When using the Borda Count, BC, intransigent voters may be tempted to truncate their ballots... and if everyone casts only a 1st preference, the voting procedure morphs into a plurality vote (which is not what Jean-Charles de Borda wanted). In J-C's procedure - today's Modified Borda Count MBC - the rules of the count encourage all voters to submit a full list of preferences.
Majority voting? Well, as the saying goes, turkeys don't vote for Christmas. With the MBC, however, the more each voter participates, the better his/her result... and this applies to everyone in society, not just the majority. See what Canada is now saying: https://electowiki.org/wiki/Borda_count