Jeff Fisher wrote:
If a faction sees a Condorcet paradox looming, can it gain an advantage by
insincerely approving of the contender that it expects to defeat pair-wise?
I have been asked for a scenario. I don't have much experience, but I'll
try my hand at ABC's.
In this scenario, many 'A' supporters fear 'B', but the 'B' supporters hate
'C' and are ambivalent toward 'A'. 'D' has views that cut across partisan
lines. A real election would have more permutations, but I think this
illustrates my question. I hope this isn't completely irrational
(mathematicians, please check my numbers):
Sincere preferences/advance polling data:
20: A | C > B
16: A > D | C
14: B | A > D
19: B | D > A
12: C > A | B
6: C | D > B
13: D > C | B
Defeats ranked by approval:
Ap: Defeats:
48 A ( 52 B > A )
33 B ( 57 C > B )
31 C ( 69 A > C ) ( 62 D > C )
29 D ( 62 A > D ) ( 65 B > D )
If I counted correctly, the DMC winner is 'B'. However, if the 36 voters
putting 'A' first extend their approval cutoffs to boost C's approval over
B's approval, then 'B' will be doubly defeated by 'C', and 'A' will become
the winner. Even if 'A' voters boost C's approval above A's approval, 'A'
will still win, so there's little risk that their strategy will backfire...
Until 'C' supporters, sensing a first-place approval position, decide to
grant more approval to 'B' in order to doubly-defeat 'A' before A can win...
'B' supporters, completing the tactical cycle, would extend approval to 'A'
and/or 'D' in an attempt to kill off 'C'.
Tactical voting pattern after extending approvals:
20: A > C | B
16: A > D > C |
14: B > A > D |
19: B > D > A |
12: C > A > B |
6: C | D > B
13: D > C | B
(same) Defeats ranked by tactical approval:
Ap: Defeats:
100 A ( 52 B > A )
100 C ( 69 A > C ) ( 62 D > C )
94 D ( 62 A > D ) ( 65 B > D )
61 B ( 57 C > B )
'A' wins. That's not necessarily a bad thing (in this example), but the
approval scores have been badly and visibly warped by tactical voting,
which may undermine public perception of the validity of the system.
Is this scenario illuminating or preposterous? If you were a faction
operating under a DMC system, would you employ such tactics? Can anyone
devise other such scenarios?
Regards,
-- Jeff Fisher ><> Vancouver WA
http://jeffryfisher.net/Statesman
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