4) Add a government share of council tax. I've assumed above that a rise in revenue would go to councils, but some authorities (counties, police, mayors) already take a share (a 'precept'). If the money is needed for Government priorities could they take a precept too?

3) A separate mansion tax. Likely not a runner. Anticipate long delays due to legal challenges over valuation, second homes, etc. Should values be based on 1991, like council tax, or on a more recent date? If the latter, why not revalue everywhere? Etc.

This can be done very quickly, by an Order in Parliament. The Scottish Government has done this twice in the last decade, raising the band ratios for bands E, F, G and H.
The effects would - time permitting - feed through to the review of council funding that is due to take effect in April.

2) Adjust the band ratios. Currently, in any given council, the council tax bills in different bands are in fixed ratios. So a band H bill is always double a band D bill, for instance.
However, this could be changed so that, for instance, a band H bill is 3x a band D bill

That points towards doing a full revaluation. That would take a long time, thus increasing the time for argument over what new bands should look like, and also creating more delay before councils actually see any extra funding from this source

1) Add extra bands - I, J, K etc - and charge them higher rates.
BUT to put properties in those higher bands you really need to check all properties. You can't assume that properties that belong in higher bands - however defined - are all currently in (say) bands G and H

www.project-syndicate.org/commentary/c...

There are - very initial - signs that sub-national government in England is on this track: collaboration, integrated funding, local innovation. Can these lead to real change in governance practices?

4) Data, data, data. But also analysis, and narrative. This is important as the foundation for relationships with central govt and localities, but also for building some level of trust with the electorate. If they don't know what mayors do, tell them, then tell them again.

3) Convening isn't a substitute for hard power. Mayors need to bring something to the table: powers, funding, managing upward (of govt depts).

2) Shared understandings of priorities are important. Government guidance, conditions for mayors' funding, central regulatory priorities need to be telling the same story. The current Bill, and adjacent work, clearly appreciates this but we have yet to see coherent partnership develop.

1) Leadership, vision, strategic planning, convening, whatever you want to call it: it's real and it makes a difference to local actors in the public, private and third sectors. It's not everything but it is something.