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FYI, Sidecar did this in 2013 - you could set your own price, both as a rider and driver. Then, when you request a ride, it would be more like market-making, with you getting matched with the driver whose price is closest to your requested price, but under it. I personally tried using this many times - it was a poor experience for riders. I can imagine it wasn't very pleasant for drivers either.

The theoretical ideal price for a ridesharing trip changes in realtime and depends on many different factors like how many drivers are nearby, how many other riders are nearby, each driver's willingness to drive to your destination, etc. Letting riders and drivers set their own prices would make the market significantly less efficient, and would make both the experience for both sides of the marketplace quite miserable, especially during events like demand spikes. There is literally a several hundred-strong organization at Uber (Marketplace) whose single focus is to make a maximally efficient marketplace. It's honestly kind of dismissive to suggest something like this, and to call it "a simple change".

Disclaimer: the above is not meant to be a representation of how Uber pricing works, just my own theoretical musing

Honestly, even trying to achieve the "theoretical ideal price" based on supply and demand is already screwing up with the market. Regular people are not like HFT algorithms, with infinite pools of money available and ability to turn opportunity cost into profit. Having a stable and predictable price is important when deciding whether or not order a taxi/rideshare at all.

(At least, that's my experience. I wonder what your data has to say on it.)

As a customer, I'd be happiest if taxi companies charged a rate per-km, that's calculated off their consumables + car amortization + some reasonable profit margin. I think drivers may be happier too - recent personal experience with myTaxi shows this. They offered a promotion in which the passenger would pay a fixed cost known immediately in the app, but which calculations changed every day or so. Some days, it would become a good deal for the drivers; other days, the drivers would be working at a loss. I had a lot of problems getting a ride when using this promotion, and chatting with the drivers revealed that they instinctively ignore those requests, as from their POV the profits are unreliable.

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