I've proved absolutely nothing,[ there was no requirement in the question posed]. Tony posed a very direct question ..."why do you think that electricity is something like 3x the price of gas per delivered kWh?"; my answer was that PRICE, which he asked about, has a non-linear relationship to COST and his premise is illogical/ PRICE is what the customer will pay, no more , no less!
The true answer to his direct question is that consumers won't pay more than
3x (approx), or why should the generator/distributors sell it for less than 3x (approx) If the PRICE of electricity climbed much more than 3x the PRICE of gas (per Kwh delivered); we'd all be investigating the PRICE of gas-fired ovens; gas-burning tumble driers and gas-fuelled 'gennies for the CFL's the Government will permit us to buy!