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Thursday, August 12, 2004

Risk, Utility, and Iraq

Each person has a different amount of aversion to risk. The level of aversion to risk also varies by subject. For example, someone may ride motorcycles but be unwilling to fly in airplanes, even knowing the exact rational probabilities of injury or death from the two different activities.

In utility theory, risk is subjective, but can be quantified. After the risk is quantified, tools can be used to analyze problems to arrive at optimal solutions.

As an example of how risk aversion might be characterized for a given individual for a given subject, consider the following. Let's say an individual is 50 years old with total net worth of $500,000 and is trying to balance their portfolio in order to maximize his or her risk adjusted return, where the risk reflects his or her subjective utility as opposed to standard risk adjustment methods based on volatility. The individual might be asked if they would bet their entire net worth for a 99% chance at 10 times that net worth. Then a 90%, 50%, 25%, etc. chance. Then for a chance at 8 times, 5 times, etc. the net worth. Then the bet limited to a half, quarter, etc. of the net worth. Different time frames for the bet would also have to be explored.

From these number, a multi-dimensional risk profile can be created, which then allows an objective analysis to maximize the expected risk adjusted return of the portfolio going forward. The general idea is that some individuals assign such low utility to any approach that can produce outcomes with any losses at all that it makes sense for them to invest very conservatively. Others aren't concerned in the least with downside, and for them a maximally aggressive strategy is optimal.

Neither investing approach is inherently correct, better, or right for everybody. The approach is and must be based on subjective preferences. It is also important to understand that if by the above analysis an individual rationally chooses a highly aggressive investment strategy, it was the right choice, even if it turns out that the investment strategy produced large losses going forward. It doesn't mean that the individual was stupid or crazy, just that the individual was unlucky.

Now consider Iraq. Invading Iraq had/has many potential downsides, many of which were/are horribly catastrophic. Invading Iraq also had/has potential upsides. In this case, each voter wants to optimize his or her utility with respect to invading Iraq and vote for representatives based on that utility.

Like the above financial example, the utility profile of an individual voter with regard to our approach to Iraq could be estimated. Unlike the above financial example, once the utility profile is created, we can't restrict ourselves to objective mathematics to find the optimal solution (i.e., whether or not to invade, occupy, assist, etc.) since the information regarding the likelihood of each outcome is extremely sparse and unreliable, forcing intuitive and subjective analysis.

However, the point is that even if the information regarding Iraq were perfect and the analysis perfectly rational, the utility to each individual voter regarding our approach to Iraq and the possible outcomes would still vary substantially because of each person's subjective risk profile for this subject. Also, even if Iraq ends catastrophically, it doesn't mean it was the wrong thing to do. Vice-versa, if it ends well, it doesn't mean invading Iraq was the right thing to do. The decisions are inherently affected by subjective utility.

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