In multiple European cities now I see taxis being allowed to use the bus lane (while of course regular cars are not).

What's the policy justification for this?

Public service vehicles. The more we use the less pollution. Is this not obvious?

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But taxis are cars and have about as many end-user occupants as regular cars, so it seems like they would pollute as much as any other cars?

I would say that usually - especially in business hours - regular cars will have single occupants and according to to the U.S. Department of Energy, the average occupancy rate for personal vehicles in the U.S. is about 1.67 passengers per vehicle.

In the uk we tv campaigns that suggest taking buses or taxis/car share to reduce the amount of single person emissions

However the before mentioned article also says “Traditional taxis typically have higher emissions per mile compared to personal vehicles due to lower fuel efficiency and more time spent idling.”

So perhaps I’m completely wrong. I’ve always held the believe that public transport is better for the environment - I could just be brainwashed by the media. 

Now I’m doubting everything.

Right, but back to the original point: I think taxis are allowed to use bus lanes because it is perceived that it Increases efficiency -  Allowing taxis to use bus lanes can avoid traffic congestion and provide quicker service and its perceived that it reduces Single-Occupant vehicles on the road which can potentially lower overall traffic congesstion and emissions. 

Now allowing taxis but not personal cars in bus lanes might create a perception of unfairness, especially if taxis are  in fact not significantly reducing congestion or pollution.

I dont know the official statistics or figures on this admittedly it could all be "tish tosh" promoted by local governments to get money back into the system. 

To quote harry potter: "One hears many things My lord. Whether the truth is among them, is not clear"

"Taxis" and "car share" are very different things though.

In my experience, sharing cars is about as common when the car is a taxi as when the car belongs to someone.

There have been things like uberpool, which tried to find a missing middle between single-person taxis and buses, but unfortunately generally ended up being worse than both (primarily because you have like 3 people who can each arbitrarily delay you, so your worst-case arrival time ends up worse than if you take a bus).