[EM] "Push-over Invulnerability" criterion

[Chris Benham]

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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