[EM] Party lists and candidate multiwinner elections

[Kristofer Munsterhjelm]

Say we have two settings: one is an ordinary multiwinner election with, 
say, 10 seats. The other is a party list PR election to a very large 
assembly (say 500 seats), but where the number of distinct parties has 
been limited to 10. That is, no more than 10 parties may be represented 
in that large council.

Furthermore, assume that the voters' ballots are completely identical in 
the two settings. So if a voter in setting two ranks party A > party B > 
party C, then in setting one he would rank candidate A > candidate B > 
candidate C.

Now, my question is: is there any situation where we would expect the 
candidates elected in setting one to differ from the parties that get at 
least one seat in setting two?

I can't think of any off-hand, but if there are none, what implications 
do the fact that different parties have very different numbers of seats 
in party list PR have for ordinary multiwinner elections? Is it simply 
an artifact of parties being a lot harder to start than to run as an 
independent candidate in ordinary multiwinner PR? Or is it a consequence 
of party list methods being based on Plurality?

Or are there cases where the party composition would differ from the 
candidates elected in an analogous multiwinner election? Perhaps party 
composition should be more like the results of Minmax Approval (i.e. 
should obey Warren's "representativeness" criterion) and one should use 
relative seat counts to even out the power imbalance? What do you think?