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 by mmiguel, 19 September 2012 - 10:24 AM.