Category: Logic

Taxi driver problem

There’s a guy who travels by taxi every day from his work to his home (20km). One day he finds out that a colleague of his also takes taxi every day from work, the same direction, but he lives only half a way of the first guy (10km). So, they decide to share a taxi and also to share the costs. How should they share the costs?

First answer could go like this: First guy travels twice longer so he should pay twice as much as the second guy. So, the first guy should pay 2/3 of the total cost and the second guy only 1/3.

Second answer could go like this: Both of them travel the first half together, so they should split this part in half. The first guy travels alone the second half of the way, so he should pay the full amount of the second half. In total, first guy should pay 3/4 and the second one only 1/4.

Which one is fairer?

Let’s assume that first guy pays double for his trip as compared to the second one, when they travel separately – in two taxis. This is usually not correct, because of the initial charges, but let’s assume that the charge is proportional to the distance. Let’s assume that it’s fair if both of them get the same “discount” (percentage wise) when joining together. The first one would have to pay 2p(1-k) and the second one p(1-k), where k is the discount, p is what the second guy usually pays and 2p is what the first guy usually pays. So the first one should still pay twice as much as the second one, which leads to the first answer.

Let’s assume now that it’s fair if they all get the same discount (absolute cost reduction). So, the first one would pay 2p-q and the second one p-q, where q is the discount amount. Then (2p-q)+(p-q) = 2p => p = 2q => q = p/2, which leads to the second answer.

Let’s say that one day the first guy finds out that his neighbour also takes taxi every day from work home and accidentally, he works very close to where the second guy lives, just one block away, so he comes to a cunning idea. He will share the second part of his trip with his neighbour and he will reduce his costs even more. Obviously, he would prefer for the first formula to be applied, because in that case his colleague will pay 1/3, his neighbour also 1/3, which lives him with 1/3 as well. The problem now is that his colleague must not know about his neighbour and vice versa, because in that case they would ask for splitting the costs proportional to the distance, which would be 1/4 for the colleague, 1/4 for the neighbour and 1/2 for the first guy. Obviously, the first formula is not transparent and it allows for speculation. Second formula would give the totally transparent solution in which case the first guy wouldn’t care if his colleague and his neighbour know about each other.

Moral question: In case of applying the first formula in case of 3 guys sharing the taxi, when everybody pays 1/3 of the total price, do you think the first guy would be a cheater or a good businessman? How do you think the other two guys would react when they find out about it? Would they be angry? Would they be like: “Wow, you really tricked us professionally. Well done!”. Or would they just be glad they found it out, so from now they would pay less.

From where I come, he would definitely be a cheater, because the base of his “success” is in hiding the truth from the other two guys. On the other hand, we’re all aware that much of today’s businesses are based on hiding the truth from the others. Sometimes it’s some intellectual property information, but very often it’s just a cheap fact. If a famous chef hides the details of his recipe, that’s kind of fine. But if a job agent hides the details about how much of your contract he gets from your employer, that’s kind
of completely different story, isn’t it? This brings up more serious question: Is hiding the truth in today’s businesses unethical? Is hiding the truth in politics and diplomacy unethical?

I could write a lot about this and I already went quite far away from initial “logic” problem to an ethical one, that’s probably the reason why I post so rarely, so I’ll stop here :)

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