I can only reemphasize what Edwin and others (and myself) have already told you--if the house feels this cold, in undoubtedly _IS_ colder than
80F and _SOMETHING_ isn't right. If the actual temperature is somewhere in the 60's, it's no wonder your power bills are astronomical. Your first step needs to be to find out independent of the thermostat what the air temperature is and get the A/C guy out to find out why you're running so cold. I suppose it's possible the thermostat is located in a very poor location and is being affected by something else so it thinks the temperature is 80, but a thermometer will tell you that, too.A 12 SEER unit isn't very efficient these days (I don't think it would qualify for Energy Star rating) but is probably better than what was there, but if it's running all the time or is actually keeping the house at 65F, see above.
I also have to agree w/ Edwin and others in that your brother may be an electrician by trade and capable of performing the mechanical processes of wiring, etc., but he definitely is way off base on this hypothesis. It just isn't the way electricity "works". It's certainly not uncommon that many tradesmen don't know much theoretical behind what they do routinely.
In summary, given this additional information, the A/C is almost definitely the problem and the reason is almost certainly that something isn't right so you need to get the installer out to find out what the problem actually is and fix it.