Energy efficiency: boiling water using electric kettle, gas or microwave?

This question reminds me of the cookbook recipe for Ox Tail Soup: 'First, slaughter your ox.'

All of the methods described in the question have the underlying assumptions: that all of those resources are available to you. In the case of electric kettle and microwave, we have to have electricity at a nearby outlet waving away the whole question of generation and reticulation of electricity, and the same assumption with respect to gas. In both cases, there is the huge cost of energy and infrastructure which has magically disappeared.

The question is essentially unanswerable because of all of the variables which are involved.

In terms purely of a kettle containing a defined amount of water and a magical source of energy directly to the kettle, the resistive electric kettle is most efficient in terms of converting energy to heat with only a little wasted to the surroundings.

Technology Connections has a youtube video titled "Why don't Americans use electric kettles?" in which he compares a few methods for bringing the same amount of water to a boil. The electric kettle was faster than a kettle on gas and electric stovetops.

https://www.youtube.com/watch?v=_yMMTVVJI4c