Be real sure that’s what you want, because one of the two of you may well have to ride that junk truck off the property for good.
I am not a lazy hoarder by any stretch. But a “surprise” like you’re proposing would be a marriage-altering experience for me/us.
I realize that - but it’s not a “surprise” in the sense that I haven’t told him that if he doesn’t get rid of it, I will. I’ve told him that repeatedly and I’ll tell him again before I do it. It’s a “surprise” in the sense that he will be surprised when it happens, because clearly on some level he doesn’t believe it will. ( The only reason it hasn’t happened already is because I haven’t had time)
Ah, that’s different. Quite different. Best of luck! I’ve not lived with a messy semi-hoarder, but I’ve known folks who did. It takes the patience of a saint.
I see no benefit, mathematical or otherwise, to working extra hours to afford a more expensive home than you want, when those extra hours are hours you won’t be spending in said home because you’re at work working. (Even if you’re working from home, you’re still not enjoying the full benefit of the house while you’re working.) You’ll never get those worked hours back. The only person who should be working the extra hours is the person who wants the more expensive home.
The economic issue here is a positive externality.
If both people are working 40 hours, and they get an 80-hour house, and Brian is happy with that, then that means the marginal benefit to additional hours of work matches the marginal disutility to Brian of working any more hours for a larger house.
Extra work by Brian is not worth extra house. He stops there.
But if Brian stops there, and Angie has a different choice? If Angie puts in another 10 hours voluntarily, because she’s “comfortable” doing so? (This seems to be the implication of Option 1.) She does this because she thinks it is still worth her own while, even though Brian isn’t helping out with it.
Then that means the 41st hour of labor is worth the 81st unit of house to Angie (which also, marginally, benefits Brian but not enough for him to put in the effort by himself). Then the 42nd hour of labor is worth the 82nd unit of house for Angie, and so on. That continues until the 50th hour of labor to Angie is personally worth the 90th unit of house. She would be “comfortable” putting that work in on her own, even with Brian staying at 40 hours.
But that information (if I continue to interpret Option 1 in this fashion) rules out option 4 entirely. There’s almost no way Option 4 could be optimal for the two of them together. (The exception is constant marginal benefit, which seems unlikely.)
Angie was willing to put in 50 hours of labor to get 90 units of house. She was “comfortable” with that, according to Option 1. (That doesn’t mean she’s happy that Brian isn’t helping out. Just that she would do it, if she had to.) This is to say that the added benefit of the 90th unit is worth the 50th hour of labor.
But then Option 4 doesn’t make any sense.
If Angie already has a house 90 units large, and she would’ve put 50 hours of effort into getting that by her own efforts, but she has only put in 45 hours of labor so far (and the 46th through 50th hours of labor are progressively more stressful than the 45th, which is generally the case), then the marginal effort to Angie of more labor is still worthwhile to her to get an even bigger house to enjoy, even if Brian stops at 45 hours.
Solving the positive externality here involves asymmetrical efforts.
Brian puts in more than his 40 optimal hours. Why? Because he’s enjoying the extra house, too (just not as much as Angie). If we were solving this as a system of equations, then Brian’s extra effort needs to balance the extra house that he gets from Angie’s extra-extra-extra efforts. He’s willing to put in a few extra hours, because she absolutely lurves big house. And she’s willing to put in these efforts above and beyond what he is, because she values the extra house more highly than he does. But him helping out a bit beyond his comfort level is what makes the deal work.
If we could specify utility functions, then we could find the exact optimal point of effort for them both.
That’s probably not necessary here.
But what “should” happen (if they’re acting “optimally” according to the scenario as I am currently interpreting it) is that the person who wants more house should work more than the other partner, and the other partner should also put in a bit more effort, beyond what he would do on his own, in order to “pay back” the extra-extra-extra benefits from the other person that he’s receiving.
Both benefit from asymmetrical efforts more than they would from equal efforts, if they can make the deal work.
I am accepting the premise as is, and so I do not go into practicalities of home ownership or marriage.
Seems to me that this is a simple negotiation situation. We do not know how much each person would value the bigger house.
One person proposes a spilt of working hours, and then they negotiatie until they meet somewhere. If they are not able to do that, they will have to go with the smaller house.
EDIT: I see now that there are a lot of house at different prices. You would then start negotiating for the bigger house, and then go down a price level each time the negotiations break down.
An analogs situation is that if one person is very hungry and another is a little hungry. How much should each contribute to making dinner?
I knew Hellestal’s response was gonna be the best when I saw that.
The reason why so many people are dancing around the mathematical question is because we don’t know the utility functions. If we know the utility functions, then the answer becomes trivial. If we don’t know the utility functions, then no answer is possible.
Of course, some non-mathematical solutions are still possible. And we can still say some things about the mathematical solutions, even with the very limited information we have. In particular, I don’t think option 4 would end up as the mathematical solution for any utility functions, subject to some reasonable assumptions such as that they be monotonic (at least within the domain of interest). We assume that both of them would prefer to work fewer hours (if they could somehow magically still get the same standard of living), but the marginal value of extra hours means less to Angie than to Bob, and so the optimal solution would end up with Angie working more hours than Bob. If they decide on 90 combined work hours between the two of them, then those 90 hours should be more Angie-hours than Bob-hours, because Angie-hours are cheaper than Bob-hours.
It’s fascinating, and surreal, to me that people see this as a mathematics or economics question, instead of a relationship question. I know the word “mathematics” is in the title, and it probably shouldn’t be–I was referring there to the numbers of hours worked, not suggesting we needed differential equations to figure out the number of hours.
It was worded in a way that made me think of mathematics at least, but we could also talk about the relationship aspects of it. I was not sure if it was meant as a hypothetical about contributions and wants in a relationship or if you actually wanted to discuss the concrete house-buying scenario.
My wife and I are both economists.
That was a relationship discussion.
Don’t leave us in suspense, man.
What was the shape or your preference frontiers? Was it Pareto efficient? Enquiring minds want all the salacious details. Talk mathy to me baby! 
Funny how often it’s the men who “tolerate clutter” and women who “tolerate cleaning”. This may not be at the deliberate plate breakage level, but still verges on weaponized incompetence.
Or weaponized OCD.
But in general I agree with your point. My now-deceased first wife was much more tolerant of clutter than I ever was. She was no slob, and liked things clean. But having her “stuff” out in piles everywhere was comfortable for her. Not for me. Many of our friends remarked on how we had the gender thing backwards.
Appears that Angie and Brian are both underperforming in their jobs If they can so easily adjust their salaries. What are they? Soap salespersons?
I believe both must contribute the same effort in order to avoid future resentment. It’s a 100%/100% deal. The best compromise is for each to increase buying power by increasing work hours the same amount and find a house they can afford . That would be 80% of what they qualify for. In that case each has increased their contribution and each has achieved some percent of their goal. Angie has increased buying power and Brian has a cap on the commitment. ie compromise - #3 in the OP
Knowing how dopers are, this did not surprise me at all 
Still, I think the posts digging into the math show that there’s at least one more type of compromise, as Hellestal points out - maybe Brian (or is it Bob?) works 42 hours and Angie works 48 hours and they get the house worth 100. This feels like the best option to me, since in #1 and 2, Brian is a bit of a freeloader, and with #3 and 4, Brian seems to have to put in more work relative to the benefit he feels he is getting, and #4 nobody seems to really get what they totally want.
When you talk about the situation between you and your wife, where you clean a little more than you’d like and she cleans a little less than she’d like, do you both clean the exact same amount? Or does she still clean a bit more than you, which would be closer to choice #5?
There is an argument to be made for equal distribution of the work, because that is easy to track and it is hard to gauge relative feelings. Who is to know, if Angie and Brian agreed to work 48 and 42 hours respectively to get the house worth 100, whether Brian is still freeloading a bit? I suspect that is why your wife doesn’t just clean a little bit more than she does now to get to her preferred level of cleanliness - if you are cleaning different amounts, you might claim that you are cleaning more than you feel comfortable cleaning (choice #5) but you might actually be only cleaning the amount you want (choice #1 from your post about cleaning, but corresponding to choice #2 from the original post). Either that, or your wife actually prefers having the extra bit of free time vs. having a perfectly clean house.
I see how you might think that–but it happens not to be the case. I lived comfortably in my own level of clutter for years when I lived alone, and we had explicit conversations when moving in together about what levels we could each handle. When I’m by myself, I go back to a significantly greater level of clutter, and before she comes back home I do a big clean to get it back to where I know she’ll be comfortable.
Beyond that I won’t go into detail, because it’s obviously nunya.
Math just makes explicit what the relationship issue is.
Take me and and my wife.
I am pretty content with little marginal changes one way or the other within a pretty wide range but outside that range the drop off is very sharp. My wife cares more about the range that means little to me. I just don’t want to spend inordinate time deciding. And I am happy to be able do things that make her most happy. Up to very specific points.
Practical compromise then pans out that I prefer just to do things her way for most things. But on items that fall out of my range I am unlikely to compromise at all. Mostly she knows that.
Saying each should usually give in equal fractions most of the time would lead to less happiness.
How much unhappiness does more hours cause one? Likely it depends on how many more hours; there is likely a threshold that more hours increases misery by much more each extra minute. How much happiness does the bigger house result for the other? Unhappiness in a smaller? How much happiness do they each get from doing something that makes the other happier?
Ultimately those are max min math questions as they play out.
My bolding.
You wrote the title of this as the mathematics of compromise and you are surprised that people are answering the question you wrote instead of the question you were thinking in your own mind?
On to the greater discussion of compromises, I think couples can work out things overall. My wife is better at taking care of things out of places and I prefer the sweeping and washing things so we tend to split things that way.
If only you had bolded the very next sentence.