favorite betrayal in rank-order voting systems (is it forced?) settled I think
- The proof of Gibbard's theorem given pages 6-7 of my paper #79
can be reinterpreted to show this somewhat-stronger theorem-statement
(stronger that what I and Gibbard had said):
If a single-winner voting system based on rank-order ballots with
ranking-equalities permitted (and #candidates>=3 and unanimously
top-ranked candidates must win) never encourages voters to
strategically betray either their 1st- or 2nd-favorites (or both),
THEN it is a dictatorship.
On the other hand, there IS a nondictatorial single-winner voting system
(in which unanimously top-ranked candidates must win)
for C-candidate (here I'll do C=3, but in fact this works for any C with small
modifications) elections based on rank-order ballots with
rank-equalities permitted, in which no voter ever wants to betray his favorite:
approval voting, based on rank-order ballots converted to approval votes.
(And "A>B>L" is converted to "A=1, B=0.5, L=0" but that is not going to be
a uniquely best strategic vote in any complete information scenario.)
So that is a sense in which this strengthening of Gibbard's theorem
cannot be strengthened any further.