The Conservatives may wish to have First Past the Post elections for Mayors, for Police and Crime Commissioners, and for the London Assembly. But that would only help Labour, in all three cases.
First Past the Post is now something of a curiosity even in the United Kingdom, lingering on only for the House of Commons, and for English and Welsh local elections other than the foregoing.
Of course, being the system used for the Commons means that it still dictates the shape of the parties, although that is so established and entrenched that it would be unlikely to vary much, anyway.
If there really is to be a reduction in the number of constituency MPs from 650 to 600 (and if the Conservatives won again, then they would have done so twice in a row on boundaries that were supposedly unfair to them), then an opportunity presents itself.
Scotland, Wales and Northern Ireland, and each of the nine English regions, would elect five additional MPs, with each elector voting for one candidate, and with the top five elected at the end.
The main parties would be required, and the other parties would be permitted, to submit their shortlists of two for those nominations to an independent, binding, publicly funded ballot of all registered electors in the relevant area.
This would be extended to local government, with the additional Councillors elected by this means from each of the parts of a given municipal area falling within a particular parliamentary constituency.
All of this could still be put in place in time for the General Election of 2022.
These primary and proportional aspects are essential to the restoration of the powers of Parliament and of local government, and to the extension of those powers beyond their historical limits.
Although the most essential thing of all to that restoration and extension, and then to their entrenchment and protection, is far greater economic equality, so that no one's vote effectively counted far more than anyone else's.