Plan a fair shared-house rota without the arguments

Help me make a fair rota for our shared house.

Housemates: [names, and who works shifts or is away a lot]
Shared spaces: [e.g. kitchen, bathroom, lounge, hallway]
Jobs: [e.g. bins, recycling, bathroom clean, hoovering, buying loo roll]
Bin day: [day]
What's causing friction: [e.g. dishes left, nobody does the bins]

Before you start, ask me up to 3 short questions if anything important is missing. Wait for my answers.

Then:
1. Weight each job by time and grimness, so the rota is fair on effort, not just the number of jobs.
2. A four-week rotating rota table.
3. A swap rule and what happens if someone skips.
4. A six-line house agreement we can all sign up to.
5. A friendly, non-blaming message for the group chat suggesting the rota.

Only use the people and jobs I've given. UK English.

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