Maximum Constrained Approval Bucklin: Difference between revisions
Maximum Constrained Approval Bucklin (view source)
Revision as of 22:47, 26 January 2020
, 4 years agoAdd example where Hylland vote management works
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Suppose B is elected in round p and then later, the method arrives at round q.
A voter who votes B ahead of C will contribute to C's support when the method makes the case for C regardless of whether he voted B ahead or not, unless B would not have been elected in any earlier round without his support. In that respect, Hylland free riding has no impact on FAB. However, suppose there is another voter who votes B ahead of D. When making the case for D, FAB needs to allocate a Droop quota of votes towards B since B was elected earlier. The B>C voter makes himself available to cover B's deficit when FAB makes the case for someone who is not C. Had he not voted for B, he would not be thus available, and perhaps FAB would have needed to exclude the B>D voter instead, electing C instead of D. So while doing Hylland free riding is more risky than in BTV, it can still pay off, and thus FAB fails weak invulnerability to Hylland free riding.
==== Example ====
Without vote management:
* 12: A>B>C>D
* 38: A>C>D>B
* 13: C>A>D>B
* 27: B
The first two ranks are the same as in the Schulze STV example, so A and B are elected.
With vote management:
* 12: A>B>C>D
* 22: A>C>D>B
* 29: C>D>A>B (dishonest A>C>D>B and C>A>D>B voters)
* 27: B
In the first round, A wins. In the second round, the optimal allocation when making the case for B is to remove 22 A>C ballots and 8 A>B ballots. B's score is thus 31. C's score is unchanged, so the free-riding pays off: C wins.
=== Monotonicity ===
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