Do high voltage power lines attract lightning strikes?

A few things I can think of straight away:

• Power line pylons are usually the tallest objects in the countryside. They are giant grounded metal objects. As lightning wants to move along the path of least resistance, they are preferred over other objects. Power lines also usually have one or two grounded wires on top, which act as lightning rods which protect the powered conductors from most lightning strikes.
• High voltage lines ionize the air around the conductors, this is especially true for 220kV+ lines (they even glow purple in a dark night, the glow comes from something called corona discharges). Ionized air is a better conductor than ordinary air.
• The voltage(potential) difference between a power line and a storm cloud can be significantly lower than the difference between storm cloud and ground. The maximum difference for a 220kV line can the peak voltage, which is $220kV\sqrt{2}$, while the ground is at $0V$. Lightning strikes usually overcome a few hundred to more than a thousand $kV$. Therefore lightning only has to overcome 2/3 of the usual voltage difference.
• Lightning can kill you even if you are not struck by it. Like dropping a stone in a pond, the voltage is spread out around the place of the strike, falling off with distance. If both your feet are one meter apart and in line with the strike point, you will experience a voltage difference between your legs. Animals like cows and horses are susceptible to this, as the distance between fore- and aft legs is significant.
• Electromagnetic influence is the last factor. A charged cloud attracts a charge of the opposite sign on the ground, this affects a large area. When the final discharge(lightning) occurs, the charge that was bound at this location won't have anything holding it there. Therefore it will move back to where it came from creating currents on the way. This can damage power lines and electrical equipment. This could be interpreted as an EMP-like effect.

I hope that I didn't miss anything.