Richard Katz writes:

Although it seems intuitively reasonable that PR would preclude
gerrymandering because the minority generally gets some representation,
whereas FPTP is a winner-take-all system, that actually oversimplifies the
problem.  Winner-take-all is a special case of the more general phenomenon
that the translation between vote percentage and seat percentage must be a
step function (because seats only can be won in whole numbers).  For FPTP
there is only one step, and with two candidates it would occur at 50%.
With multi-member districts, there are more steps.  Exactly where they are
depends on the particular PR formula and the way the votes break among the
competing parties (just as the step for FPTP would not be at 50% with more
than two parties).  For example, as a rule of thumb one would expect steps
at 25%, 50%, and 75% for a three member district (no seats for a party
with less than 25% of the vote; one seat for a party with 25-50%, etc.),
or at 20%, 40%, 60%, and 80% for a four seat district. 
In fact, there are two ways to gerrymander with PR. One is to manipulate
the district boundaries to bring the favored party's vote to just over a
step and the disfavored party's vote to just under one, as in FPTP
gerrymanders.  The other is to change the number of seats per district.
For example, a party with 55% of the vote uniformly across 4 three-seat
districts would expect to win 8 seats (2 in each district) but if the
territory were redistricts into 3 four-seat districts (same 12 seats),
they would win only 6.  On the other hand, if the distribution of voters
were not uniform, so that the districts could be drawn giving them 62% in
two of the 4-seat districts and 41% in the other, they would expect two
more seats.

The classic chapter on this is by Peter Mair in Grofman and Lijphart,
Electoral Laws and Their Political Consequences.


Dick Katz