Originally posted on Facebook on 2017-06-09
Here’s a weird thing that happened with our car a while back and an even weirder way that Bethany and I (meant to) decide what to do about it. I say “meant to” because the situation fixed itself before we had to decide anything. But the story works better if I describe it as if it happened this way.
So, the weird thing with the car: We had parked on the street all day and when we started to drive away we heard an awful noise so we checked it out and found a big stick wedged into the chassis underneath the car and scraping on the ground. We can’t fathom how that happened, but there we were.
I was convinced that nothing bad would happen if we just drove away with the stick there. The road would sand it away or it would work itself out, right? Bethany, generally more risk-averse than me, insisted, after our bare hands failed, that we jack up the car. But our jack didn’t work.
So now we had to decide between two possible actions:
My intuition was strongly in favor of #1 and Bee’s was strongly for #2. How would you resolve such a disagreement? Probably not like this… First we agree on some assumptions. Like, if the stick did cause damage it would cost, in expectation, $1k to fix. And, pulling another number out of our butts, option #2 would be $200 of hassle.
Basically we’ve agreed on everything except the probability of the stick causing damage. We can now resolve the disagreement by betting with each other, like so:
Those bets give us probabilities. Specifically, the market-determined probability of “car requires mechanic” is $1/($1+$9) = 10%. That means the expected cost of Risky is $1k (what we agreed we expected repairs to cost) times 10%, or $100. The cost of Safe is just the $200 of hassle. That means Risky costs, in expectation, $100 to Safe’s $200. So Risky wins!
If Bethany’s intuition is still screaming that this is a Horrible Idea then she can change the outcome by betting more money. Say she bumps up her bet to $10. That makes the implied probability of car damage close to 50% and Safe becomes the right choice. But I can also ratchet my bid higher. If we’re each pretty sure we’re right then we may do that until the amounts get scary. Maybe I’ll end up bidding $9k to Bee’s $1k. That means we’ll pick the Risky action like I want but I’ll have to pay Bee $9k if we damage the car in the process. If she’s still convinced that damage is likely then that’s a fine deal for her. My crazy insouciance means damaging the car is now fine with her since I’d be paying her enough to buy a whole new car. And if I’m totally convinced that there’s no way the stick will cause damage then it’s a free $1k for me. So we’re both happy with that bet, and with the decision it implies!
PS: Then Bee had the bright idea to drive halfway up the curb, since that should be similar to using a jack. Amusingly just backing up was enough to make the stick fall out. So the whole thing was moot, but now you know how we resolve such things in principle!
PPS: The conditional bets as decision mechanism is inspired by Robin Hanson’s Futarchy idea.