One method, say FPTP, of electing a single-member electoral district versus a different method, say a preferential system, of electing a single-member electoral district, since they’re single-member elections in both cases, cannot in and of itself be a determinant in whether or not we get a minority government.
A proportional system, on the other hand, since its purpose is to ensure that every party is elected according to some granularity of the popular vote – with more parties we will get more, but smaller blocks of support, which will show a much pronounced tendency to minority governments.
In this respect, given that with a preferential ballot we no longer discourage voting for non-mainstream candidates or non-front-runner candidates as with FPTP, the chances are better for such candidates to win. In this sense we could elect more independents and smaller parties, which would, as for proportional representation, increase the possibility of minority governments.
But with FPTP, as well, independents and candidates of smaller parties still do run, and we still do, sometimes, elect them, which means that, again, the likelihood of a minority government increases.
The likelihood of minority governments with a preferential ballot, just as with FPTP, is more about the number of parties involved in the election and their relative support by the voters than whether the ballots are counted in terms of FPTP vs. some preferential method.
We have as an example the House of Representatives elections in Australia. Australia uses AV (IRV) in single-seat electoral districts to elect its House of Representatives, used first in a 1918 by-election and continuing to this day. There have been only two minority national governments in this time: 1940–43, and 2010–2013 – only two minority governments in over ninety years! — Hung Parliament(Australia)
There is also the argument that, even if it is true that we’ll get more minority governments, maybe that’s not such a bad thing: while a minority government has to work harder to “get things done,” it generally cannot do so autocratically since it needs to work with other parties to achieve consensus.