It was funny hearing you muse about this idea. A million years ago, a bunch of girls and I rented a big house on a lake. It was a lot less drama than it could have been because we decided to come up with a system to share the work/rent that made a lot of sense to us. We had a list of "chores" and each room was assigned a different dollar value depending on its desirability. It ended up being a percentage of the total rent plus maybe 20%. So each chore was assigned a dollar value. Each person had to come up with enough chore value and rent to cover their room rate. What happened was if you didn't cover your chore quota, you paid an equal number of dollars into a community fund. That fund went to cover any rent that wasn't paid and we always had a surplus. Periodically, the fund would get a little large and the excess funds would go toward a party fund. So your contribution for a month might look like this:
Your room rate: $500
You pay your minimum of $300
You do dishes for $5 per time x3 times for a point total of $15
You vacuum the common areas twice for a total of $14
You make dinner for the family twice for $50 (because paying for food is expensive)
You rake the leaves for $30
You clean the bathroom for $20
You pay $71 into the communal fund.
Someone else does the same thing, but adds another $80 of chores. If there is left over from the communal fund for that month, they may choose to take that money out of the communal fund. There is still some money left over to cover short money months later or if the buildup gets pretty big, we make a trip to the wine store and enjoy a nice evening in and order some take-out.
It was the most drama-free living I've ever had, but it took about a day of all of us sitting down and inventing this system and assigning values to each chore and room, but once it was done, no one fought or argued about who was doing more or less and nobody had to be the boss. Magic.