People worry about all sorts of ridiculous small probabilities. Small probability events tend to loom large in their minds, making them worry about rare disasters (planes crashing, being eaten by sharks) and placing their hopes in things that are extremely unlikely to happen (winning the lottery, cheap online viagra actually working).
But you can use this to your advantage and help out your friends at the same time.
First, find some medium size loss that the friend is unusually worried about. For instance, a few months ago a friend and I were driving around looking for a parking spot. We saw a place that we thought might be connected with the restaurant that we were going to, but we weren't sure.
My friend seemed worried that this might cause him to get a parking ticket. I judged this pretty unlikely - I was maybe 80% sure that the parking lot was for the restaurant, and that even if it weren't, we had at most a 10% chance of getting a ticket over lunch.
So, I made the following offer. "Tell you what", I said, "I'll indemnify you against the cost of the parking ticket, should we actually get one. I'll pay the whole lot."
And people love this kind of offer. If they are a worrier, you've given them peace of mind, and you make yourself look cool as the man who is willing to (in the immortal words of Warren Buffet) "retain [his] risks, and depend on nobody."
And the best part? It costs you next to nothing, at least in expectation. My expected chance of getting caught is 2% - if the ticket is $50, each guarantee only costs me a dollar. But to your friend, the salient comparison is the offer to pay $50 and their peace of mind.
B-b-b-b-bargain.
Behavioural Economics and micro-insurance, man. It's what the cool kids are doing.
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