Rather lengthy, so a kind of summary:
I don't get the extra charge since it will be the exact same room in all of those situations. Yes, the same room but more cost for the hotelier. In general at least all the following (where relevant) will cost more for more people: chocolates etc, cleaning, cooling, electricity, heating, ice, laundry, lighting, loo paper, maintenance, stationery, tea & coffee, toiletries, and water.
At first I thought the logic might have been that the price for 1 or 2 occupants had been adjusted to meet market conditions (for example lowered for a time when general occupancy was expected to be low) and that rates for 3 and 4 occupants had been left unadjusted (might have been too much bother to keep updating for what was likely a rare requirement).
However there is far more logic to the pricing than I would expect from hoteliers. The prices are essentially $46 +$24 per person. Just with a twist that 1 person is counted as 2 people.
Where rooms are double it is normal to charge for two people. Any discount for single occupancy is likely as much a result of negotiating skills as any regular difference in price. If for instance the bed is a double then just as much changing and washing of linen is required for one as for two people.
But if there are two beds to change and launder then there is more cost than for one, so it is fair to charge less for usage of one bed and more for usage of two.
As pointed out by @Relaxed, market forces are at work. These however are not accurately quantifiable because it also takes time and effort (ie cost) to fine tune tariffs very frequently – and keep any selling agencies up to date. So prices at any one time may not appear to make much sense when compared with other time periods.
Working back to how the numbers were calculated might go something like this:
- Annual Fixed cost (lease, permanent staff, insurance, fixtures etc) $xM or about $30/room/available night (say)
- Variable costs (electricity, water, laundry, toiletries etc) per night per resident say $20
- Scale up the fixed rate to cover room-nights not rented, say to $40
- Add a return (say ~15%) and when occupied this is $46 per night per room when let and $24 per occupant/night.
Those hotels that charge a rate per room may do a similar calculation but simplify their tariff by selecting a little more than the rate for two people – in relative terms charging slightly more for couples but slightly less for 3s and 4s. Overall they may also be making some savings by such simplification.
Based on the above the prices part of your question might be expressed as "Is $20 per person per night a fair costing?". In my view it is not, quite. Labour is probably a large element of it (cleaning, housekeeping, maintenance) and that is mostly per room (when occupied). Electricity/(part of) heating is likely mostly "per room" – but bedside lights and appliance use (eg personal computers) would not be. Water, loo paper, minor damage etc is likely 'per person'. Toiletries and towels etc may be either.
However I think near enough equitable for the approximation to be justified.
Combined into a per room rate the prices you mention might be something like $110/night, to recover the same amount from the same number of guests spread across rooms in the same way. But in that case some singles and couples could be expected to be put off. For them it would be a price hike of $16/night. So the occupancy rate would go down and the price have to increase beyond $110 to compensate for that. Whereupon even more potential guests may be discouraged!
I think your questions with question marks have been answered but:
Why do hotel booking sites ask for the number of people?
Most hotels do charge per person. I tried a group that does not, for 1 double for 1, 2, 3 and 4 people and the price was the same for 1 and 2 and twice that for 3 and 4 (but the same as each other). I doubt many of the 'per night' hotels (in UK) offer family rooms. 3 and 4 above were for two rooms. This being one reason to ask for number of people.
Does it matter how many I say?
Yes. There is almost certainly an upper limit per room (if only for fire security reasons, as mentioned by @Shannon). My experience is much the same as @Kate Gregory's regarding fire drills and even for real (minor) fires I have noticed no headcounting, but in the case of something more serious the consequences for a hotelier failing to keep proper records could be expected to be severe. (It is no joke to risk lives for 'people' that are not in the hotel at the time of a disaster.)
Do most hotels do this?
If I just book the room specifying 2 people and bring a 3rd is there any risk involved?
Definitely. For example that your third person will have to seek other accommodation. Hoteliers have to juggle a lot of unknowns and at times don't live up to expectations. Given a choice between downgrading you (with financial compensation) to a double (that appears to be all that you really need) for your one night stay and turning away a large party that requires all the family rooms the hotel has for a full week including your 'one night' … you can predict the result!
And as mentioned by @Gagravarr, you risk being charged the (often very much higher) walk-in rate for all three.