How to stop coil burners from cycling off and on
Painful though this is, the correct answer is learn to cook with electric.  The stove works differently and you have to learn to deal with that.  

For instance, I found that to quickly arrest heat (say, when something is boiling over), the answer is to quickly move the pot off the burner.  Obvious though it may be in hindsight, it was a real eye-opener at the time.  

I do see where it has its charms, for instance if an unattended pot runs dry on an electric burner, the electric will simply hold it at target temperature and not destroy the pot.