[QUOTE]Originally posted by tritium_pie
this is a fun discussion.

 

Although "risk" is a noun, it functions as an adjective in this sentence, modifying both "identification" and "mitigation"; it is what is known as an "attributive adjective". The subject of the sentence is "identification and mitigation"; this plural subject requires a plural verb.

 

[QUOTE]Originally posted by magician

 

[QUOTE]Originally posted by tritium_pie

 

This thread is very educational.

From a purely mathematical I see your point regarding the envelopes. However, (and I'm not mathematician so I may not be explaining very clearly), this assume that the dollar amount and it's value to you (i.e., how happy it makes you) grows linearly proportionally indefinitely. If the dollar amount grows exponentially relatively to it's value to you (i.e., it takes a lot more money to make you only slightly ), then this doesn't always apply.

For e.g., one envelope contains twice the dollar amount of the other. I open one and I see $10 million, which as far as I'm concerned will last me a life time. I can get $20m and that'll make me happier but not as much as getting $5m unhappy. That would be a different scenario wouldn't it?

 

[QUOTE]Originally posted by magician

 

You're point is a valid one, but is solved with a simple change of premise, based on cardinal utility theory in economics. Let one envelope contain twice as much Utility as the other, where utility is simply another measure (like dollars) of the value to you of a bundle of goods. The mathematics and the conclusion are the same.

The problem is posed using dollars because more people understand money than understand utility theory.

 

I'm sorry Magician, I have to disagree with game theory in this example too. jeez, I suck, but let's say before you even pick a door Monty Hall says, "Hey, I'm gonna make this easier for you. Lemme get rid of one of the doors that I know is a loser." he opens one and there's a donkey.

so by eliminating one of the doors, he reduces your chances to 50/50 whether or not it is before or after you have taken an initial guess. one of the bad choices was never even in the mix, because you can guarantee that it'll be eliminated.

consider this: what if he says, "Look bud, you made the wrong call." he opens the door you picked and yup, it's a camel. he says, "Pick again." what are your chances? 50/50.

consider this too: assume 100 doors, you pick 1, he opens 98 and shows you they're empty. so you're down to 2 doors. well, you were always down to 2 doors; 1 winner, 1 not. guaranteed. even if he did this tediously, 1 door at a time-- 98 times-- and you're given the choice to switch, why bother? tell him to hurry up and get rid of all the bad choices so you can get down to the last 2 doors, flip your coin and take your (even) chances.

your first pick is does not count as a pick at all because you have not gained any insight into what is behind your door, or the remaining door(s). it is irrelevant. just good dramatic television.

the fact of the matter is, you only ever had 2 doors to pick from, because you could count on Monty getting rid of (all but) one of the bad choices.

therefore, flip a coin if you want to switch. it doesn't make a bit of difference.

(and once again, this could be tested empirically)

EDIT: ok, I'm done editing I think. feel free to quote-n-shred my argument as posted above.

 

[QUOTE]Originally posted by tritium_pie
I'm sorry Magician, I have to disagree with game theory in this example too.

 

[QUOTE]Originally posted by tritium_pie
consider this too: assume 100 doors, you pick 1, he opens 98 and shows you they're empty.