Part of my demonstration of many methods' failure of the Unmanipulable
Majority
criterion has inspired me to suggest another strategy criterion:
"Push-over Invulnerability":
*It must not be possible to change the winner from candidate X to candidate Y by
altering some ballots (that vote Y above both candidates X and Z) by raising
Z above
Y without changing their relative rankings among other (besides X and Z)
candidates.*
I might later suggest a more elegant re-wording, and/or suggest a simplified
approximation
that is easier to test for.
25: A>B
26: B>C
23: C>A
26: C
B>C 51-49, C>A 75-25, A>B 48-26
Schulze/RP/MM/River (WV) and Approval-Weighted Pairwise and DMC and MinMax(PO)
and MAMPO and IRV elect B.
Now say 4 of the 26C change to A>C (trying a Push-over strategy):
25: A>B
04: A>C
26: B>C
23: C>A
22: C
B>C 51-49, C>A 71-29, A>B 52-26
Now Schulze/RP/MM/River (WV) and AWP and DMC and MinMax(PO) and MAMPO
and IRV all elect C.
For a long time I thought that only "non-monotonic" methods like IRV and
Raynaud (that
fail mono-raise) were vulnerable to Push-over, so therefore there was no need
for a separate
"Push-over Invulnerability" criterion.
But now we see that the Schulze, Ranked Pairs, MinMax, River algorithms (all
equivalent with 3
candidates) using Winning Votes are all vulnerable to Push-over (as my
suggested criterion
defines it).
Now I know that Winning Votes' failure can be seen as functionally "really" a
failure of Later-no-help,
because those C-supporting strategists could more safely achieve the same end
just by changing
their votes from C to C>A instead of from C to A>C. But that is hardly a
bragging point for WV.
I think this Pushover criterion can be seen as a kind of "monotonicity"
criterion, in the sense that all
else being equal methods that meet it must be in some way "more monotonic" than
those that don't.
I have shown that WV fails "Pushover Invulnerability". I strongly suspect (but
not at present up to
proving) that both Margins and Schwartz//Approval (ranking) meet it.
Can anyone please give an example (or examples) that show that either or both
of Margins and
S//A(r) fail my suggested "Push-over Invulnerability" criterion?
Chris Benham
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