## Conditional probabilities and evil insurers

July 30, 2009
Mike Konczal picks up on a great Taunter post about conditional probabilities, which comes with a nasty sting in the tail. When you buy health insurance, the main thing you're concerned about is tail risk: you want to be sure that in the unfortunate event you have stratospheric medical bills, the insurance company will be there to pay them.

The problem here is that you can't be sure of that.

Mike Konczal picks up on a great Taunter post about conditional probabilities, which comes with a nasty sting in the tail. When you buy health insurance, the main thing you’re concerned about is tail risk: you want to be sure that in the unfortunate event you have stratospheric medical bills, the insurance company will be there to pay them.

The problem here is that you can’t be sure of that. Indeed, by Taunter’s math, if you have stratospheric medical bills (this is where the conditional probability comes in), the chances of the insurance company paying them are quite possibly no higher than 50-50. The term of art for an insurer not paying an insured’s medical bills is “rescission”: the insurer rescinds the policy rather than pay the bills.

Here’s James Kwak:

The legal basis for rescission is that when you sign an insurance application, you are warranting that the information on the application is true; if it turns out not to be true, the insurer can get out of your insurance contract. It’s particularly nasty in practice because the insurer does not immediately investigate your application to determine if it is accurate before selling you the policy (that would be impractically expensive); instead, the insurer waits – years, in many cases – until you actually need expensive health care, and then does the investigation, which at that point is worth it because of the payments the insurer could potentially avoid. Also, you can lose your coverage for innocent mistakes, which are easy to make since the application form asks you if you have ever seen a doctor for any one of a long list of medical conditions that you are certain not to recognize or understand. (In a Congressional hearing, the CEO of a health insurer admitted that he did not know what several of the conditions listed on his company’s application were.)

Kwak’s parenthetical about how insurers can’t examine applications before they’re approved on the grounds that that would be “impractically expensive” misses the true evil here: the insurer wants to cash the insurance-premium checks of people who made fraudulent applications. Those are the most valuable insureds of all, because the minute they make claims which cost more than their premiums, their policies can be immediately rescinded. As Taunter puts it, you are free to play, you just aren’t free to win. And that’s why you get people being denied breast-cancer surgery on the basis of having had acne in the past.

This is a huge problem with any private-sector health insurance: it’s essentially impossible to gauge the quality of that insurance until it’s too late.

More generally, as Konczal says, this applies to other insurance policies too: CDS, for instance, or even hurricane insurance. In general, if you’re making a series of small payments now on the grounds that you will be paid a large sum of money if something bad happens, you’re running some large and unhedgeable counterparty risk. Which just goes to confirm what everybody deep down suspects: that a significant part of the money we spend on insurance policies is wasted.