> Per mile basis is weird in a metro system because of distortions like how a mile in the centre is both slower and far more in demand than a mile at the edges.

What's the problem supposed to be? Passenger-miles automatically take that effect into account. They go down when speed goes down, and up when demand goes up.

> both slower and far more in demand

By the way, it sounds like you think this is something strange about a metro system, but higher demand means lower speed for every form of transportation.

> Basically, per passenger served.

This is a mistake; the guy who crosses the whole city has gotten more value out of the metro system than the guy who goes one stop.

I think that you're trying to force metro travel patterns into a normalized format for comparison with other modes that doesn't match actual usage patterns.

If we have to do that, then for my original post, the relevant factor is passenger minutes/hours travelled because the driver's cost scales with time not distance.

My cost is not proportional to either, though. If I go to my nearest station and go the next tube stop or if I go five tube stops the fare is the same. If anything it's inversely proportional e.g. the longer I spend on the train, the less I contribute to the driver's hourly wage.

The amount of time I spend and the amount of value I derive is entirely irrelevant to any of this.

I'm not especially interested in any of this beyond my original point that the cost of the driver is trivial on a per passenger basis, my back of the envelope calculation gives the same result (doesn't matter) even if you 3x or 0.33x the outcome.

> "the guy who crosses the whole city has gotten more value out of the metro system than the guy who goes one stop."

Not necessarily. The value you receive from a transportation service is mostly a function how badly you want/need to be at the destination, as well as things like how comfortable and fast the ride is. If anything, the guy travelling a shorter distance got more value because his ride took less time!

Or to put it another way, there is little value to me in travelling a long, laborious route all the way across the city if I don't have a pressing need to be at that destination. But if I need to be at work in 30 minutes I get huge value from taking the metro to the nearby station, even if it's only 2 stops away.

Your analysis doesn't work. In your terms, the guy who crosses the city has paid more (by spending more time) for what he received, and so you still assess him as having valued the trip more than the one-stop guy.

> But if I need to be at work in 30 minutes I get huge value from taking the metro to the nearby station, even if it's only 2 stops away.

Not really; as you just noted, the subway is a very slow method of covering distance. If you're in a hurry, it's not going to beat the alternatives.

> "the guy who crosses the city has paid more (by spending more time) for what he received, and so you still assess him as having valued the trip more than the one-stop guy."

No, I think you misread or misunderstood what I wrote. My point is that the "value" derived from a trip is _not_ proportional to the distance travelled.

> "Not really; as you just noted, the subway is a very slow method of covering distance. If you're in a hurry, it's not going to beat the alternatives."

In London, the tube or train is often the fastest way to get somewhere, particularly at rush hour. But if I place a high value on comfort, perhaps I'd consider that I get more value from a taxi ride even if it takes the same amount of time: the tube can be very hot and crowded! I'd then have to consider whether the extra value gained is enough to justify the higher cost of the taxi ride.