Why is taxi fare (in the UK at least) the same price for 1 as for 4 people

i have never been in a country where the taxi fare changed depending on the number of passengers. If there are seatbelts for 3 passengers, you can take 3 passengers. Some countries charge for bags, others only if there are a lot of bags or the driver handles them.

In general, the weight of the passengers is rather small compared to the weight of the vehicle, and does not make a significant difference to the operating cost.

Surcharges for Extra Passengers

Here are two counterexamples. In both Italy and France, if I recall correctly, taxis charge extra when the number of passengers require one to seat on the front seat next to the driver. Furthermore, a surcharge can be applied when the customer requires a car with more than 5 seats (including the driver). Note that the concept of a 5-backseats taxi is somewhat unique to the UK, hence in the aforementioned countries when 4 people take a cab one of them usually sits at the front.

Italian Taxis

Indeed, surcharging by person seems to be a relatively common practice across Italian taxi companies. Take for example the pricing list for the Taxis in Padova, Italy:

Supplemento oltre la terza persona trasportata € 1,05/persona

Stating that there is a 1.05€/person surcharge for any number of passangers greater than 3. This applies to both 5-person cars as well as cars with more seats.

The taxi consortia in both Naples and Turin on the other hand, apply a surcharge for any number of passengers greater than 4. The Neapolitan taxi service website says:

Per ogni passeggero oltre il 4° (se l'utente chiede una vettura con un numero di posti superiore a cinque) 1,00€

I.e. when the customer requests a car with more than 5 seats (including the driver), a surcharge of 1.00€ will be applied to each passenger. The Turin taxi service website says:

Supplemento PASSEGGERO oltre il quarto

• € 3,50 per quinto passeggero
• € 1,00 per sesto passeggero e oltre

I.e. when the customer requests a car with more than 5 seats (including the driver), a surcharge of 3.50€ will be applied to the fifth passengers, and 1.00€ for each additional passenger.

French Taxis

Similar surcharges apply in France too. Parisian taxis charge 3.00€ for the fourth and any other additional passenger:

Supplement per person over and above 3 passengers € 3.00

The same applies in Nice, where the surcharge is 1.58€:

• Majoration 4ème personne : 1.58 €.

Turns out these values are usually limited by municipal (administrative) regulations.

That is 600 lbs (~ 43 stone) more than the original ride for 1 person.

Quite a significant increase, which has got to affect the fuel consumption of that taxi cab noticeably.

You are mistaken there. The weight of the car is really a very minor part of the fuel consumption and an even more minor part of the total costs of running a car. So for example the Audi A4 (2002 model) that I sometimes drive (a more or less average size vehicle suitable for 4 persons) as en empty weight of 1665kg, so the 600lbs (less than 300kg) extra would increase the weight by less than 20%. So let's say that my vehicle would consume 8 liters of diesel/100km (which is already a sign of a quite rough style of driving) and let's say weight would be the only parameter which is important, then the fuel consumption would rise by 20% (1.6 liters/100km). So a quick search of diesel prices in the UK suggests a price of around 115.6/liter which would mean an extra of 184p/100km need to be taken into account which is less than 2p/km extra. If we assume a taxi fare of £2.75/km (that's what I found on google without too much verification, but sound realistic) the extra £0.02 is really not worth discussing about whatsoever.

And that's even though I calculated the extra 2p/km considering the weight much more into account than in the reality. The weight of the car only makes a difference while you hit the brake, because that is where you throw away all the kinetic energy that you have. With careful driving and utilisation of remaining energy (e.g. slowly decelerate without hitting the brakes well before reaching that red traffic light in front of you) the total effect can be brought to almost zero. I never noticed a difference in fuel consumption in my cars whether I drove alone or with multiple people.

When I learned that e.g. on the British Virgin Islands taxi fares are per person, which means that a taxi with 3 passengers costs 3 times as much as a taxi with one person, I felt seriously ripped off.

Even in the UK there can be additional cost of additional passengers. This is from guildford council's Taxi Fare Procedure (http://www.guildford.gov.uk/media/14270/Item-4-1---Hackney-Carriage-Fares-App-1---Taxi-Fares-Procedurepdf/pdf/pdf15_1.pdf):

57. In addition to the charge per mile, we will apply an extra charge for each passenger carried in excess of two. We base this on current practice and local circumstances and this assists the drivers of larger vehicles, which have a lower fuel economy. These vehicles are predominantly wheelchair accessible so we set this extra charge to provide an incentive for such vehicles to remain licensed. We identify this extra charge as Item 9 on the fare calculator.

In reality, the meter makes it hard. We have the technology, but it most countries Taxis are highly regulated, and you pay for the car by the meter. Published notices display the fare and tariff structure. This is generally law, however you can come to an arrangement with the driver and have the meter off. In Australia, there are small differences between states and even cities. The usual driver scams abound. It is perfectly acceptable in Sydney to share a taxi and each fare pays upon alighting a "weighted proportion". But not for the same destination. As for mass, braking is a "total loss" open circuit drain of energy unless the taxi is a Prius or similar (?). So a lot of stop start is going to add up, but not much. E=(0.5)(m)(v)(v) or a half mass times v squared. Idling and crusing cost the same, and riding lower may increase rolling resistance but reduce drag due to wind resistance.

Too hard, just go with a meter and everybody understands. Otherwise catch a bus.

As an Australian, I still try and grab the front seat in UK taxis, almost crippling myself on a number of occassions.

In Israel they have service taxi and special taxi (taxi = monit) ... while the special taxi are just as it's common in Europe (occasionally Mercedes even) - those service taxi work a little different: they just drive around and try to pick up people from bus stops, along the way - while several passengers share the cost of the travel, all having a similar destination. the doors are also to be opened by hand, fold outward, pretty funny. overall, when such a service taxi is full, it's cheaper than the bus ...and more secure.