Comment by mindslight

By "perfect information" do you mean the ability to predict the future? Because that is what is necessary to make your statement true.

Because in general no, people buying insurance do not pay in what they will individually cost (plus margin). Rather most will be paying in much more than they will ever cost, whereas some will cost much more than they have, or ever will have, pay in. One total property loss or serious at-fault auto collision (say ~$400k) will dwarf a lifetime of premiums ($2k/year for 50 years?).

The point is that such things are rare, so most people will have zero of them over their lifetime. But even perfectly knowing the a priori chance that each person may suffer a catastrophic loss, you can't know which specific people it will be.