Rashunal

[mmiguel]

-Assume this takes place in the real world, no magic, wizardry or other funny business exists-

King Rashunal rules over the kingdom of Logicia with a level head.

He is well known for using logic and data for making important decisions, and never makes a decision with his gut.

One day, the king's most trusted advisor, Ethos, who has never been wrong before in consultation to the king approaches the king.

"I have come bearing a most ominous warning!" exclaims Ethos.

"It has been revealed to me, by discerning the relative positions of the celestial bodies, that a plague, a million-fold worse than the great plague of 100 years ago may fall upon this city if immediate preventative action is not taken."

"The precision of my instruments indicate that if no action is taken, disaster will occur with probability 15%."

Knowing nothing of the stars, and remembering the many difficult decisions that Ethos has guided him through before, listens patiently.

Ethos continues: "The alignment of Jupiter and Saturn tell me that the only way to prevent this tragedy is for the King to encircle the entire capital city 5 times, hopping on one foot, in a bunny costume, while the townsfolk pelt him with fruits..... and also 20,000 pieces of silver are given to me, ... and a statue should be erected with a great plaque that says Ethos,... the savior of Logicia.".

King Rashunal then speaks: "We are a people of analysis! We will consider all options and make the most reasonable decision! Court historians, scribes, calculators, economists, men and women of learning, provide to me an estimate of the costs the kingdom shall incur if the great plague were to resurface if and we do nothing, and also the costs of implementing this preventative action".

For two days, the men and women of learning in the court make estimates of costs incurred due to loss of life and cattle from the plague, costs incurred due morale and threats of enemy invasion to the weak image of the kingdom from the shamed King in his bunny suit, .... and many other such costs.

In the end, the King is presented with the following information:

If the great plague resurfaces at a million-fold, then the costs to the kingdom would be -10,000,000 pieces of silver.

If Ethos' preventative plan is implemented, then the costs to the kingdom due to the plan will be -100,000 pieces of silver.

If the preventative plan is implemented, we expect there to be no plague.

The King then draws a 2x2 box with columns corresponding to whether the plan is taken or not, and rows corresponding to whether the disaster will occur or not. He populates each cell with the corresponding cost.

Realizing he cannot control which row the kingdom might end up in, Rashunal focuses on the columns, and calculates the expected value of cost across each column.

By his reasoning,if taking preventative action, the kingdom can expect to lose 100,000 pieces of silver with certainty.

With no action, the expected value is a loss of 1,500,000 pieces of silver (considering both whether the plague does or does not occur).

The king knows what he must do...

Question: What went wrong here, and how can one defend in general from this type of problem if it were more subtle (yeah the bunny suit is overkill).

Now, what do you think about this - is this the same breed of argument, or do you think the problem is not of logical nature?

Before anyone sends any angry posts - I'm only interested in the logical validity of the argument in the video, not trying to debate the underlying topic. I'm not asserting that anything in the video is as ridiculous as Ethos' proposal.

Edited September 19, 2012 by mmiguel

[CaptainEd]

It appears that Rashunal's analysis and decision is the same used by people evaluating insurance: should I pay a low cost with high probability, or accept a high cost at low probability?

So does the argument on the video.

The presence of the bunny suit might make one question the notion that the OP is concerned about logic.

[Rob_Gandy]

As far as the video goes, I think the problem comes with working with only the extremes. Absolutely nothing happens or the worst thing imaginable happens. We take no action or we take extreme action. So the analysis of the situation, the possible outcomes and the number of possible actions are limited.

[curr3nt]

What happens if they take action and it doesn't stop the plague? Now they have the effect of the plague plus the embarassment and cost of taking action. Just because advisor has been right in the past doesn't logically make anything he says in the future correct.

In the video he assumes that the worst case for the first box is just economic. If the climate change isn't human caused then won't we still get hit by all the disasters listed in the fourth box? Just because in that case it isn't our fault the climate is changing doesn't mean the problem goes away.

[Yoruichi-san]

What's the probability of the plague happening? It seems like an easy enough value analysis...

Expected value of preventative measures = Cost of preventative measures - (Probability plague happens)(cost of plague)

E=100,000-10,000,000p

Hence if p<0.01 (1 percent), then then no point of taking action.

Also, is it certain that the preventative measures will prevent the plague? If not, then modify:

Expected value of preventative measures = Cost of preventative measures - (Probability plague happens)(cost of plague)(probability preventative measures will succeed)

[TheChad08]

Wow, so the big conspiracy is that this guy just changed the headers on Pascal's wager.

If scientists listen to him then all scientists should believe in God and be religious.

[Rob_Gandy]

The difference I see between the video and Pascal's wager is that in Pascal's wager those really are the only posibilities. Either God is or isn't and either you follow him or you don't.

[plasmid]

My answer would depend on a clarification of the OP. But I think I should put the clarification questions in a spoiler because I feel like understanding what clarification questions need to be asked is really the heart of the riddle.

When you open the problem by saying that this happens in the real world, meaning that no magic, wizardry or other funny business exists, do you mean to imply that we must also account for the possibility that the astrological prediction of Ethos may be wrong despite the fact that he's never been wrong before? Also, when it says that the king makes decisions based only on logic and not using his gut, and that he knows nothing of the stars, does that imply that neither he nor any of his advisers would consider the possibility that Ethos is wrong? If he can consider the possibility that Ethos is wrong, is there any extra data available that he could use to estimate Bayesian probabilities of Ethos really being an infallible astrologer based on the information that the king has at his disposal (like the number of predictions he's made correctly before, the probability that those predictions would be correct based purely on chance, whether or not Ethos was selected from a pool of potential advisers by having the potential advisers all make predictions on events and then weeding out adviser candidates who made a wrong prediction until just Ethos was left?) And would the king would be willing to make a baseline estimate of the probability that astrology is true in the absence of any of the data mentioned above?

As for the video, curr3nt and Rob_Gandy already made the main points about not accounting for non-extreme cases, and not accounting for the possibility that interventions will fail. I would also add the need to account for the possibility that environmental destruction through pollution and whatnot might not be the factor that ultimately determines when humanity devolves into a mess of savages barely able to survive. World War III, comet collisions, and alien invasions might all happen first. In fact, excessive pollution might be just the thing that kills off a mutating multidrug-resistant bacteria before it fully evolves and spreads to cause a plague that makes the Black Death look like a case of the sniffles.

Edited September 20, 2012 by plasmid

[Yoruichi-san]

The difference I see between the video and Pascal's wager is that in Pascal's wager those really are the only posibilities. Either God is or isn't and either you follow him or you don't.

Really? I'd say the opposite. In fact, I think I did...(in an essay I wrote in college). One of the major problems about Pascal's conclusions is that he doesn't take into account all the possibilities. To summarize, his argument is:

Probability God exists > 0

Amount of happiness you gain from following God = infinity

Hence expected value of following God is infinite happiness at a relatively small cost in this lifetime

One of my arguments was:

Probability that a different god exists, that will condemn you to infinite suffering if you follow the wrong god > 0

(or multiple such gods, for that matter)

Hence countering the infinite benefit of following God (the Christian God if I remember correctly, which was what Pascal was espousing)

[mmiguel]

What's the probability of the plague happening? It seems like an easy enough value analysis...

Expected value of preventative measures = Cost of preventative measures - (Probability plague happens)(cost of plague)

E=100,000-10,000,000p

Hence if p<0.01 (1 percent), then then no point of taking action.

Also, is it certain that the preventative measures will prevent the plague? If not, then modify:

Expected value of preventative measures = Cost of preventative measures - (Probability plague happens)(cost of plague)(probability preventative measures will succeed)

The advisor said the probability was 15%.

[mmiguel]

Wow, so the big conspiracy is that this guy just changed the headers on Pascal's wager.

If scientists listen to him then all scientists should believe in God and be religious.

Awesome! I was looking for an example of this in religion, but couldn't find it -- didn't know the right search term.

[mmiguel]

The advisor said the probability was 15%.

i know i know.... it doesn't matter what the phony says... the real probability is whether or not he is right.

the 15% is just there to distract people - so that they think they are considering probability, but in actuality they are not considering the right one.

probably not something that people on this site would fall for, but i posted this not really to challenge you fine folks, but to think about things.

i feel like the video used a lot of distraction, and disarms the viewer into thinking that no matter what numbers they put in, the videomaker will be right.

people who enjoy logic puzzles are not likely to be fooled by distractive techniques though

[mmiguel]

My answer would depend on a clarification of the OP. But I think I should put the clarification questions in a spoiler because I feel like understanding what clarification questions need to be asked is really the heart of the riddle.

When you open the problem by saying that this happens in the real world, meaning that no magic, wizardry or other funny business exists, do you mean to imply that we must also account for the possibility that the astrological prediction of Ethos may be wrong despite the fact that he's never been wrong before? Also, when it says that the king makes decisions based only on logic and not using his gut, and that he knows nothing of the stars, does that imply that neither he nor any of his advisers would consider the possibility that Ethos is wrong? If he can consider the possibility that Ethos is wrong, is there any extra data available that he could use to estimate Bayesian probabilities of Ethos really being an infallible astrologer based on the information that the king has at his disposal (like the number of predictions he's made correctly before, the probability that those predictions would be correct based purely on chance, whether or not Ethos was selected from a pool of potential advisers by having the potential advisers all make predictions on events and then weeding out adviser candidates who made a wrong prediction until just Ethos was left?) And would the king would be willing to make a baseline estimate of the probability that astrology is true in the absence of any of the data mentioned above?

As for the video, curr3nt and Rob_Gandy already made the main points about not accounting for non-extreme cases, and not accounting for the possibility that interventions will fail. I would also add the need to account for the possibility that environmental destruction through pollution and whatnot might not be the factor that ultimately determines when humanity devolves into a mess of savages barely able to survive. World War III, comet collisions, and alien invasions might all happen first. In fact, excessive pollution might be just the thing that kills off a mutating multidrug-resistant bacteria before it fully evolves and spreads to cause a plague that makes the Black Death look like a case of the sniffles.

yeah that is pretty much the heart of what i concluded from thinking about this ---> there is another probability that should always be considered whenever anything is heard --- what is the probability that everything that i am hearing is correct?

this may seem obvious to always assess this probability, but i felt that the video maker was able to skillfully disarm the viewer into forgetting this fundamental suspicion.

if something is completely outrageous - like a bunny suit stopping a plague, then it might not even be worth considering as a possibility. if you do consider it as a possibility, they could lie about the numbers in such a way that it makes it seem like you should do whatever they suggest. you would only be safe if you make your own judgment about the probability of them telling the truth to offset the effect on the expected value from whatever numbers they throw at you. what if you don't go low enough?

how do we determine this probability when we make conclusions about things?

is it a judgment call?

does it come from the gut?

maybe the king is too scared to make that leap.

this probability is certainly subjective, and changes from case to case;

stuff to think about, if anyone is still reading

Edited September 20, 2012 by mmiguel

[TheChad08]

Really? I'd say the opposite. In fact, I think I did...(in an essay I wrote in college). One of the major problems about Pascal's conclusions is that he doesn't take into account all the possibilities. To summarize, his argument is:

Probability God exists > 0

Amount of happiness you gain from following God = infinity

Hence expected value of following God is infinite happiness at a relatively small cost in this lifetime

One of my arguments was:

Probability that a different god exists, that will condemn you to infinite suffering if you follow the wrong god > 0

(or multiple such gods, for that matter)

Hence countering the infinite benefit of following God (the Christian God if I remember correctly, which was what Pascal was espousing)

You are assuming that god requires you to follow his religion.

There is also the assumption that faith is required for access to heaven, not your mortal actions.

Don't forget to include that assumption that we aren't ignorant to our punishment/reward.

What good is heaven/hell if we aren't aware of our eternal bliss/damnation?

I know Pascal's wager and I'm still an atheist

[Yoruichi-san]

You are assuming that god requires you to follow his religion.

There is also the assumption that faith is required for access to heaven, not your mortal actions.

Don't forget to include that assumption that we aren't ignorant to our punishment/reward.

What good is heaven/hell if we aren't aware of our eternal bliss/damnation?

I know Pascal's wager and I'm still an atheist

Hey! Don't attribute Pascal's arguments to me . I was summarizing Pascal's argument, as I understand it.

Obviously, from the fact I argued against Pascal's Wager, I disagree with him . And yes, as I mentioned, that was only one of my arguments, the one that was pertinent in regards to "considering all the possibilities", which my post was in response to.

Edited September 20, 2012 by Yoruichi-san