The usual rule is that whoever finishes the toilet paper must replace the roll. I think this is a poor allocation mechanism. It assigns a future service obligation to the person whose demand for the service has just fallen to zero.
When I leave the bathroom, I know that I no longer need toilet paper. I do not know who will enter next, whether they will need any, or when that need will arise. The next user will possess all of this information. There is an obvious efficiency argument for allowing the decision to remain with the better-informed agent.
My girlfriend objects that eventually someone will need a new roll. This establishes eventual demand. It does not establish that installation should occur now, or that I am the appropriate person to perform it. A replacement is sitting on the cistern. There is no supply shortage. The dispute concerns whether I must move it approximately eighteen inches before I leave.
This may seem like a trivial distinction. But the smallness of the task cuts both ways. If replacing the roll is genuinely negligible, assigning it to the next user cannot constitute a serious burden. If it is sufficiently unpleasant that she objects to doing it, then it is a real labor cost and my interest in avoiding it belongs in the analysis. It is inconsistent to price the same movement at zero when I perform it and above zero when she does.
The conventional defense appeals to responsibility: I used the last sheet. Yet consuming the last unit of a good does not ordinarily make one responsible for replenishing another person's supply. The rule becomes intuitive only after we assume that the holder must remain continuously stocked. That is the policy under dispute. Repeating it in the language of consideration does not establish its value.
There is a stronger practical objection. Discovering the empty tube after sitting down may impose an awkward reach. I accept that this is a cost. It should be compared with the certain cost of my replacing the roll in advance, weighted by the probability that the next visitor actually needs paper. People tend to visualize the inconvenient case and then silently assign it probability one. The bathroom is also used for brushing teeth.
In practice, the roll is always replaced eventually. The person with an immediate use for it performs the work, and the bathroom resumes normal operation. This is evidence that demand supplies an adequate incentive without a separate norm compelling advance provision.
My girlfriend has observed that she is usually that person. I agree that the resulting labor allocation is unequal. I would expect an efficient allocation to become unequal when one participant repeatedly demonstrates a stronger preference for maintaining the service. The fact that she finds an empty holder intolerable is a reason to expect her to replace it, not an explanation of why I should.
Third post about our apartment, for anyone keeping count. I've started replacing the roll when it gets about halfway down so it's never empty when he uses it. He hasn't noticed. I take that to mean he doesn't check the holder before sitting down, which doesn't fit the part of the post about being the better-informed agent.
Replacing a half-used roll destroys half a roll of option value.
The half roll goes on the shelf by the window. Nothing gets destroyed.
The information argument has a bigger cost argument sitting next to it. The next user knows their need, sure, but they discover the empty tube at the worst possible moment, sitting down and mid-use, which is exactly when replacement costs the most. The person leaving is standing up with free hands. Same task, very different cost depending on who does it. That's the efficiency case for the conventional rule, and it's stronger than the responsibility case the post argues against.
The cost differential is real but small. The spare is on the cistern, within reach of the seat. She has never been stranded.
"The bathroom is also used for brushing teeth." What fraction of visits in a two-person apartment don't need paper? Even if it's a third, the expected cost to the next user is far bigger than your eighteen inches.
What about a bond? Whoever takes the last sheet posts a small deposit, returned when they replace the roll. It puts the cost on the person who triggered it without anyone having to argue about norms.
A bond creates an incentive to leave a single sheet on the roll, which is worse than an empty tube for everyone.
Practical note, a vertical stand holder makes replacement take about two seconds. Most of the misery in this is the spring-loaded spindle.
That's an improvement in replacement technology. It lowers the cost without changing who should bear it.