The Risk Paradox

In economics, the theory goes, actors can be risk loving, risk neutral, or risk averse. Most people, the theory continues, are risk averse. Insurance institutions are risk neutral and rarely you will encounter perhaps a gambling addict or some such individual who is actually risk loving.

Risk loving actors introduce a paradox which is not often discussed. Consider a proposition which includes some level of risk, even if the level of risk is small. The risk averse actor obtains a level of utility which is less than the risk-absent level of utility. The risk neutral actor obtains a level of utility which is equal to the risk-absent level of utility. The risk-loving actor, however, gains more utility than that actor would gain in the risk-absent but otherwise equivalent transaction.

Now, consider the alternative where there is no risk. In this case the risk averse, risk neutral, and risk loving individuals all have an equal level of utility. Because real transactions are a mix of risky and non-risky transactions, the risk-loving actor is expected to maximize overall utility. The gain is even more pronounced when one considers that real world transactions are a very uneven mix, with the majority of transactions being uncertain or risky.

However, risk-loving actors are also subject to rational robbery. A great example of rational robbery would be a gambling game, but there are other examples as well. In the gambling game I propose the following: let us flip a coin. If it lands on heads you give me a dollar and if it lands on tails then I will give you a dollar. This is a fair game and a risk neutral actor would play, but gain no net utility. The risk neutral actor would be indifferent. The risk loving actor would both play and also gain a utility premium, which has some dollar value. If I can identify the value of this premium held by the risk lover then I can rationally rob him with an unfair version of the game, regardless of my own level of risk preference.

Let’s say the risk-lover values the fair dollar game at a rate of $.10 per game because the risk is enjoyable to that actor. Now I could invite the risk lover to play an unfair coin game in which a heads means he pays me $1.05 and tails means I pay him $1. Notice that his expected loss is less than his utility from the game, which makes the game rational from his perspective. Yet it won’t be long before the guy is broke, and it takes money for him to engage in the game or otherwise to obtain utility.

So we have reached the crux of the risk-lover’s paradox. In one sense it utility maximizing to be a risk lover and in another way it is not. So what’s the solution? The solution is that being risk neutral is efficient and preferable.

We know that risk neutrality is efficient because it is the long run market outcome. In the short run risk aversion and risk loving may be viable options, but in the long run neither of them are. Risk loving in the long run is not viable due to rational robbery and risk aversion is not viable because it will always result in an insurance profit opportunity. Insurance transactions will occur until market risk neutrality has been reached.

We know that risk neutrality is not only efficient, but also preferable or moral, due to the moral argument I call nature as a worldview filter, which is essentially an argument for the morality of efficiency per se and generally. Consider that risk lovers are more likely to get killed through risky actions, and also that economic flourishing will lead risk neutral actors to overtake the population through a gradual out-competing of others in a sort of evolution process.

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