TO: Condeleeza Rice, National Security Advisor
FROM: Jane Feng, Intern to National Security Advisor
Re: Quantitative Assessment of North Korea Plan Proposals
Introduction:
Ensuing discussions with North Korea, the Chairman of the Senate Foreign
Relations Committee has returned with a proposal from the North Koreans asking for the
US, ROK, and Japan to provide ten electric generating plants, an electric distribution
system, and fuel oil. In return, North Korea would comply with the IAEA by freezing the
construction of nuclear weapons and turning over the plutonium generated at Yongbyon.
However, the Secretary of Defense rejects this proposal and instead, offers an alternative
proposal of immediately launching a “surgical” attack on the nuclear facilities at
Yongbyon. This paper conducts a quantitative analysis of the two alternatives.
Analysis
Based on the state of information given, I created a decision tree representing the
two alternatives, the uncertain variables with their probabilities, and the possible
outcomes.
70%
Comply
-2.5
-2.5
30%
Cheat
-1
-54
50%
NK attacks
-100
-103
30%
NK rebuilds
0
-3
20%
Rhetoric only
0
-3
Alternative A
0
-17.95
Root
0
-17.95
Alternative B
-3
-53
Alt. B
-3
-54
50%
NK attack
-100
-104
30%
NK rebuild
0
-4
20%
Rhetoric
0
-4
Alternative A
The cost of North Korea’s proposal includes $3B for ten electric plants (at $300M
each), $2B for the distribution system, and $2.5B for fuel oil ($500M for five years).
This amount of $7.5B split evenly among the three allies results in a cost of $2.5B for the
US. However, given that North Korea has backed out of its agreement before, there is a
fairly strong possibility that it will cheat again. In this case, the time that it will take to
uncover the situation will have resulted in two years of sunk cost for construction in the
amount of $1B for the US ($2.5 x 2 years / 5 years). As soon as cheating is discovered,
alternative B will be exercised immediately.
Alternative B
The uncertainty in this proposal brings along extremely risky consequences.
First, this plan of action costs $3B, which includes the cruise missile operation of $1B
and the cost of precautionary troop reinforcement of $2B. Following this attack, there is
a 50% chance of North Koreans immediately launching a full-scale attack on South
Korea, which requires the US to spend $100B to win the war. The 10,000 US casualties
will not be taken into account for now but will be discussed later on.
Result
Using the presented information, the best alternative is to agree to North Korea’s
proposal. Using the decision tree, one can see that the expected cost of alternative B is
$53B, which results from $3B in addition to the 50% possibility of spending $100B. On
the other hand, alternative A has an expected of cost of $17.95B, which is calculated
from 70% chance of spending $2.5B if NK complies and 30% chance of spending $54B
if NK Cheats. By agreeing to North Korea’s proposal, the US can expect to save
$35.05B, or 66% over launching a cruise missile attack.
Why It Makes Sense
The expected cost gap between the two alternatives is so wide that not many
factors could change the result quantitatively. One can get an intuitive sense of the
difference by looking the worst-case scenarios for each proposal. For alternative B, the
worst that can happen is if NK immediately attacks in response to the US surgical attack,
resulting in a total cost of $103B. In alternative A, the US discovers cheating and carries
out plan B, resulting in a total cost of $104B. There is only a $1B difference between the
worst-case scenarios of the two proposals. However, in alternative A, there is only a 15%
chance (30% possibility of cheating, 50% possibility of attack) of getting to that point,
whereas alternative B has a much larger - 50% - chance of 90-day war.
Sensitivity Analysis
Given the huge discrepancy between the two alternatives, the decision is not very
sensitive to changes in the uncertainties. The most important factor that differentiates the
two proposals is likeliness of NK to comply or cheat on the agreement.
60.00
50.00
30.00
20.00
10.00
0%
10
%
20
%
30
%
40
%
50
%
60
%
70
%
80
%
90
%
10
0%
0.00
% chance of NK compliance
Cost
40.00
Alternative A
Alternative B
Even so, the chance of cheating would need to increase dramatically in order to conclude
that alternative B is the better option. As the probability of NK compliance increases, the
cost saving of alternative A over alternative B amplifies. Unless NK has lower than a
1.942% chance of compliance (the intersection of the two cost structures), alternative A
will always serve as the more economical choice (Appendix A).
While the analysis proves to be quite insensitive to a probability shift in NK
compliance, the probability of NK attacking has absolutely no impact at all in changing
the decision (given that the other factors remain the same). At a 70% compliance rate,
the probability of NK attacking does not matter – alternative A will always have a lower
cost.
120.00
100.00
60.00
Cost
80.00
Alternative A
Alternative B
40.00
20.00
0%
10
%
20
%
30
%
40
%
50
%
60
%
70
%
80
%
90
%
10
0%
0.00
% chance of NK attack
The only exception is if the US were 100% certain that NK would not counterattack. In
this case, precautionary troop reinforcement would not be necessary, therefore
eliminating the need for the $2B expenditure. The total cost would then be $1B, cheaper
than alternative A’s cost of $2.5B.
To further investigate the impact of these two important variables, I conducted a
multi-variable sensitivity analysis. The following graph shows the probability of NK
compliance and the chance of a NK attack that would make the decision-maker
indifferent to the two proposals.
100%
80%
60%
break even line
40%
20%
28
%
13
%
16
%
19
%
22
%
25
%
7%
10
%
0%
1%
4%
% chance of NK attack
Break even line between the two alternatives
% chance of compliance
Any combination above the line represents support for alternative A, whereas
combination of probabilities below the line means that alternative B is more cost
effective. Looking at the shape of the curve, one can see that as the probability of
compliance gets higher, the probability of a NK attack matters less and less. However, if
the probability of compliance were low – say 5%, then the chance of a NK attack would
greatly influence the decision since the curve is so steep in that area.
Additional Considerations
Several factors were not entered into the above analysis due to certain limitations.
First, the 10,000 American casualties were not quantified because of disagreements on
values of human life, ranging from several hundred thousand to several million. In my
own calculation, I subtracted the age at death from life expectancy and multiplied that by
the GNP per capital (which represents earning potential). Accordingly, I computed
(76.91 - 28.42) x $34,1003 to be $1.65M per life. With this amount included in the
analysis, it offers further support that alternative A is the better choice.
Another factor that could not be fully incorporated is the 30% chance that NK
would rebuild its facilities given a US attack. Because the time frame is 5 years, the
possibility of further attacks is not considered. When included in the decision tree, the
expected costs for both alternatives increase (Appendix B). The expected cost of
alternative A increases 26.6% whereas the cost of alternative B increase 30%, so this also
gives alternative A further support.
Finally, the impact of additional costs on the construction of electrical plants
could very well affect the decision. For one, perhaps Japan and South Korea do not agree
to help pay the costs. Secondly, North Korea could continue to ask for more economic
support if the electricity generated is insufficient. In the case that US would be willing or
forced to continue this support, alternative B could be the better choice. However, the
cost must be more than $52.6M in order to switch to the missile attack plan (Appendix
C).
Conclusion
In conclusion, alternative A is a much more economical than its counterpart. The
decision tree shows that the cost savings are huge. The sensitivity analyses show that this
decision is not susceptible to changes in the variables. There must be drastic change in
order to call for a switch to plan B.
___________________________________________________________________________________________________________
1. United States Department of Health and Services, 10/10/2001
http://www.hhs.gov/news/press/2001pres/20011010.html
2. Department of Defense Almanac
http://www.defenselink.mil/pubs/almanac/
3. GNP Per Capita 2000
http://www.iea.org/public/studies/beyond/table7.pdf
Appendix A.
A 98% chance of cheating would make two alternatives have equal expected costs. The
lower the chance of cheating, the lower the expected cost of alternative A.
1.942%
Alternative A
0
-53
98.058%
Root
0
-53
Alternative B
-3
-53
Appendix B.
Comply
-2.5
-2.5
Cheat
-1
-54
50%
NK attacks
-100
-103
30%
NK rebuilds
0
-3
20%
Rhetoric only
0
-3
Alt. B
-3
-54
50%
NK attack
-100
-104
30%
NK rebuild
0
-4
20%
Rhetoric
0
-4
70%
Comply
-2.5
-2.5
30%
Cheat
-1
-69.9
50%
NK attacks
-100
-103
Alternative A
0
-22.72
Root
0
-22.72
Alternative B
-3
-68.9
Alt. B
-3
-69.9
30%
NK rebuilds
0
-56
20%
Rhetoric only
0
-3
50%
NK attack
-100
-104
30%
NK rebuild
0
-57
20%
Rhetoric
0
-4
US attacks again
-3
-56
US attack 2
-3
-57
50%
nk attack
-100
-107
30%
rebuild
0
-7
20%
rhetoric
0
-7
50%
nk counterattacks
-100
-106
30%
rebuild again
0
-6
20%
only rhetoric
0
-6
Appendix C.
80
70
60
Cost
50
40
30
20
10
0
Alternative A
Alternative B