Published on December 23, 2024 3:40 AM GMT
An incredibly productive way of working with the world is to reduce acomplex question to something that can be modeled mathematically andthen do the math. The most common way this can fail, however, is whenyour model is missing important properties of the real world.
Consider insurance: there's some event with probability X% under whichyou'd be out $Y, you want to maximize the logarithm of your wealth,and your current wealth is $Z. Under this model, you can calculate (more)the most you should be willing to pay to insure against this.
This is a nice application of the Kellycriterion, though whether maximizing log wealth is a good goal isarguable (ex: bankruptcy is notinfinitely bad, the definition of 'wealth' for this purpose is tricky).But another one thing it misses is that many things we call"insurance" have important properties that diverge from this model:
There can be a collective bargaining component. For example,health insurance generally includes a network of providers who haveagreed to lower rates. Even if your bankroll were as large as theinsurance company's, this could still make taking insurance worth itfor access to their negotiated rates.
An insurance company is often better suited to learn about howto avoid risks than individuals. My homeowner's insurance companyrequires various things to reduce their risk: maybe I don't knowwhether to check for Federal Pacific breaker panels, but my insurancecompany does. Title insurance companies maintain databases. Specialtyinsurers develop expertise in rare risks.
Insurance can surface cases where people don't agree on how high therisk is, and force them to explicitly account for it on balancesheets.
Insurance can be a scapegoat, allowing people to set limits onotherwise very high expenses. Society (though less LW, which I thinkis eroding a net-positive arrangement) generally agrees that if aparent buys health insurance for their child then if the insurancecompany says no to some treatment we should perhaps blame theinsurance company for being uncaring but not blame the parent for notpaying out of pocket. This lets the insurance company put downwardpressure on costs without individuals needing to make this kind ofpainful decision.
Relatedly, agreeing in advance how to handle a wide range of scenariosis difficult, and you can offload this to insurance. Maybe two peoplewould find it challenging to agree in the moment under whichcircumstances it's worth spending money on a shared pet's health, butcan agree to split the payment for pet health insurance. You can useinsurance requirements instead of questioning someone else'sjudgement, or as a way to turn down a risky proposition.
There are still cases where the model is useful: none of thesebenefits would apply to insuring my mandolin, computer, or a flight,and none of these are a large enough portion of my wealth for thecalculator to say I should get the insurance. But if you apply themodel without thinking about how well it applies in a particular caseit will often tell you not to buy insurance in cases where insurancewould actually help.
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