Statistics Question (about invading Iraq)

[jasonfish11]

I recently calculated how much evidence is needed to make invading Iraq the correct decision (death toll wise). I figured there are 4 possible outcomes.
1)Invasion of Iraq kills 82,000 Iraqi civilians whether they have WMDs or not (2 of the 4 outcomes)
3) Iraq does have WMDs and we dont attack. (assuming they would plan to use them in a very populated area like NYC). Population of NYC is 8,200,000.
4) Iraq doesnt have WMDs and we dont attack. No one dies.

I used the entire population of NYC (which is probably more than will actually get killed by a WMD).

Here is the formula I came up with. Please let me know if you see flaws.

X = % of time that invading Iraq will result in a smaller death toll. I took half the population of NY because if we dont attack and they have WMDs 8.2 million people die, but if they dont have WMDs 0 people die. (8.2+0)/2 =4.1 million

82,000x = 4,100,000 (1-X)
82,000x = 4,100,000-4,100,000x
4,182,000x = 4,100,000
X = .98

So if as little as 2.1% of the evidence gathered it would suggest that invading Iraq will have a smaller death toll than not invading and taking the risk. (Both the 82,000 Iraqi civilians and the population of NY were verified by reliable sources online.)

I am wondering if the math is messed up or I made too many assumptions (I think I used a formula usually used to calculate 2 possible out comes when there are actually 4 possible out comes). Because this number seems really low.

Once again I am looking to make sure that math and formula is right. I know that not everyone in NY would die I just took that number to see if the formula worked. If everything is correct I will figure out a more realistic number.

Any help would be appreciated.

[tshort]

Your analysis is right on. It follows directly from the most important poker concept that any time you have two possible outcomes they are, of course, equally likely.

[jasonfish11]

My analysis that created the formula. Or my analysis that is second guessing the formula because I have 4 possible outcomes not 2?

And yes that is where that formula came from. Use it every day and then decided to apply it to this argument I was having.

[madnak]

You're assuming a lot.

For one thing, even if Iraq had huge stockpiles of nukes, they probably wouldn't have used them on us. Having and using are two different things, but your calculations don't distinguish. Also, even a nuke in NYC wouldn't kill anywhere near 8 million. That's ridiculously large. Smaller-scale biological and chemical weapons would kill significantly under 82,000.

You assume that only 82,000 Iraqis die if we invade. If we invade and Iraq has weapons, then Iraq will almost definitely use those weapons, and the death toll may be extreme. The war still isn't over and people are still dying, so the 82,000 figure may be significantly lower than it should be. You also ignore the American deaths (over 3,000) that resulted from our invasion.

Of course, even the basic approach may be flawed - there are tremendous costs to war aside from the deaths. There are also considerations like our limited resources and the ethics of invasion. A good example is that if we only have the resources to invade one region, then Iraq has to be the best place to invade - if some other country is more of a threat, then that's the country we should be invading. Finally, the question of how much diplomacy/investigation we should do before declaring war is highly relevant in the decision.

Sticking with your reasoning - statistically, you can't just go half and half on the cost of avoiding war. That itself depends on the likelihood of WMDs. Other than that, you seem okay. So the cost of going to war is always 82,000, but the cost of avoiding war is 8,200,000x. We see an equilibrium when 82,000=8,200,000x, so we're "justified" by that reasoning when we are >.1% scertain of WMDs.

[tshort]

[ QUOTE ]
My analysis that created the formula. Or my analysis that is second guessing the formula because I have 4 possible outcomes not 2?

And yes that is where that formula came from. Use it every day and then decided to apply it to this argument I was having.

[/ QUOTE ]

I'm referring to your assumption when we don't invade. You have listed two possibilities:

1) They have WMD and kill 8 million people. It is important to assume here that if we don't invade and they did have WMD they would surely kill 8 million people in New York.

2) They don't have WMD and no one dies.

Two possibilities so they must each have a 1/2 chance of happening, right?

[jasonfish11]

[ QUOTE ]
Two possibilities so they must each have a 1/2 chance of happening, right?

[/ QUOTE ]


Yes and that is the biggest problem I have with the formula I have come up with. I think I might have come up with a better solution but still not sure.

As I stated the amount of NYs that will die is grossly overstated. In a real life situation the givens wouldnt be the death counts but instead you would know the amount of evidence you have. I thought that giving the non invasion options both 50/50 chance of happening is wrong. So how about this formula? Lets assume that we have 20% of the evidence says they have WMDs AND are planning on using them on the US. Lets also say we assume 100,000 people will die if we go to war. Can I modify the formula to what is below to find out how many lives must be at risk before invading is correct?

100,000(1) = (.2)X + .8(0)
100,000 = .2X
500,000 = X

Basically if we invade 100% of the time with only 20% of the evidence showing they have WMDs AND are going to use them on the US then there must be more than 500,000 people at risk to warrant invading. Does this seem like a better formula? Since you will have the % evidence as a given, and this differentiates the odds of them using WMDs on American (or what ever country) soil from them not having those WMDs and not using them. This way those 2 outcomes are not equal (because they wouldnt be in real life).

Oh and I think chemical weapons used correctly would kill way more than 82,000 people. For instance you could kill all 250,000 people in the stands of the Daytona 500 with a crop duster.

[Jamougha]

[ QUOTE ]

Oh and I think chemical weapons used correctly would kill way more than 82,000 people. For instance you could kill all 250,000 people in the stands of the Daytona 500 with a crop duster.

[/ QUOTE ]

You don't know much about chemical weapons then, especially the type that Iraq had the technology to make. This is not a realistic scenario, and I would be astonished if a chemical attack were to kill more than a few thousand people.

[Drag]

You forget about the probability that they would actually use them, even if they had them. You also forget about economical loses. I'd make a rough estimation that every $200.000 lost due to the war equals one saved life. (May be even less.)

All-in-all terrorists are way over estimated, the probability of death due to the terrorists attack is way below 1:10.000, compare it to the probability of death due to the traffic incidents 1:100.

[chezlaw]

You seem to have missed 5) Iraq has no WMDs and the invasion of Iraq kills lots of people and makes the use of WMD by a country that also didn't have WMDs more likely.

For obvious reasons it seems a bad plan to miss that possibility.

chez

[jasonfish11]

Ok. We were worried and had evidence (all be it small) that they were making NUCULEAR weaponry which would kill a lot more people than chemical weaponry. I was using that information not whether or not they had chemical weapons. Hell they have used chemical weapons we KNOW for a 100% fact they had the ability to make them. Chemical weaponry is irrelevant Im talking about the possibility of them having the ability to make nukes (that is why we first attacked).