In electrical installations what three factors influence the selection of a protective device?

Answer 1

There are way more than three factors to consider. The top three might be voltage, current and accessibility. See the following link for more in-depth info.

Answer 2

If by "protective device" you mean a device for protection of people against shock, the second answer provides good info, although the emphasis is on methods and hazards rather than devices (e.g., although it refers to ground faults, it doesn't mention ground fault interrupters.)
If you mean circuit or appliance overcurrent protection, I'd say the 3 most important parameters are max current, speed of opening, and voltage. Too low a voltage rating risks arcing after the device opens. Of course a choice must also be made among the various kinds of protection, such as fuse, breaker or industrial-type interrupter. Another kind of circuit/appliance protection would be overvoltage (spikes, etc.) Again there are choices of device types and parameters (crowbar, arc, or interrupter, power absorption capability, trigger voltage, speed, etc.). I think your question needs some context for anyone to provide a really complete answer.

Answer 3

Max Current, Sensitivity, Internal/external. Maybe?

Answer 4

UK-BS7671

1)
In (current rating of the circuit protective device) must be greater than Ib (design current) (protective device type also selected based on type of equipment(eg motor load, lighting etc)
2)
Short circuit current rating of device must be greater than the prospective short circuit current.
3)
Protective device must be capable of disconnecting within a prescribed time (generally 0.4s (sockets)and 5s (fixed equipment)) (other times are give for specialist locations(ref BS7671)

Answer 5

Max current, time, and coordination would be my top three. I can think of a few more.