The rotten fish problem

On the first day, all the fish at the fish stall are fresh.

Some sell, some don't.

The second day, the sold fish are replaced by newer, fresher fish. The unsold fish remains, even though it isn't so attractive.

By the third day, of course, the unsold fish is noticably unfresh, and it doesn't take much effort to avoid them.

At this point, part of the fishmonger's stock is demonstrably unappealing, bringing down the quality of the entire counter.

Pretty soon, of course, the dropoff in business means that the owner can't afford to buy the freshest fish, even to replace his sold inventory, and the end is near.

The alternative? On day two, discard the unsold fish.

Obvious, but difficult. So difficult that we rarely do it. We'd rather lower the average and see if we can get away with it instead.