The simple answer is yes, electric stoves can cause fires. However, there are a number of factors that contribute to the risk of fire with an electric stove. The most common cause of fires from electric stoves is unattended cooking. If you leave your stove on and walk away, it's possible for something to catch fire. This is especially true if you're cooking with oil or fat, as these can easily ignite. Other causes of fires from electric stoves include faulty wiring, overloaded circuits and overloading outlets.
If you're using an electric stove, it's important to take precautions to prevent a fire. First, never leave your stove unattended while it's on. If you have to leave the kitchen for any reason, turn off the stove first. Second, make sure your stove is properly wired and that circuit breakers are in good working order. Third, don't overload outlets by plugging in too many appliances at once. Finally, always keep a fire extinguisher handy in case of an emergency.