Monday, November 19, 2012

Risk Management


When asked to put a monetary value on life, we are inclined to assert that life is priceless and that no amount of money can compensate for a life.  However, when life and death becomes impersonal and more statistical, looking at the big picture, monetary values can be put on life.  Life insurance companies, for example, thrive by doing just that.  They are able to use probability models to calculate expected payouts and assign premiums accordingly.  Feldman’s discussion of Broome’s paradox challenged these models, reminding me of what we have been talking about regarding game theory and the cold war.  Feldman brings up the example of building a tunnel that will socially benefit people living in the area.  However, the construction of the tunnel is bound to put some of the construction workers’ lives at risk.   The government evaluates this risk, and generates a figure representing the “life cost” of this project. They then take these figures to a contractor and work out a contract that compensates for these potential risks.  The government then proceeds with the project, asserting that this “life cost” is less than the overall social benefit that will be gained in completion of the project.  However, as Broome suggests, this model falls apart when we know ahead of time which workers will die in the process.  If these people who were expected to die were then asked to assess how much money it would take for them to compensate for certain death, this figure would become exceedingly high, perhaps infinite. In this case, the “life cost” will no doubt exceed the project’s net social benefit.  Applying this same concept to war, we run into similar problems.  War-related decisions are typically evaluated based on the big picture.  These decisions tend to ignore the value of individual lives, and instead look instead toward net social benefit.   Game theory works the same way.  When applying game theory, we are asked to find the best option overall, looking for a point of equilibrium. However, in either of these cases, the individual value of life tends to be underestimated.  If infinite value was given to each individual life, we likely would not see the number of casualties that we do. How might our lives have been changed if mathematic models did somehow incorporate the value of individual lives? 

Along those same lines, we are all aware of the existence of terrorism, but it is interesting to consider how much of what we know has already been filtered by risk analysts.  Fischoff explains how experts can choose to magnify risks in order to motivate citizens, or they can trivialize real risks in order to limit the worries of the citizens.  In this way, Fischoff also shows how the individual person is not necessarily considered in risk analysis.  Instead, risk analysts tend to look at the big picture.  Sure, only five people died from anthrax.  This is relatively insignificant considering the population of the United States far exceeds this figure.  However, to each of those five families, the threat of anthrax is not something that should be trivialized.  How much of what we know about terrorism today is either exaggerated or down played in these ways?  Is this a problem?  What, if anything, should be done about it? Is there any way to both mathematically evaluate risk and consider each person’s value individually? 

9 comments:

  1. Erin, I like the questions you raise at the end of your first paragraph. I had some of the same questions as I was reading the articles. Risk assessment is a fascinating area of mathematics, I think, because it attempts to quantify uncertain future outcomes on a macro scale, while largely ignoring individual qualities, behaviors, and choices that make persons unique. Risk assessment is uncomfortable for many and often perceived as “cold and calculating,” I think, because it attempts to assign value (monetary or other) to arguably invaluable items, such as human life, health, and safety. Both Feldman and Fischhoff’s articles are interesting to consider alongside modern health and life insurance plans which no doubt use risk assessment to determine coverage premiums. Erin mentions Feldman’s hypothetical scenario, in which a tunnel is constructed and a “life cost” is assessed based upon the relative risks builders are exposed to during construction. Of course, if the deaths of specific individuals were certain during the construction of the tunnel, then those individuals would require a huge sum of money, perhaps even an infinite sum as Feldman mentions. Much the same way, life insurance policies (and health insurance policies, for that matter) come at enormous cost and may even be impossible to obtain for those with serious pre-existing conditions or the elderly. In general, it seems that premiums (somewhat analogous to Feldman’s “life cost”) increase as perceived likelihood of payout increases. If mathematical models incorporated the complete value of each human life, I think institutions which operate on the principles of risk assessment, such as life and health insurance companies, would be unable to function effectively, and decision-making in times of crisis would be paralyzed since all decisions in such situations carry some risk for some individuals. If infinite value was given to each and every person's life, then any possible plan would be too potentially harmful to implement since it would carry with it enormous potential life costs.

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    1. I think it is interesting that you mention that institutions such as life and health insurance companies that employ risk assessment would not be able to function if they used the complete value of human life. The cost would then be too high to carry out any agenda. While I do agree that putting a cost on a human life makes living and dying impersonal and lowers the value of life, however, if every life had infinite value, no decisions would ever be made and the institutions previously mentioned would not operate effectively, as Michael suggested. It seems cold but might there exist some situations where quantifying a life may save many or have a better outcome than considering the life value infinite? So, I agree with Michael's point that institutions that use risk assessment would not function or be able to make critical decisions if every life had an infinite value.

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  2. Going off of your first question, I think that.. well honestly I'm not sure such a question can be adequately answered - personally, I think that the value of individual lives is too relative to be accurately described by a certain mathematical model. I mean technically the VOT model proposed by Feldman is far more "certain" than the value of life parameters, but where in real life does that kind of linear certainty of life extension exist?
    Now, in terms of corporate economics or government politics, of course you can set an average value to a life and use that to make a half-assed (excuse my German) attempt to justify an action or to very loosely generalize a situation such as that made by government contractors; and really I mean they don't usually do too horrible of a job with that. But if we were looking for a model that truly and accurately predicts the values of individual lives.. well, if such a thing existed it would be a lot more complicated than could be explained in under 24 pages.
    Indeed, I really think there is something to be said about the individual's perceived value of life - when Feldman was working over the probabilistic value of life model, I think one of the most crucial points he brought up was how the model predicted that as altruism increases, VOL decreases, and the opposite relation for fear of death. I find that this is perhaps one of the most realistic statements that he made (and indeed remarkable that he was able to predict it with the model) because I don't know about you guys but those are exactly the relationships I've observed, and thus I find them extremely realistically applicable.
    Really, I guess it all depends on the point of view. Like I said, if we were to accurately determine the value of an individual life, we would have to expand our relation to an infinitely complex study of quantifying an individual's perceived state of altruism. Unfortunately, because of such difficulties, we tend instead to focus on the value of an individual life from the viewpoint of the movers and shakers; and that value [especially in terms of war] often tends to be astonishingly low.

    How might our lives have been changed if mathematical models incorporated the value of individual lives? Well in either case, I might have to say they would be made worse; they could either be measured from the individual's perspective on their own life and thus have to incorporate such a wide range of relativity that the social benefits of things like construction is so heavily outweighed that all social benefits come to a halt.... or they can be considered from the corporate perspective wherein each individual is just one tiny ant in a colony of billions.

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  3. Erin, you bring up an interesting point of evaluating what acceptable risk is, especially in terms of terrorism. My paper for this class focuses on terrorism and game theory, so several of the questions you ask in your second paragraph are questions I asked when researching for the paper. In a lot of the literature I've read, the authors usually steer away from talking about the value of human life since it is such a sensitive topic. The other authors who discuss placing a value on human life usually do so in terms of a monetary value, which seems very cold and calculating, but the costs are usually in terms of something else, such as safety equipment. For example, in 2006, the Department of Transportation monetized the value of human life at $2.86 million dollars for cost-benefit analyses of safety equipment. Very rarely do the authors actually incorporate the value of human life into their analyses because the quandary of quantifying human life edges on other issues that make people uncomfortable, such as the definition of life (abortion debate) and whether one life is worth more than another (eugenics-esque). The value of life is something I don’t think will be decided anytime soon.

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  4. The concept of "life cost" is a very interesting thing that our government does. For instance, in my research of the paper I stumbled upon how the EPA uses mathematical models to "assess" the risk a new pesticide would have on the environment. It seems that when a new chemical is going in to public domain, they test to see if the risk is at an acceptable level. It is interesting how even the EPA will determine whether or not a chemical will be sprayed on our food is by running test, and then checking to see if "life cost" is adequately outweighed by the social benefits. This is something that I feel while may be useful in a business sense, like for insurance agencies, it should be used when it is something that could affect all of our lives.

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  5. Erin, I wanted to comment on your mention of how experts can manipulate stats by whether or not they "magnify" them. Fischoff in his article points out how the American people often want to know all the facts regardless of what they signify, but at times can do without the information if it means their safety. In the latter case, this arises from a public trust in the institution withholding the facts. It is here where our "experts" have a great responsibility to act morally, justly, and with good reason. Sometimes, and especially recently, this trust in "experts" can wane.

    A current illustration is the Patraeus scandal. Now I will not speculate on conspiracy theories without more facts as some in the general media will. However, I do think that it is important the facts of the case do become public if any conclusions are drawn of national concern. If I am not mistaken, the trial is currently closed to the public. This US government is ultimately the employees of the people. I think at times this role is confusingly reversed.

    Finally, I appreciated everyone's analysis of Feldman's article. One aspect that I would like to point out is an argument Feldman claimed against the "probabilistic willingness-to-pay" approach. He states that people tend to undergo activities that increase their probability of death (i.e. climbing Mount Everest, base jumping, skiing, etc.). I wonder if there is a way to mathematically explain people's willingness to complete activities that increase their current chances of death in order to experience life more? Is this reasonable irrationality? Or is this just pure human madness?

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  6. Erin, I am glad you brought up Broome's Paradox (the tunnel) because as I was reading this I just found it enlightening and disturbing that this counts as academic research in economics from someone at Brown as the theory behind the "willingness to accept" is crude at best.

    So lets make the same initial assumptions that a government planner wants to make a tunnel and needs N workers to do so who incur an increased risk of death with probability P (which is how sane human beings denote fixed probabilities... not with this "box" nonsense) and each person has an identical cost C to accept the risk. Lets use some real numbers shall we?

    Lets say N=1000, P=0.001 and C=$10,000. Then it follows immediately that one would expect that NP=1 person on average will lose their life. Furthermore, we find that the "probabilistic willingness-to-accept" (which as I understand is essentially the value of a life based on the known risks) is C/P=$10,000,000 which I suppose isn't too unreasonable.

    What happens if the project is extremely risky? Say P=0.999 but all else remains the same (as they are being treated as constant values at that point in the paper) then NP=999 and C/P=$10,010.01 implying that increased risk of death actually lowers the value of a life. How does that even make sense? This kind of phenomena reminds me of Kurt Tucholsky line in his book "French Joke" (this quote is often misattributed to Stalin) "The death of one man: that is catastrophe. One hundred thousand deaths: that is statistics."

    So it seems that this whole willingness-to-pay is based on a really crude model from the get go. I thought to myself, well, maybe it is just the case that it is a historical aspect that is lost in the modern version of the model. Sadly, this is not the case. Right there under assumption one (bottom of page 6) we see that the insurance value of a person's life is their premium divided by the probability of death. So really, this isn't the value of life to anyone other than an insurance company. This model really does explain why insurers really don't want to cover people with preexisting conditions, their probability for death or some form of monetary compensation is much higher than those of us who have no (apparent) preexisting conditions.

    So, if the value of someone's life is modeled in such a way why do we (as a modern civilization) bother doing it like that at all? Should we really be tempting people with increased risk of death for monetary compensation? Hell, those who are most likely to be exploited are likely to be unaware of the full set of risks that they take from jobs with a "large" compensation for the risk. Should it not be the case that we do something that is of such risk out of personal desire to do so and not out of (essentially) artificial economic concerns?

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  7. I also find risk assessment very interesting and believe that although it is impossible to financially quantify an individual life it is necessary in this world. Broome suggests that the "life cost" model falls apart when it is known which individuals will die, which seems obvious to me. As humans we generally fear death and avoid it at all cost. Obviously there is no sum of money people would willingly accept death for, but that is why it is important to discard human emotion in these calculations. When considering the greater good the primary concern cannot be that everyone lives or is free of the risk of death. For social productivity we must accept that some will die. It is unnecessary risk that mathematically modeling life helps us avoid.

    So why, if we so desperately want to live, do humans engage in dangerous activities. This is discussed in Feldman's article who points out people tend to participate in activities that increase probability of death. I would say this is often because such activities, skydiving, skiing, climbing, etc., are activities that can make us feel more alive. I can't imagine a mathematical model that is able to account for the human desire for fun. How can we account for activities that are seemingly irrational?

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  8. Erin, I thought your analysis was really great as I had many of the exact same questions as I was doing to readings. Although I agree that reducing human lives to numbers isn't pretty- It is an unfortunate but necessary part of life as long as the world we are living in is imperfect. The inventor of the automobile could arguably be considered one of the greatest mass murders of all time, yet I don't think anyone would say that they wish cars had never been invented. Furthermore, there are many, many things/principles/people that other people consider far more valuable then their own lives, so how does a risk model account for this? Everyone I think knows of someone or something that they would willing die for. Without putting lives at risk, the industrial/scientific revolution would have never happened and America would still be a slave nation. It isn't popular to say so, but there comes a point when one simply has to put emotions aside and risk management/game theory are good examples. In most cases logic creates a better result than emotions.

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