Growing up in Africa
generally you didn't want to drink untreated water (at least if you valued your ringpiece anddidn't want to become a walking colony) so filling the kettle all the way up made sense as you could pour the cooler boiled water into bottles to drink later. So boiling half a kettle was very wasteful.
EDIT: Mind you you should boil water for at least 7 mins. to kill most waterborne stuff so meh...

Also water has quite a (relatively) high latent heat and stores that heat fairly efficiently so therefore a greater volume of water will hold it's latent heat for longer thus taking less time and energy to re-boil than a half a kettle of cold water.
Any boffins can weigh in here?
(Misery McUglywife an attention seeking sociopathic fuckstain., Fri 5 Oct 2012, 22:58, 1 reply)

Basically not - in essentially all cases, you are best boiling the very smallest amount of water you can.
I would copy and paste a lengthy analysis I made on this topic, but I cannot be arsed.

I note that my normal 'wiggly element' kettle is quite happy boiling a half a cup of water.
You can investigate how little yours can boil safely by boiling when observing the element as you reduce the amount of water.
Violent boiling at the edges of the water = not safe.
(speedevil, Fri 5 Oct 2012, 23:48, closed)