:15 2018 No.9949256 >>9949249 >You know it landed on heads or tail, therefore you ought to make a bet Why?

Anonymous Mon Aug 20 19:24:26 2018 No.9949270

>>9949252
okay think about it this way:

say we have two mutually exclusive possibilities A and B and two choices x and y

if given A, you prefer the result of x to the result of y
AND if given B, you prefer the result of x to the result of y

Then you should prefer x to y. because regardless of whether A is the case or whether B is the case: the result of x is preferable to that of y

say:
x= {£100 if H, £70 if T
y={£80 if H, £50 if T

then x is preferable to y whether H or T -- therefore it must be preferable under uncertainty.

this is called the Sure Thing Principle. the paradox is that above -- it's quite difficult to solve

>>	Anonymous Mon Aug 20 19:46:45 2018 No.9949294 Why the hell would I want £?

>>	Anonymous Mon Aug 20 19:49:42 2018 No.9949302 >>9949294 you can exchange for things you want

>>	Anonymous Mon Aug 20 19:53:36 2018 No.9949313 >>9949249 if i know it has landed on either heads or tails, i make a bet, if I don‘t know, I don‘t bet, because I could be wrong, 50% of the time assuming a fair coin... where is the paradox?

>>	Anonymous Mon Aug 20 20:01:23 2018 No.9949324 >>9949249 I know it'll land on either head or tail, but I don't know whether it'll land on head or it'll land on tail. Expected profit for betting is 0<95. No bet.

>>	Anonymous Mon Aug 20 20:04:38 2018 No.9949327 >>9949270 >it's quite difficult to solve It's actually not. Just look at the expected earnings.

Anonymous Mon Aug 20 20:04:54 2018 No.9949328

>>9949270
>Then you should prefer x to y
Nope, because you are not given A and you are not given B. Only having knowledge of what the coin landed on BEFORE the bet is placed is preferable. But since you are not given that information, not betting is preferable. You're just reasoning off of vague language.

>>	Anonymous Mon Aug 20 20:07:39 2018 No.9949330 >>9949249 Me betting in any certain way doesn't influence the outcome. Whether I "ought" to bet or not is completely irrelevant. I'd take the free money over the 50/50 bet on an uncertain outcome.

>>	Anonymous Mon Aug 20 20:08:59 2018 No.9949331 >>9949249 This paradox can be solved by having more than 6 brain cells to rub together

>>	Anonymous Mon Aug 20 20:11:07 2018 No.9949332 >>9949249 >>9949270 What is the paradox?

Anonymous Mon Aug 20 20:15:31 2018 No.9949341
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>>9949313
>>9949324
>>9949327
yes: the reason it's paradoxical is because the answer is so obviously "DON'T BET"

the problem is that this violates the Sure Thing Principle:
"In decision theory, the sure-thing principle states that a decision maker who would take a certain action if he knew that event E has occurred, and also if he knew that the negation of E has occurred, should also take that same action if he knows nothing about E."
https://en.wikipedia.org/wiki/Sure-thing_principle

>>	Anonymous Mon Aug 20 20:16:54 2018 No.9949344 >>9949331 t. someone who can't even understand why this is paradoxical

>>	Anonymous Mon Aug 20 20:17:40 2018 No.9949345 >>9949341 LOL no it doesn't. The sure thing principle says that you should take the same action. Betting on A is not the same action as betting on B.

>>	Anonymous Mon Aug 20 20:21:23 2018 No.9949351 >>9949341 You are so dumb

Anonymous Mon Aug 20 20:22:20 2018 No.9949353

>>9949345
okay smarty-pants ;)
this is the first attack to the paradox. "betting" is not an action. "betting on H" and "betting on T" are the actions.

Now consider this.

1. your friend flips the coin
2. you can now decide to go to his house or to stay at home
3. if you are at his house, you must bet on either Heads or Tails
4. if you stayed at home you recieve £95, if you bet correctly you get £100, if incorrectly: £0

so just after you're friend flips the coin, do you make the action to visit him or do you make the action to stay at home? visiting your friend is surely a single action -- which is the best choice given certainty in H or certainty in T

>>	Anonymous Mon Aug 20 20:23:31 2018 No.9949355 >>9949351 do yo know what a paradox is you nut? im not saying you should bet. I'm asking you to resolve the paradox. do you think tarski literally thought you could clone a tennis ball?

>>	Anonymous Mon Aug 20 20:24:38 2018 No.9949357 >>9949355 >do you think tarski literally thought you could clone a tennis ball? Yes

>>	Anonymous Mon Aug 20 20:25:36 2018 No.9949359 >>9949353 If you have some point to make here then you are not expressing it very well. And stay off the drugs, okay?

>>	Anonymous Mon Aug 20 20:26:01 2018 No.9949360 >>9949353 If I know the outcome of the coin flip, I visit my friend. If I don't, I stay at home. Where's the paradox?

>>	Anonymous Mon Aug 20 20:29:00 2018 No.9949363 >>9949360 >Doesn't have a friend to visit I found it!

Anonymous Mon Aug 20 20:29:43 2018 No.9949365

>>9949353
>so just after you're friend flips the coin, do you make the action to visit him or do you make the action to stay at home? visiting your friend is surely a single action -- which is the best choice given certainty in H or certainty in T
Stay at home. The sure thing principle has no relevance since the actions are now "visiting your friend and betting A" and "visiting your friend and betting B" which is not the same. Simply visiting your friend with knowledge does not guarantee you the £100 since you have to bet correctly.

Anonymous Mon Aug 20 20:30:18 2018 No.9949366
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>>9949357
pic related

>>9949359
"In decision theory, the sure-thing principle states that a decision maker who would take a certain action if he knew that event E has occurred, and also if he knew that the negation of E has occurred, should also take that same action if he knows nothing about E."
This is intuitive. But implies that you ought to bet, which is unintuitive.
We must throw out the Sure Thing Principle, or else accept the result. We probably want to throw out the Sure Thing Principle -- which would be disastrous for decision theory and game theory

also
>stay off the dugs
youre never gonna make it

Anonymous Mon Aug 20 20:31:41 2018 No.9949368

>>9949360
im not gonna repeat myself
if youve never heard of the Sure Thing Principle then please just fucking google it

"In decision theory, the sure-thing principle states that a decision maker who would take a certain action if he knew that event E has occurred, and also if he knew that the negation of E has occurred, should also take that same action if he knows nothing about E."

>>	Anonymous Mon Aug 20 20:32:34 2018 No.9949371 >>9949368 Betting on A is not the same action as betting on B, so your thought experiment has nothing to do with the STP. You can't get around this.

Anonymous Mon Aug 20 20:33:20 2018 No.9949372

>>9949249

The answer is This is not a paradox under any definition.

The first two statements are conditional on your knowledge and are exactly the same as saying "if you know the answer you should bet."

The third statement is simply restating the options or possiblities.

So to translate into english:
1. if you know the answer you should bet
2. there are two answers
3. Therefore you should bet.

Does that make sense to you?

They are not the same story and are not connected in any way, so why would they violate exclusivity?

Anonymous Mon Aug 20 20:33:49 2018 No.9949373

>>9949365
so now we are lead to this:
what we think are sequences of actions are actually a single action.
every "sequence" actually being a distinct action

so i dont "brush my teeth" and then "comb my hair" and then "eat breakfast" etc -- but rather choose a single path from now until the end of time. seems sketchy

>>	Anonymous Mon Aug 20 20:33:56 2018 No.9949375 >>9949249 "You know it landed on heads or tails" is different from "You know it landed on heads OR You know it landed on tails". Stupid logiclet.

Anonymous Mon Aug 20 20:35:40 2018 No.9949376

>>9949371
yes, this is the initial reply that's used. but it was quickly modified:
>>9949353

ps: this isnt something ive come up with. i am aware of the responses. i just wanted to see what /sci/ thought about apparent paradoxes in axiomatic decision theory

>>	Anonymous Mon Aug 20 20:35:51 2018 No.9949377 >>9949368 E and not E do not lead to the same action in any of your scenarios

Anonymous Mon Aug 20 20:36:57 2018 No.9949380

>>9949373
In order to apply the STP to your thought experiment, you have to treat the sequence of actions as one action. This does not mean that all sequences of actions have to be combined into one action in all contexts. You really should take a basic logic course, because you're not arguing logically.

Anonymous Mon Aug 20 20:37:52 2018 No.9949383

>>9949368
>"In decision theory, the sure-thing principle states that a decision maker who would take a certain action if he knew that event E has occurred, and also if he knew that the negation of E has occurred, should also take that same action if he knows nothing about E."

that is nonsense

what you mean to say is if a person will take the SAME action regardless of whether a known outcome occurs or not, they can safely take the SAME action if the outcome is unknown.

>>	Anonymous Mon Aug 20 20:37:54 2018 No.9949384 >>9949372 it's not a logical paradox. if you want me to make it a logical paradox for you then add the assumptions 1. The Sure-Thing Principle 2. One should NOT bet,

>>	Anonymous Mon Aug 20 20:38:03 2018 No.9949385 >>9949376 The modification does nothing to respond to the point, since it still requires you to conflate betting A with betting B.

>>	Anonymous Mon Aug 20 20:38:31 2018 No.9949388 >>9949376 The negation of "I know it landed on heads" is "I don't know it landed on heads", not "I know it landed on tails"

>>	Anonymous Mon Aug 20 20:38:57 2018 No.9949389 >>9949375 lmao: this contradicts the Sure Thing Principle, not propositional logic, mr. reading-comprehension-let ;)

>>	Anonymous Mon Aug 20 20:40:07 2018 No.9949391 >>9949377 it leads to you making a bet or if you use the standard attack that betting is not an act (but rather "to bet H" and "to bet T") then you change to this:>>9949353

>>	Anonymous Mon Aug 20 20:41:17 2018 No.9949393 >>9949391 What about >>9949388

Anonymous Mon Aug 20 20:42:21 2018 No.9949394

>>9949383
yeah so Savage was speaking nonsense.
the most renowned Decision Theorist hmmm.

"A businessman contemplates buying a certain piece of property. He considers the outcome of the next presidential election relevant. So, to clarify the matter to himself, he asks whether he would buy if he knew that the Democratic candidate were going to win, and decides that he would. Similarly, he considers whether he would buy if he knew that the Republican candidate were going to win, and again finds that he would. Seeing that he would buy in either event, he decides that he should buy, even though he does not know which event obtains, or will obtain, as we would ordinarily say. It is all too seldom that a decision can be arrived at on the basis of this principle, but except possibly for the assumption of simple ordering, I know of no other extralogical principle governing decisions that finds such ready acceptance."

>>	Anonymous Mon Aug 20 20:43:32 2018 No.9949395 >>9949385 no. we are NOT deciding between whether to bet on H or T. we are deciding whether to visit you friend or not. there is no conflation of betting on H with betting on T

Anonymous Mon Aug 20 20:44:47 2018 No.9949397

>>9949384

You could add that "ice cream is liked by many" or " the space shuttle no longer flies" or anything else extraneous, it won't make your word salad mean anything more.

You simply have three disconnected premises and from them you are drawing a conclusion that has nothing to do with either premise using a rule that does not apply.

>>	Anonymous Mon Aug 20 20:45:43 2018 No.9949398 >>9949388 >>9949393 this is not a paradox in propositional logic. the point is it contradicts the Sure Thing Principle, which is extralogical criterion for rationality

Anonymous Mon Aug 20 20:45:55 2018 No.9949399

>>9949353
adding the friend‘s house does nothing.
you have 3 options if we assume we do not know the outcome of the coinflip:
1) go to your friend‘s house, bet H and win 100 units 50% of the time
2) go to your friend‘s house, bet T and win 100 units 50% of the time
3) stay at home and win 95 units 100% of the time

I ask again: where is the paradox in your example? It seems the better option to stay at home and that is the better option statistically.

Anonymous Mon Aug 20 20:47:46 2018 No.9949402

>>9949397
fucking hell

the point is that "the sure thing paradox" and "you ought not bet" are both things that are intuitively necessary criteria for rationality. hence the problem

"ice cream is liked by many" is not intuitively necessary so a paradoxical conclusion from that wouldnt trouble anyone

jheeeezus christ

>>	Anonymous Mon Aug 20 20:48:13 2018 No.9949403 >>9949394 your example has nothing to do with that, it is a completely different setting

>>	Anonymous Mon Aug 20 20:49:25 2018 No.9949404 >>9949403 yes. obviously savage would not use an apparent counterexample to the Sure Thing Principle when introducing it as an axiom in his theory

>>	Anonymous Mon Aug 20 20:51:25 2018 No.9949407 >>9949249 > knowing (x or y) > (knowing x) or (knowing y) two different things, I don't see the paradox

Anonymous Mon Aug 20 20:51:31 2018 No.9949408

>>9949399
adding to that: we can apply the STP if we can go to our friend‘s house, look at the outcome and then bet, winning 100% of the time 100 units, but then there still is no paradox, since it seems better to go to your friend‘s house, and it statistically is.

>>	Anonymous Mon Aug 20 20:52:53 2018 No.9949409 >>9949407 again. not a paradox in propositional logic. but paradoxically negates the Sure Thing Principle

>>	Anonymous Mon Aug 20 20:53:58 2018 No.9949411 >>9949408 >>9949373

>>	Anonymous Mon Aug 20 20:58:12 2018 No.9949414 >>9949411 I still do not see anything paradox, independent of seeing the actions taken as a sequence of as independent decisions resulting as one. Please expand on that.

>>	Anonymous Mon Aug 20 20:58:22 2018 No.9949415 >>9949409 You are so dumb

>>	Anonymous Mon Aug 20 21:00:44 2018 No.9949419 >>9949415 okay professor. im sure youre a real marvel of prestige

Anonymous Mon Aug 20 21:04:11 2018 No.9949421

>>9949414
well. if we want to save STP and "ought not bet"

then we have to say "visiting your friend", "betting h" and "betting T" are not an actions.

but rather "visiting you friend and betting H" and "visiting you friend and betting T"

in fact, there can be no sequences of actions. actions correspond to an entire history of states from now until forever.

this is a bit of a blow to decision theory, where we do want to consider sequences of actions. denying this would be about as weakening to us as denying STP

Anonymous Mon Aug 20 21:04:49 2018 No.9949422

>>9949395
As I already said, visiting your friend while knowing that the coin landed on heads or that the coin landed on heads does not get you more money. You have to actually bet on the correct answer to get the money. The STP has nothing to say about visiting your friend's house.

Anonymous Mon Aug 20 21:06:53 2018 No.9949425

>>9949407
I thought the sure thing principle was for doing the same thing, not for doing different things.

IE John might be coming to my house on Sunday, Should I buy some beers?

If John comes to the house I would like to have some beers in the fridge to share with him.

If John does not come to the house, I still would like to have some beers in the fridge.

there fore you can use the Sure Thing Principle to not worry about the uncertainty around if john will visit or not.

Anonymous Mon Aug 20 21:11:06 2018 No.9949432

>>9949421
>then we have to say "visiting your friend", "betting h" and "betting T" are not an actions.
Wrong. They are actions, but the STP has nothing to say about visiting your friend's house since visiting your friend's house with knowledge does not guarantee you the money. Similarly, betting H with knowledge does not guarantee you the money, and betting T with knowledge does not guarantee you the money.

The STP only applies when the action with knowledge guarantees you the desired result. Your argument is a straw man.

Anonymous Mon Aug 20 21:11:24 2018 No.9949433

>>9949394
What if the businessman decides that he will buy house A if Democrats win, and house B otherwise? Then no matter the outcome of the election, he buys house. So he should therefore buy a house without knowing who wins. This is exactly what you've done (combining different actions into one)

Anonymous Mon Aug 20 21:19:33 2018 No.9949442

>>9949433
say that he needs to first go to an estate agent
then under either certainty of D or R, he should go to the estate agent
therefore under certainty of (D or R), he should go to the estate agent

the paradox arises if we replace "estate agent" with "casino", "D,R" with "H,T" and "buy house A/B" with "bet on H/T"

>>	Anonymous Mon Aug 20 21:25:44 2018 No.9949452 >>9949442 then under either certainty of T or H, he should go to the casino therefore under certainty of (T or H), he should go to the casino

>>	Anonymous Mon Aug 20 21:26:08 2018 No.9949453 >>9949442 Nope, going to the estate agent doesn't mean he buys the correct house.

>>	Anonymous Mon Aug 20 21:27:10 2018 No.9949454 >>9949452 Nope, going to the casino doesn't mean he makes the correct bet.

>>	Anonymous Mon Aug 20 21:28:10 2018 No.9949456 >>9949453 But it does means he will buy a house

>>	Anonymous Mon Aug 20 21:29:17 2018 No.9949460 >>9949456 Yes, so what? STP only applies when going to the real estate agent with knowledge guarantees you buy the correct house, not just buying a house.

>>	Anonymous Mon Aug 20 21:30:54 2018 No.9949463 >>9949460 STP applies because no matter the outcome, the businessman will buy a house. Therefore the businessman should buy a house

Anonymous Mon Aug 20 21:36:30 2018 No.9949474

>>9949249
this might be the stupidest thing i've seen on the board

>If you know it landed on heads, you ought to make a bet.
>If you know it landed on tails, you ought to make a bet.
>You know it landed on heads or tail, therefore you ought to make a bet

you're trying to say that where I know it landed on heads OR I know it landed on tails is the same situation as knowing that it landed on heads OR tails, but it obviously isn't. there's no paradox

Anonymous Mon Aug 20 21:38:04 2018 No.9949477

>>9949463
>STP applies because no matter the outcome, the businessman will buy a house.
No, buying a house is not a desirable outcome. You changed the example so that the desirable outcome is buying house A if Dems win and house B otherwise. So simply buying a house can lead to the wrong result. The entire point of the STP is that you want to guarantee the desired result.

Anonymous Mon Aug 20 21:40:11 2018 No.9949479

i feel like this thread is the OP trying to troll; he's making 50% of the posts and they're all disagreeing with the common sense answers, 40% of the posts are people saying the obvious common sense explanation, and then 10% are idiots getting confused by OP.

can we just /thread plz?

>>	Anonymous Mon Aug 20 21:42:47 2018 No.9949482 >>9949479 OP is incorrectly applying a principle of decision theory, that's all.

>>	Anonymous Mon Aug 20 21:45:07 2018 No.9949487 >>9949479 It's one thing to give someone the correct answer, it's another to explain where their reasoning went wrong.

>>	Anonymous Mon Aug 20 21:50:57 2018 No.9949494 >>9949249 ITT: OP desperately tries to infect people with his brainletism and fails spectacularly

>>	Anonymous Mon Aug 20 21:51:07 2018 No.9949496 >>9949376 why don't you link to someone with a clear head writing about this then because it's either nonsense or you put it across very poorly

Anonymous Mon Aug 20 21:52:34 2018 No.9949498

>>9949479
in a sense, i am trying to troll. because thats the purpose of an apparent paradox
im 50% of the posts because im replying to peoples responses
and the "common sense answers" are literally just "assume EUH and there's no paradox. even though STP is more primitive than EUH in most foundationary decision theory.

appeal to common sense is NOT a solution to an apparent paradox -- because common sense is precisely the assumptions it uses

>>9949482
2. im not a fucking brainlet. im literally doing research in axiomatic decision theory

the point is that *clearly* this is a misapplication of STP. however on the naive formalisation of STP -- it applies.

thats the fucking paradox. im not saying you should bet on the house. the point is that naive formalisations such as
>"In decision theory, the sure-thing principle states that a decision maker who would take a certain action if he knew that event E has occurred, and also if he knew that the negation of E has occurred, should also take that same action if he knows nothing about E."
suggest you should.

this isnt a recent paradox. it's very difficult to formulate STP without leading to counterexamples like this

Anonymous Mon Aug 20 21:57:49 2018 No.9949506

>>9949498
>thats the fucking paradox. im not saying you should bet on the house. the point is that naive formalisations such as
>"In decision theory, the sure-thing principle states that a decision maker who would take a certain action if he knew that event E has occurred, and also if he knew that the negation of E has occurred, should also take that same action if he knows nothing about E."
>suggest you should.
It doesn't and this isn't a naive formalism. It suggests you should take a certain action that guarantees a desired result with knowledge. Your example does not have a certain action that guarantees a desired result.

>it's very difficult to formulate STP without leading to counterexamples like this
It's not, as I've already shown. The fallacy was immediately apparent to me and I had never even heard of the STP until you quoted the Wikipedia article. The explanation there is sufficient.

>>	Anonymous Mon Aug 20 22:00:13 2018 No.9949511 >>9949341 >principle=paradox kys

>>	Anonymous Mon Aug 20 22:06:26 2018 No.9949519 >>9949511 what? when did i say principle=paradox not even sure what that would mean tb(completely)h

Anonymous Mon Aug 20 22:07:03 2018 No.9949521

>>9949498
Let's take the exact wording you disagree with and apply it to your examples:

A decision maker who would buy a house if he knew that the Dems won, and also if he knew that the Dems didn't win, should also buy a house if he knows nothing about the Dems winning.

This is true.

A decision maker who would go to the real estate agent if he knew that the Dems won, and also if he knew that the Dems didn't win, should also go to the real estate agent if he knows nothing about the Dems winning.

This is true.

Once you add that he wants to buy *different houses* for each outcome, it can't be applied, since the actions are no longer the same. "Also" does not make allow you to do that. So this is the source of your alleged "paradox" and it is clearly rejected by your alleged "naive formalism."

Anonymous Mon Aug 20 22:11:36 2018 No.9949526

>>9949506
Consider this.

1. your friend flips the coin
2. you can now decide to go to his house or to stay at home
3. if you are at his house, you must bet on either Heads or Tails
4. if you stayed at home you recieve £95, if you bet correctly you get £100, if incorrectly: £0

Okay

so youre friend has just flipped the coin.
you have the following options:
1) visit you friend
2) stay at home
both of these are actions. are the question is JUST about these two actions.

under certainty of H, visit your friend
under certainty of T, visit your friend
hence under certainty of (H or T), visit your friend

if a solution is " immediately apparent" you haven't understood it. no satisfactory solution is "immediately apparent". the best solutions have been complete overhauls of STP or definitions of actions

>>	Anonymous Mon Aug 20 22:14:42 2018 No.9949531 >>9949519 you seem to have equated a nonsensical princple with a paradox. here's an example, i call it the suicide principle You ought to kill yourself. Paradox: you're still alive. How will you resolve it?

Anonymous Mon Aug 20 22:14:45 2018 No.9949532

>>9949521
okay

so we keep naive STP

but now "going to the estate agent" is not an action.
"going to the estate agent and buys house A" is the action

but this means that agents do not sequentially perform actions. rather, an action is a single path from now until forever they must commit to. this weakening of action is about as damning to axiomatic decision theory as a weakening of STP (probably more so because actions are seen as more primitive than STP, so it's probably better to adjust STP)

>>	Anonymous Mon Aug 20 22:16:40 2018 No.9949537 >>9949531 the problem is really that STP is considered quite an intuitive, sound principle, so people assume it holds. if you assume it holds, but you deny the conclusions of the betting-scenario - then that is a logical paradox

Anonymous Mon Aug 20 22:17:06 2018 No.9949541
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>>9949526
>under certainty of H, visit your friend
>under certainty of T, visit your friend
No. Again, visiting your friend includes betting on the wrong coin.

Under certainty of H you would ONLY visit your friend AND bet H
Under certainty of T you would ONLY visit your friend AND bet T

>if a solution is " immediately apparent" you haven't understood it.
I have clearly understood it better than you, my argument speaks for itself. If you need any help with your research, give me your email.

>>	Anonymous Mon Aug 20 22:19:52 2018 No.9949544 >>9949537 it doesn't hold because it assumes you know things that you don't know to bet heads, you have to know that it will land on heads AND that it will not land on tails

>>	Anonymous Mon Aug 20 22:20:14 2018 No.9949546 >>9949541 okay prof, what's your academic email address?

>>	Anonymous Mon Aug 20 22:20:43 2018 No.9949547 >>9949526 You are so dumb

>>	Anonymous Mon Aug 20 22:21:18 2018 No.9949550 >>9949544 lmao i wasnt expecting to actually convince anyone STP is invalid hahaha

Anonymous Mon Aug 20 22:22:16 2018 No.9949556

>>9949544
>to bet heads, you have to know that it will land on heads AND that it will not land on tails
If it lands on heads and tails, then you still win because you bet on heads. But it's not even possible to land on heads and tails in the first place

>>	Anonymous Mon Aug 20 22:22:57 2018 No.9949557 >>9949547 what a damning condemnation by Nameless Shitposter

Anonymous Mon Aug 20 22:26:37 2018 No.9949560

>>9949532
>but now "going to the estate agent" is not an action.
It's still an action, it's just not the desired result that the STP is applied to. You can't just ignore the reason why the decision maker wants to go to the real estate agent. Perhaps this is related in some way to Simpson's paradox, which is also resolved by focusing on causation.

>>9949546
Nah buddy, if you want help you need to put your email on 4chan, not me.

Anonymous Mon Aug 20 22:31:55 2018 No.9949565

>>9949560
casual decision theory does away with STP completely -- so that's one viable solution!
it's probably the most fashionable at the minute. and a lot of work is going into 1) formalising it without appealing *directly* to metaphysically shakey notions of "causality" and 2) deriving practical statistical decision theory and game-theory from Casual DT

>>9949560
i was being sarcastic.
i was implying you had no credentials, which was a bit immature of me

>>	Anonymous Mon Aug 20 22:34:15 2018 No.9949569 >>9949565 You are so dumb

>>	Anonymous Mon Aug 20 22:35:08 2018 No.9949571 OP here: i think i made a bit of a mistake posting this to 4chan, because posting an apparent paradox might read like a shitpost haha this might've been a bit too far into philosophy for a science forum

>>	Anonymous Mon Aug 20 22:37:16 2018 No.9949574 >>9949571 Haha

>>	Anonymous Mon Aug 20 22:40:32 2018 No.9949580 >>9949560 >Nah buddy, if you want help you need to put your email on 4chan, not me. vonneumannwittgensteinandeinsteinaintshit@undergrad.edu

>>	Anonymous Mon Aug 20 22:41:35 2018 No.9949582 >>9949580 >:(

>>	Anonymous Mon Aug 20 22:50:06 2018 No.9949588 >>9949565 No need for a different decision theory, just don't ignore relevant information that you've been given if you want to come to the correct answer. The STP also can't be applied if the probability of the event is affected by the desired action.

>>	Anonymous Mon Aug 20 22:52:34 2018 No.9949591 >>9949588 the probability of the event is not effected the coin is flipped before any decision is made

>>	Anonymous Mon Aug 20 22:57:02 2018 No.9949594 >>9949591 Yeah, I'm just giving an example of information that when ignored would lead to an incorrect application of the principle.

Anonymous Mon Aug 20 23:00:31 2018 No.9949596

>>9949496
https://plato.stanford.edu/entries/decision-theory/
The axiom in Savage’s theory that has received most attention is the Sure Thing Principle. It is not hard to see that this principle conflicts with Allais’ preferences for the same reason these preferences conflict with Independence (recall Section 2.3). Allais’ challenge will be discussed again later. For now, our concern is rather the Sure Thing Principle vis-à-vis the internal logic of Savage’s theory. To begin with, the Sure Thing Principle, like State Neutrality, exacerbates concerns about the Rectangular Field Assumption. This is because the Sure Thing Principle is only plausible if outcomes are specific enough to account for any sort of dependencies between outcomes in different states of the world. For instance, if the fact that one could have chosen a risk-free alternative—and thereby guaranteed an acceptable outcome—makes a difference to the desirability of receiving nothing after having taken a risk (as in Allais’ problem), then that has to be accounted for in the description of the outcomes. But again, if we account for such dependencies in the description of the outcomes, we run into the problem that there will be acts in the preference ordering that are nonsensical (see e.g., Broome 1991a: ch. 5).

There is a further internal problem with Savage’s theory associated with the Sure Thing Principle: the principle is only reasonable when the decision model is constructed such that there is probabilistic independence between the acts an agent is considering and the states of the world that determine the outcomes of these acts. Recall that the principle states that if we have four options with the following form:

E ¬E
f X Z
g Y Z
f X W
g Y W

Anonymous Mon Aug 20 23:01:34 2018 No.9949598

>>9949596
then if g is weakly preferred to f, g must be weakly preferred to f. Suppose, however, that there is probabilistic dependency between the states of the world and the alternatives we are considering, and that we find Z to be better than both X and Y, and we also find W to be better than both X and Y. Moreover, suppose that g makes ¬E more likely than f does, and f makes ¬E more likely than g does. Then it seems perfectly reasonable to prefer g over f but f over g.

Why is the requirement of probabilistic independence problematic? For one thing, in many real-world decision circumstances, it is hard to frame the decision model in such a way that states are intuitively probabilistically independent of acts. For instance, suppose an agent enjoys smoking, and is trying to decide whether to quit or not. How long she lives is amongst the contingencies that affect the desirability of smoking. It would be natural to partition the set of states according to how long the agent lives. But then it is obvious that the options she is considering could, and arguably should, affect how likely she finds each state of the world, since it is well recognised that life expectancy is reduced by smoking. Savage would thus require an alternative representation of the decision problem—the states do not reference life span directly, but rather the agent’s physiological propensity to react in a certain way to smoking.

Anonymous Mon Aug 20 23:02:36 2018 No.9949600

>>9949598
Perhaps there is always a way to contrive decision models such that acts are intuitively probabilistically independent of states. But therein lies the more serious problem. Recall that Savage was trying to formulate a way of determining a rational agent’s beliefs from her preferences over acts, such that the beliefs can ultimately be represented by a probability function. If we are interested in real-world decisions, then the acts in question ought to be recognisable options for the agent (which we have seen is questionable). Moreover, now we see that one of Savage’s rationality constraints on preference—the Sure Thing Principle—is plausible only if the modelled acts are probabilistically independent of the states. In other words, this independence must be built into the decision model if it is to facilitate appropriate measures of belief and desire. But this is to assume that we already have important information about the beliefs of the agent whose attitudes we are trying to represent; namely what state-partitions she considers probabilistically independent of her acts.

The above problems suggest there is a need for an alternative theory of choice under uncertainty. Richard Jeffrey’s theory, which will be discuss next, avoids all of the problems that have been discussed so far. But as we will see, Jeffrey’s theory has well-known problems of its own, albeit problems that are not insurmountable.

>>	Anonymous Mon Aug 20 23:46:21 2018 No.9949663 >>9949526 visiting your friend can be marginalized into 2 sub-actions, betting H and betting T, where one wins and one loses, averaging the action of going to your friend‘s house to £50. The 2 different outcomes cannot be ignored in the decision-making

>>	Anonymous Mon Aug 20 23:50:26 2018 No.9949666 >>9949532 you grow the path of decisions by introducing additional outcomes, why are you so surprised that adding complexity to the problem makes the decisionmaking more complex?

>>	Anonymous Mon Aug 20 23:51:31 2018 No.9949668 >>9949249 i dont see the paradox op 95 is a lot higher than the expected earning so you should never bet unless you are a complete brainlet

>>	Anonymous Mon Aug 20 23:52:41 2018 No.9949670 >>9949537 it cannot hold on circumstances that have a different premise

Anonymous Tue Aug 21 00:44:22 2018 No.9949729
File: 49 KB, 600x737, 1534370243550.jpg [View same] [iqdb] [saucenao] [google]

Soo too me this seems like a people playing with words.

how hard would it to actually draw a drawing.
and stop this ratatard word mumbo jumbo

and how is this a paradox.
why would you not take 95€
and no bet. I fucking hate word games. cause i cant mentaly fucking process them. it just fucking confues the shit out of me.
make a drawing soo i can understand

Anonymous Tue Aug 21 03:09:20 2018 No.9949834

Holy shit the state of /sci/.
Ill explain where the paradox is and then resolve it.
It's a shitty paradox based on pure word usage and lack of formalism so fuck you OP but everyone ITT who didnt post an explanation is a brainlet.
The "sure thing principle" which OP is referring tos tates that (A => C and nA => C) => C.
I.e. if you would do C in either case, A or nA, you should just do C.
Why does this cause a "paradox"? Let's try to apply it to OPs problem.
C is "I bet"
if we set A to "coin is heads" then we cant use it because we are interested in "you know that A" kind of statements which are completely different.
If we set A to "I know the coin is heads" Then nA does not imply C and we cant apply the principle.
This is because nA is "I dont know the coin is heads" which DOESNT mean B: "I know its tails".
In addition "I know it landed heads or tails" is not "A or B".
So as soon as you even think this through a little bit you realize it's bullshit.

Anonymous Tue Aug 21 07:50:00 2018 No.9950138

>>9949834
Your description of the principle is very wrong. It's more like (knowing A => C and knowing nA => C) => C

The problem is not that the negation of knowing A is not knowing A, the problem is that knowing A leads to a different action in this case than knowing nA.

Anonymous Tue Aug 21 08:37:08 2018 No.9950190

>You can now bet £100 on whether it has landed on heads or tails
50% chance of it being heads
50% chance of it being tails
100 % chance of it being either heads or tails (assuming we're not going to play some no game no life bullshit where the coin gets trapped in a sidewalk crack after 10 minutes of over analyzing the odds of a coin flip)

I'm going to bet this £100 because there's a 100% chance of winning £100 from this lad.

>>	Anonymous Tue Aug 21 08:42:12 2018 No.9950202 >>9950190 Betting on =/= betting that

>>	Anonymous Tue Aug 21 09:19:17 2018 No.9950242 >>9950202 But that's not how the OP worded it.

Anonymous Tue Aug 21 09:48:12 2018 No.9950268

>>9950242
You can now bet £100 on whether it has landed on Heads or Tails.

Betting on means you bet that the event occurs in a particular way
If I bet on a horse race, I'm not literally betting that a horse race will occur.
I'm betting that it'll occur in a particular way

>>	Anonymous Tue Aug 21 09:49:50 2018 No.9950271 >>9949249 Expected values are pretty useless for evaluating single events.

Anonymous Tue Aug 21 09:51:14 2018 No.9950273

>>9949366
>"In decision theory, the sure-thing principle states that a decision maker who would take a certain action if he knew that event E has occurred, and also if he knew that the negation of E has occurred, should also take that same action if he knows nothing about E."
Doesn't apply because if you know it landed heads, you bet heads. If you know it landed tails you bet tails. It's misleading to lump those two separate actions into one action called "bet".

>>	Anonymous Tue Aug 21 09:52:21 2018 No.9950274 >>9949249 So, A \|\| B == A && B That can't be right.

>>	Anonymous Tue Aug 21 10:24:53 2018 No.9950297 Get away with <95$?

>>	Anonymous Tue Aug 21 10:26:30 2018 No.9950301 >>9949249 >Get away with <95$?

>>	Anonymous Tue Aug 21 10:53:20 2018 No.9950323 >>9949249 >If you know it landed on heads, you ought to make a bet. well you can't make just any bet.

>>	Anonymous Tue Aug 21 10:57:09 2018 No.9950328 >>9950323 or rather, the "correct" bet exists. yes, you aught to make a bet. there's no paradox here. just like i aught to go to the racetrack and pick all the winning horses. easier said than done.

>>	Anonymous Tue Aug 21 11:00:08 2018 No.9950332 >>9950273 >>9950328 >>9949526

>>	Anonymous Tue Aug 21 11:00:51 2018 No.9950334 >>9950328 but then you get into free will, whether or not i really have a choice on my bet, etc. and it gets messy.

>>	Anonymous Tue Aug 21 11:02:51 2018 No.9950337 >>9949249 >hether it has landed on Heads or Tails. The way that is phrased, you should take the bet. You are betting on it landing on heads OR tails. Unless it lands on it's edge, you win.

Anonymous Tue Aug 21 11:03:23 2018 No.9950339

Tbf this did actually cause an overhaul in the foundations of decision theory. It's the main reason we use currently use causal decision theory, not evidential decision theory.

OP is a bit of brainlet for not explaining the paradox very well, but most of y'all being really dense

>>	Anonymous Tue Aug 21 11:05:13 2018 No.9950344 >>9950334 Free will isn't that relevant. Any performative system which satisfies a naive formulation of STP will have to play a bet

Anonymous Tue Aug 21 11:11:04 2018 No.9950350

>>9949327
expected value is a shit way to look at these things anyway. it's only relevant if you're looking at the outcome of many, many trials. if you're only performing one trial and you want the highest probability of getting any money at all, that's a much different proposition

very few people are going to throw themselves under the bus for the sake of expected value.

Anonymous Tue Aug 21 11:16:42 2018 No.9950365

>>9950350
Yeah this is true
The Bernoulli method of saving the Expected Utility Hypothesis is saying that we maximise the expected value of utility of money.

Say you need £100 kidney transplant tomorrow or you'll die, and currently have no money.
Then it actually is rational to make the bet, because that's 50% chance you live.
The guaranteed £95 has as much utility as £0

>>	Anonymous Tue Aug 21 11:16:56 2018 No.9950367 >>9950332 just because you're certain of (H or ~H) does not mean you're certain of H or certain of ~H. the truth value of H is independent of your belief.

Anonymous Tue Aug 21 11:20:02 2018 No.9950378

>>9950350
>>9950365
Also, STP is considered more primitive than EUH in most foundations of Decision theory

Eg: von neumann-morgenstein uses an Independence Axiom in his representation theorem
The justification of EUH is the VNM theorem, and the justification of Independence is STP

>>	Anonymous Tue Aug 21 11:22:15 2018 No.9950387 >>9950367 This isn't a paradox in epistemic logic, but rather it violates STP which is: If certainty (x) -> perform (a) And certainty (not-x) -> perform (a) Then perform (a)

>>	Anonymous Tue Aug 21 11:30:08 2018 No.9950404 >>9949249 how is this a paradox? the action is not "make a bet" its "make a bet on heads," or "make a bet on tails" you wouldn't bet on heads every time, because the coin could land on tails so it isn't even a sure thing, you are applying it wrong

>>	Anonymous Tue Aug 21 11:33:33 2018 No.9950418 >>9950404 Well done HOWEVER >>9949526

Anonymous Tue Aug 21 11:46:01 2018 No.9950446

>>9950418
what the fuck do you mean heads or tails is certain?
do I just telepathically know what the result of his coinflip is? or do I just look at the coin when I get to his house?
either way, you are still wrong about what an action is, going to his house is part of an action, but the whole action is go to his house, and place a bet on heads, or go to his house, and place a bet on tails
you cant apply the sure thing principle if your actions are not specific

>>	Anonymous Tue Aug 21 12:01:35 2018 No.9950466 >>9950446 If you were certain that H, you would perform a If you were certain of T, you would perform a STP says that you should perform a, even though you don't know whether H or T In game theory, a is called a dominant strategy

>>	Anonymous Tue Aug 21 12:07:00 2018 No.9950473 File: 44 KB, 352x550, 45320678-352-k517364.jpg [View same] [iqdb] [saucenao] [google] >133 posts >34 posters

Anonymous Tue Aug 21 12:08:02 2018 No.9950477

>>9950446
but this means that agents do not sequentially perform actions. rather, an action is a single path from now until forever they must commit to. this weakening of action is about as damning to axiomatic decision theory as a weakening of STP (probably more so because actions are seen as more primitive than STP, so it's probably better to adjust STP)

Also. This would completely fuck up any analysis of unbounded games - where there would be paths arbitrarily long

>>	Anonymous Tue Aug 21 12:09:27 2018 No.9950479 >>9950387 well, i don't really know what STP is, but there's no real paradox. you're essentially saying the the uncertainty of x is equivalent to the certainty of not x. which isn't true under any reasonable interpretation of the word certainty.

>>	Anonymous Tue Aug 21 12:10:21 2018 No.9950480 File: 44 KB, 658x662, surethngi.png [View same] [iqdb] [saucenao] [google] sure thing. if sure thing is X(tails) and x= tails and if x=heads. you sure thing ought to bet my friend. =100$

Anonymous Tue Aug 21 12:10:42 2018 No.9950481

>>9950466
STP doesn't say that rtard
an action, in STP's logical justification, must be specific and not intelligent in any way
placing a bet on heads would be an acceptable action when applying STP
a computer program that chooses an action based on some input would not be an acceptable action, as it fails to complete the theorem backing STP

Anonymous Tue Aug 21 12:13:10 2018 No.9950487

>>9950477
just because the statement of the STP theorem uses words like "action" doesn't mean that the word is consistently used throughout all of game theory
what matters is the theorem proving STP, and what its interpretation of what an action is
this conditional action would not be considered an action in that theorem

Anonymous Tue Aug 21 12:29:20 2018 No.9950508

>>9950479

cont.

although i think we get a deeper and more interesting question if we assume that "you aught to make a bet" is always true. OP said specifically that the coin has already been flipped. so the "correct" value exists*, and so you aught to bet on that value.
* excuse my ignorance of quantum physics and the like, i'm sure it always existed or never existed or both exists and non exists or some such bullshit like that.

>>	Anonymous Tue Aug 21 12:29:52 2018 No.9950509 >>9949249 expectation value of event P is written E(P) = X £ E("dont bet") = 95 £ E("bet heads") = 0,5 * 100 £ E("bet tails") = 0,5 * 100 £ /thread

>>	Anonymous Tue Aug 21 12:35:04 2018 No.9950519 >>9950508 cont. so i guess what follows from this is that an alternate circumstance, where you do pick the favorable choice, exists.

>>	Anonymous Tue Aug 21 12:36:07 2018 No.9950522 >>9950519 cont. so there's your proof of the multiverse theory.

>>	Anonymous Tue Aug 21 12:47:24 2018 No.9950531 >>9950509 >>9950378

>>	Anonymous Tue Aug 21 12:48:27 2018 No.9950532 >>9950487 It's quite rare for STP to be a theorem It's normally axiomatic

>>	Anonymous Tue Aug 21 12:51:41 2018 No.9950537 why do all these questions lead to determinism or indeterminism? it's so unsatisfying.

>>	Anonymous Tue Aug 21 12:52:03 2018 No.9950538 >>9950531 you are incorrect the problem is solved no further analysis is required or even possible /thread

>>	Anonymous Tue Aug 21 14:19:52 2018 No.9950654 >>9950538 so you take EUH to be axiomatic? that's quite unusual. most people see it derived a la VNM representation theorem

>>	Anonymous Tue Aug 21 14:31:11 2018 No.9950671 File: 284 KB, 1137x426, SAGE_AUTISM_THREADS.png [View same] [iqdb] [saucenao] [google] schizophrenia is a hell of a drug

Anonymous Tue Aug 21 15:13:00 2018 No.9950727

>>9950477
You are the one who placed the condition that if you go to his house, then you MUST bet, effectively turning a sequence of actions "going" and "betting" into a single one. Your so called paradox only shows up if you ignore that. If "going" and "betting" were different actions, then I should be able to go and not make a bet.

>>	Anonymous Tue Aug 21 15:17:06 2018 No.9950739 >>9950727 okay then let's accept your amendment so now your're to visit your friend -- and can choose to bet or not. BUT you've missed out on that £95 visiting your friend and not betting is the worse action there is (a la expected profits)

>>	Anonymous Tue Aug 21 21:28:11 2018 No.9951568 >>9949249 Sounds like you need to use some sort of modality in your logic (i.e. semantics can't be captured in ordinary propositional logic).

>>	Anonymous Tue Aug 21 23:08:21 2018 No.9951738 >>9949341 Look at that shitty source holy moly You could have literally made that wiki page before you posted this

>>	Anonymous Tue Aug 21 23:39:58 2018 No.9951779 >>9949249 Don't think about the coin

>>	Anonymous Wed Aug 22 00:24:22 2018 No.9951801 >>9949341 I would pick heads if it landed head, and I would pick heads if it landed tails, therefore I should pick heads. That's the only way to use the principle correctly, but to do so is not paradoxical, it's moronical.

>>	Anonymous Wed Aug 22 12:40:02 2018 No.9952521 If P(A\|B)=1 and P(C\|~B)=1, then P(A or C)=1. That’s deep.

>>	Anonymous Wed Aug 22 13:00:33 2018 No.9952544 >>9949252 welcome to schrödinger's cat. it is both states at the exact same time unless observed.

>>	Anonymous Wed Aug 22 13:01:09 2018 No.9952546 >>9950365 Of course I take the 95bongs and spend rest of the day earning the remaining 5bongs. Are you completely retarded?

Anonymous Wed Aug 22 13:12:54 2018 No.9952559
File: 875 KB, 1357x758, Stupid people oppose free speech.png [View same] [iqdb] [saucenao] [google]

>>9949249
This is not a paradox. It's just an idiot failing to recognize that the bets are not the same for the two respective outcomes, so the Sure Thing Principle does not apply here.

>>	Anonymous Wed Aug 22 14:07:58 2018 No.9952619 >>9952546 yeah, say you can't though A: 100% of £95, 100% of death B: 50% of £100, 50% of death

>>	Anonymous Wed Aug 22 14:18:58 2018 No.9952631 >>9952619 So what's the problem then?

Anonymous Wed Aug 22 14:22:03 2018 No.9952634

>>9949394
Are you retarded or something? In this example the outcome is indifferent, and therefore it is a sure thing that the action is taken.

In your example that would mean, I give you 100$ if you bet right, and 100$ if you bet wrong. Because of this, you would do it not knowing if its head or tailes. Your examples are completely wrong and the sure thing principle is no paradox.

>>	Anonymous Wed Aug 22 14:33:59 2018 No.9952652 >>9952631 well in this case you ought to take the bet because that maximises expected utility where u(£0)=0, u(£95)=0, u(£100)=1 but you though that was completely retarded lmaoo

>>	Anonymous Thu Aug 23 05:53:42 2018 No.9953982 >>9949571 These guys are literally retarded and/or autistic. Thanks for trying. I enjoyed the thread.

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