Why does injury-minimising programming disadvantage people who travel alone or in safe cars?
Because with everything else equal the rule steers the car into the smaller group and the safer vehicle — so travelling alone, or in a car that protects you well, becomes a reason to be chosen as the victim.
Two effects, both following from the same arithmetic:
Travelling alone. Suppose an injury-minimising car must choose between hitting a fully occupied car and one carrying a single person. Absent other factors that strongly affect the respective injury risk, injury minimisation will go at the expense of the individual. This matters because some people sit alone in a car far more often than others — commuters, delivery drivers, people who live alone. The general reduction of risk would be achieved at their expense, systematically and predictably.
Driving a safe car. By the same logic, those who drive the safest conventional vehicles would face an increased risk of being involved in collisions — in favour of other road users in less safe vehicles. The car reasons that you will survive it better, so you are the one it hits.
There is an important counterweight on the other side of the ledger, and it should not be skipped: an injury-minimising programming also protects the weakest road users — pedestrians, cyclists, motorcyclists. They are exactly the parties whose expected injuries are worst in any collision, so the rule shields them, which is a genuine moral gain and one that current traffic arrangements deliver poorly.
That pulls the question in two directions at once, and the paper asks it directly: can an injury-minimising programming that may not distinguish between an old small car and a new 2.5-tonne SUV, and must also ignore the number of endangered occupants, still fulfil its actual purpose? Strip out the factors that create unfairness and you may have stripped out the information the rule needs to work.
Go deeper:
Wikipedia: Euro NCAP — the crash-test rating that would become the car's targeting signal — and the buyer's.
Wikipedia: Externality — a heavy vehicle's safety advantage is partly an externality imposed on everyone it might hit.