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Liberals usually don't respond because they have no idea about economics.  They just believe "rich" people should support everyone else.

I don't want them to propose a working economic system for the flat in the story.

They should just tell me how much each of the three should pay and why that would be fair. Whether it works doesn't really matter. In real life tenants might move out if the terms were unacceptable. In this gedanken experiment, they can't. So we can do to them whatever we want.

Look at Paul and Paddy. Paul makes more because he works more. Should he contribute more to the well-being of the entire flat because he spends less time in front of the television? Why would that be fair? I don't know. I want a liberal to tell me.

Another interesting question is how the rent should change for each of the three if their bed rooms were of the same size. Should Peter pay more (or less) than Paul and Paddy if Peter's room was the same size as Paul's room and Paddy's room? Why?

For example, my own proposal is that each of the three pay rent according to room size (without regard to their income) and contribute (voluntarily) to the common good (television, washing machine) as per their individual wealth and to the common labour (washing up, cleaning common rooms) as per the available time.

This corresponds to a society in which people are taxed according to the value of the land they own (but not dependent on their productivity), contribute to charity voluntarily according to their means, and do volunteer works according to their free time. I personally think this is the fairest, best, and most efficient way.

But in my experience those that do volunteer work are usually not the unemployed trying to find something useful to do to make their CV (resume) look better.

something like this happened to my son.  There was this apartment with a huge attic bedroom that was finished and two smaller bedrooms.  My son offered to pay either $50 or $100 more a month to have the much bigger bedroom.  Since the other two guys didn't make that much money; one may not even have had a decent job they said ok. 

It turned out it really paid off because they got robbed twice in one week.  The first break in was more of a scouting adventure with change and food taken.  When the thieves broke in the second time they only took stuff downstairs like computers, tv's etc and never went upstairs.  We don't know why and they never got the thieves.   My son had his computer and all his post grad stuff on it right out in the open.  It would have almost literally killed his career if he had lost all that scientific data.   He even had his extra hard drive backup there as well as his checkbook sitting right out in the open.  

You're asking for too much. Shawn hannity asked Michael Moore if he believed he could get away with making a movie in Cuba criticizing Fidel Castro's Gov't. and Moore said he did not know. Of course he does, he just won't say yes or no, he plays it safe. Which is why he does not understand capitalism.

Reminds me of the bet I regularly propose to people who tell me that the Arabs want peace and Israelis are full of hatred:

Dress up as a Jew with an Israeli flag and walk through an Arab city. In return I'll dress up as an Arab with an Arab flag and walk through Tel Aviv. He who survives is right and gets a flight back to Ireland.

NOBODY ever takes the bet. Even those who are utterly convinced of their position are not willing to bet their lives on what they think they know. In fact they are convinced that they would lose the bet. (I think that those same people will actually believe that a random Arab sitting next to them in a plane is a terrorist while they have never feared a Jew in their lives.)

Peter pays most, Paddy the least. The TV set and washing machine are totally irrelevant. Its his own decision that he bought them for the common cause if he doesn't want others to use them he can put them into his own room but then he has to wash all his stuff alone (instead of only doing it every 3rd time) and has to watch TV alone instead of enjoying it with the others. Paddies argument that he needs the more comfortable room is total bullshit because he spends his time in the living room watching TV not in his own, also how is a bigger room more comfy? If however they agree to swap places, Paddy should pay most unless Peter doesn't care. I have to wonder how someone with a 20 hour a week shop can't afford a computer - I could see him not being interested in one but not being able to afford one?

if you apply that to taxation: those who earn more pay more, donations aren't deductable. Easy as that. I personally would abolish all taxes except the consumption/VAT tax because in my opinion that is the fairest way to tax people, you pay on what you spent for consumption, leaving no loopholes or other silly stuff, also saves billions in bureaucracy - the side effect of that is probably a few more million unemployed people but their work is useless anyways.

Why is it fair that you have to pay more if you consume more? People who consume more should be more interested in maintaining the stability of the country to secure that nothing will happen which will make them lose their status.

PS: its really confusing how you listed them : high - low - middle at first in the listing and the text at start and then in the text high - middle - low and giving them all names starting with P, 2 of them even with Pa instead of just ABC or at least different starting letters. I am a very skilled reader, reading maybe 200 to 250 books a year but I had to read those passages 3-4 times to get it right.

That doesn't translate.

You said Peter pays most, Paddy least if Peter has the biggest room. If Paddy had the biggest room, Paddy should pay most, you said.

Then you translate that into taxation: "those who earn more pay more".

But what you proposed for the flat is not "those who earn more pay more", but "those who use more pay more".

Peter and Paul are the classic two people for stories. Paddy is a poor Irish labourer, a schlepprock if you will.

sorry i meant to write "who consumes more pays more". I had to focus all my concentration on the names

That doesn't sound very liberal to me. Are you a liberal?

I would consider myself a liberal. Separation of powers and unrevocable human rights and most of the other liberal principles make a lot of sense to me.

Yeah, you are sort of not the target market here.

Where are all those advocates of progressive income taxation and social welfare systems?

The flat in the story is an easy enough society to work with. Go ahead and explain how your preferred tax and welfare system is the fairest!

Who stays where depends not on salary, but on who's prepared to pay the most. It may be that Paddy likes his space, so will pay for it. Peter might like small rooms (people do). Access to a room is most logically, and most commonly, based on who puts the highest value on it. It's a commercial decision, not a civic one.

And that's the flaw - although the sharehouse is a prison, the fact these people have lives outside the house means that their sense of connectivity is likely to be outside the house rather than with their two housemates. When all that is at stake is a room, why would they pool their income? If they had children to raise, the story might be different. But they don't - they're single men living together, not a nation-state that needs to look to the future.

The interesting thing is that they'll still probably have common milk/tea/coffee, take turns with the garbage, make house decisions rather than deferring to rich Peter, help each other get laid with Jill, Jane and Dave, and do the cleaning on some sort of equitable basis, despite the fact that some pay more than others and that their rooms are different sizes.

tl;dr - every good sharehouse is a social democracy. Taxation doesn't even come into it.