Figuring out the future and the now

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Why did your premium go up when someone else hit your parked car?

It feels unfair. You did nothing wrong. Someone else drove into your car outside your house and now you’re paying more. Surely that’s just the insurer clawing back their loss?

Maybe. But maybe not. Let me take the scenic route to explaining why.

Driving my daughter to school, I occasionally spot someone tailgating or cutting across a solid line. What’s striking is how often within seconds I’ll see them make a second and third thoughtless move. Weaving without indicating, pushing into the off-ramp queue at the last moment – all the sorts of things nobody does in the queue at Woolies when there is accountability. Ring of Gyges stuff – and frankly unfair that both types of people populate this universe.

Yes, there’s confirmation bias here. I’m sure I make mistakes that annoy others. Attribution bias too – we forgive our own lapses as innocent mistakes while judging others harshly. I don’t think that’s all of it though.

What we’re observing is that observations are usually not independent. Errors cluster. They share root causes, be it time pressure, risk tolerance, cell phone use, attitudes towards others, personality, upbringing and more. Whatever produces one lapse doesn’t reset between intersections. One observation carries information about an underlying factor you can’t directly see.

When you see a pattern, update your priors on what comes next.

Back to that not-at-fault claim. A claim happened. And empirically, one claim predicts the next. The insurer often doesn’t know why, but the signal is there in the data. Maybe your car is parked on a busy road. Maybe it’s closer to a corner than ideal, or near a distracting intersection. Maybe street lighting is poor. Maybe it’s just a high-traffic area where the probability of someone having a bad day near your vehicle is elevated. As more complex analysis tools (yes including AI…) are applied, with more data and more context, we may get closer to understanding the hidden risk factors underneath the high level outcomes. Either way, the correlation is there.

The customer likely did nothing wrong. The premium increase can still reflect rational Bayesian updating.

Now, is it always this principled? No. Sometimes it’s crude loss-ratio management. The insurer just wants to recover what they paid out over time. Sometimes the pricing model can’t even distinguish at-fault from not-at-fault, so everything gets the same treatment. These practices exist, and they’re harder to defend.

The legitimate version, where claims predict future claims for reasons the policyholder can’t fully observe or control, that’s real too. And if the signal is real, not adjusting the premium means other policyholders cross-subsidise the risk. The question isn’t whether someone pays, but who.

If you feel this is still unfair, well I think you’re correct on some level, albeit not yet a practical one:

All risk rating involves a choice about what “fair” means. Is it fair that you pay a price tailored to your risk, even if that risk stems from factors you didn’t choose? Or is it fairer that we all pay the same, pooling our luck and misfortune together? The young driver pays more not because they decided to be nineteen, but because nineteen-year-olds crash more often. Risk-based fairness says differentiate. Solidarity-based fairness says pool.

These aren’t the same definition, and better maths won’t reconcile them. We try to draw lines, some factors “feel” acceptable, others don’t, but those lines are social and political choices, not mathematical ones. Therefore they will differ between people, between firms, and over time.

So next time your premium moves in a way that feels unjust, ask whether the insurer is being lazy or seeing something real. But also ask who else would pay if you didn’t. Insurance is a group exercise, and the maths doesn’t care about fault. Only we do.


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