Home-Owner-Ist logic says that "council tax pays for local services", which is why there is a single person's discount and many councils offer discounts for second homes and empty homes (unused, derelict or being refurbished).
Fair enough.
On the other hand, a few years ago, Cornwall decided that leaving homes empty is a waste of housing, so imposes a council tax surcharge of 50% on them and also scrapped the second home discount because locals are being driven away. A few years after that, the Welsh Assembly decided enough was enough and allows local councils to impose a surcharge of up to 100% on empty homes and second homes.
So we have two entirely opposite policies for the same factual situation.
There is no need for a Single Person's Discount. By and large, they live in (or should be living in) smaller homes with a lower Council Tax bill. Families will be in a larger home and pay more Council Tax anyway.
What is the fundamental difference between:
a) a single person owns a home with some spare bedrooms in the same house (and gets a discount)
and
b) a single person lives in a flat and owns a second home somewhere else with some spare bedrooms (for which some councils give a discount and others impose a surcharge)?
Or, taking this to extremes (Bayard's real life example), a single person lives in a house and gets a 25% Single Person's Discount on the whole thing. If he converts his house into two flats, he only gets the 25% discount on the flat he lives in and has to pay (up to) double on the other one.
Far better and consistent to have Land Value Tax at a flat rate on everything. If one household owns a house worth £300,000, they would pay the much same amount of tax as another household which lives in a £200,000 house and owns a £100,000 holiday home. And I see absolutely no reason why one household should pay more (or less) than the other one.
