How to split cab fare fairly, among friends and multiple stops

I often share a taxi home with friends, dropping each of them off first, before eventually reaching mine. There are days when I get off before the rest. Typically the last person pays the full bill and allocates (if he wishes to), each of the other riders, their fare share.
This fair share often varies based on the bill payer and his own logic of allocating the total fare.

Logistically, it is simpler since seldom any of us carry the perfect change and end up paying with our cards. And since the final share is always lower than what we incur traveling alone, no one complaints.

However, is there a more efficient solution? And is it equitable?

Let's first look at the fare split. Imagine if 4 of us take 4 different taxis to home, we end up paying $6, $9, $15, $18. Now taking a taxi together, costs us $30.

As a group we managed to save (48-30) = $18

Now efficiency depends on us choosing a route that minimizes the group's time as well as total spend. It is independent of the individual split. However equity does depend on the allocation methodology.

There may be many ways to do this but let us think about one specific situation. If the last person has the power to allocate the individual share, rationally, to maximize his own self interest, he just needs to give a non-zero save back to the rest. For instance charging $5.95, $8.95 and $14.9 to the rest. Since all the three are still better off than before, the last person needs to shell just 20c for his $18 ride. Obviously, assuming there are no utility gains that needs to be compensated back to the first 3, had they travelled alone. Eg. Privacy, comfort etc.

Now is it equitable? And do we see people doing this? Well, I personally haven't, because people aren't always rational. Behaviorial economics teaches us about predictable irrationality.

We are driven by guilt, altruism and morality. We are elated to see personal gains but also a lot unhappier seeing others gain more.

Let us take a stab at it again. How about distributing the $18 saves back in the same proportion as their initial travel spend, had they travelled alone. Thus distributing $18 back- $2.3, $3.4, $5.6 and $6.7 respectively with each reducing their initial travel spend by 38%.

Since the Taxi fare also captures opportunity cost of distances and waiting time, compensating the last guy more in absolute terms makes a lot of sense.

Another split logic we commonly use is passing 10, 20, 30, 40% of saves in the order of getting down. But it fails miserably if all 4 live close to each other, with the last guy pocketing 4 times more save compared to the first even if they are just a mile apart :)

So how do you split your taxi fare. Do leave your comments. Happy cabbing !

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