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I've assumed for a long time that fares on rapit transit systems like the subway ot the BART should obey the triangle inequality: going from A to C directly shouldn't cost more than going from A to B, leaving the system, and then coming back in to go from B to C. But now I wonder why I ever thought this. A short, direct route is a valuable thing, and a passenger might be willing to pay a premium for it. Or to make the difference even clearer, suppose, that the route from A to C via B uses an old, grungy, low-speed service, and the direct route is fast and clean. You might be willing to pay more for the direct route.
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