Here some things you might do:   Militarily attack the country, pay off the dictator and restore your family friendships, place pressure on the dictator, try to get other people to kill the dictator, ignore the dictator, replace the resource, find another source of the resource, etc, etc.   One might attack a possible negative or positive risk/reward to each of these variables.   For instance, military conquest may cost x number of lives, but if it yields (in your calculation at least) y billions of dollars for Halliburton you may decide it's worth it.   Similarly, you may seek to minimize the risk that you will be arrested and tried as a war criminal while maximizing the possibility that your friends will profit to the maximum extent with respect to other resources.

The problem is how - assuming you're not a psychopath uninterested in human life - how to minimize x, lives lost, while maximizing y, Halliburton profits.    Other variables, like how you represent what you're doing and whether you lie or tell the truth, of course will have an effect on the probability of your results.   But if you are smart, you will try to figure this all out in advance so that you don't have to lie to yourself.

The example, of course, is a little sarcastic but the idea is practically applied in many other cases.   One assigns a "cost" to one variable, and a benefit to another, and tries to assess how best to minimize the cost while maximizing the benefit.    One can play with such values in order to get the best possible result.   It is almost always the case that that one changing cost is not straight forward.   One may lower costs and still lower profit, or one may raise costs and increase profits.   Note that "profits" and "costs" are not simply monetary.   They may involve other variables, like quality of life, or survival probability for your grandchildren, etc, etc.

My chief political issue is climate change, which I regard as the single most important issue faced by humanity in our time and possibly in any other time as well.    Usually when I write here, I write about nuclear energy, which can be shown to be the combinatorially minimized best option for addressing both the problems of energy supply and the environmental impact of energy, but - I'm sure detractors will appreciate it - that's all I'm going to say about that for now.

Instead I would like to give another example of a combinatorial problem.   Suppose that the world decides - and this is perfectly reasonable - that an excellent way to reduce carbon dioxide emissions is by replacing gasoline vehicles with diesel vehicles.   Diesel vehicles have better fuel efficiency after all, and, in this sense one can inject less carbon into the atmosphere if one simply chooses a diesel car.   Obviously the slowing of carbon dioxide emissons is a desirable thing, but does the decision entail any risks?   Well it turns out it does.

Increasingly - and happily - scientists are looking at these kinds of issues, and the topic is discussed in the current issue of the scientific journal Environmental Science and Technology (Environ. Sci. Technol. 2007, 41, 387-392).

Here is the abstract:

In 2001-2002 the UK began taxing vehicles according to CO2 emission rates. Since then, there has been a significant increase in consumer choice of small cars and diesel engines. We estimate CO2 reductions and air quality impacts resulting from UK consumers switching from petrol to diesel cars from 2001 to 2020. Annual reductions of 0.4  megatons (Mt) of CO2 and 1 million barrels of oil are estimated from switching to diesels. However, diesels emit higher levels of particulate matter estimated to result in 90 deaths annually (range 20-300). We estimate 570, 460, and 0 additional deaths per Mt of CO2 abated, for Euro III, Euro IV, and post-Euro IV emission class vehicles, respectively. CO2 policies are suspected to have contributed substantially to diesel growth, but the magnitude of impact has yet to be quantified rigorously. To the extent that CO2 policies contribute to diesel growth, coordinating CO2 controls with tightening of emission standards would save lives. This research shows that climate policy, while reducing fuel use and CO2, does not always ensure ancillary health benefits. Lessons from the UK can help inform policies designed elsewhere which strive to balance near-term ambient air quality and health with long-term climate mitigation.

Here is a link to the abstract.  

The full article requires a subscription, but here a few brief excerpts:

Climate mitigation policies have been promoted on the basis that reducing fossil fuel use provides dual benefits in terms of long-term climate change attenuation and short-term air quality improvements. Models predict that climate policies result in reduced fossil fuel combustion and lower air emissions, and subsequently provide public health benefits (1-4).

In Europe, diesel cars are viewed as a promising option to reduce greenhouse gas emissions from personal transportation. Diesel fuel has a higher energy and carbon density than petrol (38.5 MJ/L gross heating value and 778 g C/L, versus 34.9 MJ/L and 659 g C/L, but diesels have 25% better fuel economy based on matched pair vehicle models and thus emit 15-20% less CO2 per kilometer (5, 6). Beginning March 2001 a new vehicle excise duty (VED) was introduced in the UK whereby vehicles are taxed annually based upon certified CO2 emissions (7). In April 2002 the UK's company car benefit-in-kind tax was changed to a CO2-based system as well (8). Although a surcharge for diesel vehicles was applied to reflect their impact on air quality, the cost of owning diesel cars was and is lower...

...Changes in emissions of common air contaminants are estimated based on UK-specific emission factors for PM2.5 (2.5 micrometer aerodynamic diameter particulate), NOx, CO, HC, benzene, and 1,3 butadiene as provided in Table S2 of the SI. As with CO2, changes in emissions are quantified based on the difference between emission factors for petrol
and diesel cars...

...Humanhealth impacts resulting from changes in common air contaminants are estimated solely on changes in particulate matter emissions employing a conventional impact pathway method (20, 21). The rationale for using particulate matter is that it tends to dominate human health impacts from air pollution based on current science (20, 22-24)...

For the association between changes in ambient PM2.5 and mortality, we employ low, central, and high concentration- response coefficients. Our central mortality coefficient uses the results of the American Cancer Society cohort study from Pope and colleagues (2002) which found a 4%increase in chronic, all cause mortality per 10 íg/m3 increase inPM2.5 for a cohort of subjects age 30 and older in the United States
(33)...

...We estimate that consumers switching from petrol to diesel cars in the UK over the time period of 2001-2020 will reduceCO2 by 7 Mtand save 20 million barrels of oil. However, ancillary air quality effects hinge upon the fuel properties and conversion technology, not just the quantity of fuel consumed, and adverse air quality is estimated to result in
90 additional deaths annually (range 20-300).

Of course, one might argue that climate change involves it's own risk of loss of life, and, speaking only for myself, I think that is likely to affect far more people than the 90 dead Britons killed by the switch to diesel.

Note that this work refers to petroleum based diesel and not biodiesel or the even better option of using DME based diesels.    While biodiesel does produce particulates, they are are lowered with respect to petroleum diesel, but, in some cases at least, NOx seems to increase with respect to petroleum diesel.    I argue to the extent that it is available, biodiesel is far superior to petroleum diesel.

The best diesel option by far though is DME, about which I've written in previous diary entries.

DME produces essentially zero particulates and very low NOx, and is clearly the superior choice.   However, the means that one uses to produce DME will itself involve parameters and variables that are subject to combinatorial optimization analysis.