[EM] Is there a criterion for identical voters casting identical ballots?

[Scott Ritchie]

I was thinking about corporate elections today, and how under some
voting systems an individual would want to strategically vote by
submitting multiple, different ballots.  I soon realized that this was
generalizable to multiple voters with identical preferences in any
election.

Basically, something like "If a group of voters share the same
preferences, then their optimal strategy should be to vote in exactly
the same way."

Off the top of my head, there are a few systems that break this
criterion: Single Non-Transferable Vote is one, as is limited block
voting.  In these instances voters of a sufficiently large group
obviously need to spread out their votes a bit more.

Borda also violates it - members of a large enough group will want to
maximize their slate's points by "rotating" the list among them.

I think multi-winner STV can break this in some ways, but I'm not sure
when this occurs.  This is interesting, as intuitively it seems like
most PR methods should satisfy it (though perhaps in some cases with
perfect information, due to anticipated rounding error).  List PR could
run into trouble too, especially list PR that overfavors smaller parties
with an overly large divisor, however that seems only due to rounding
error.

What about other methods, though?  Is there a single-winner election
method that breaks this?  Is there a divisor that prevents or minimizes
this issue in List PR?

Thanks,
Scott Ritchie