I used to think that elections had three levels:
voter's vote (and transfers if any)
district results (and top-up if any)
make-up of chamber.
but now I would add a fourth level: formation of government (determination of cabinet and ruling party caucus).
elections elect the legislative chamber,
the elected members then determine who is government
by seeing if one party has majority of seats, or
what combo of party caucuses has a majority of seats and can be the most easily assembled.
I think historically voters and votes cast have always been held out of the last stage.
a cabinet that pushes laws that are not popular among majority of elected members will not be successful.
thus a proportional cabinet may be impractical,
or proportional only to the ruling coalition may work,
but that would not be proportional to the votes cast or to the legislature.
Under PR the majority of seats represent the majority of votes cast. (except in rare cases).
thus perhaps a majority of seats in a PR cabinet may represent a majority of votes but it is a bit diconnected. Certianly I see PR in the chamber being the first step.
some say that PR cannot work because you cannot parse out government. (overlooking how cabinet seats can be parsed out.
based on that misunderstanding, John Pepall's book Against Reform (2010) says that therefore PR is impossible.
He does not admit that a PR legislative chamber is possible, nor that PR does actually work in most countries in the world.
PR is successful in ensuring that majority of seats in the chamber represent a majority of votes cast.
under FPTP perhaps 24 percent in a district can take a seat,
thus it is possible that 13 percent of the votes can take a majority of seats.
under IRV, perhaps 50 percent plus 1 can take a seat,
thus 25 percent can take a majority of seats.
a party concentrating just on taking seats in districts where fewest votes are cast can achieve power with even less than that 13 or 25 percent.
under PR it takes a majority of votes to take a majority of seats.
under list PR this is done based on total party vote tallies, usually in districts.
MMP, this is done at the end with top-up where necessary, based on total party vote tallies, in Canada this would be in provincial level or smaller regions.
STV districts would likely cover a city or county or small provinces.
about half the votes go to the voter's first preference.
another 30 or so percent go to help elect candidate that are liked by voter but not the voter's first preference.
altogether 80 to 90 percent of votes are used to actually elect someone who was marked as preferred by the voter.
list PR and MMP has about same 80-90 percent or more of effective votes.
RUPR would have same percentage of effective votes, too, I expect.
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