[EM] Cabal equilibrium and Strategy overshoot

[Jameson Quinn]

The more I use the concept of Cabal equilibrium, the more I like it. (A
cabal equilibrium is when no "cabal" can strategically improve the results
from the point of view of all members). I find it the most generally-useful
definition of strategy available.

However, there is the problem of "overshoot". If there are a set of
strategies S such that:
- each strategy s in S is a cabal strategy which elects candidate X !=
current winner Y
- for any voter, all strategies in S give the same ballot change or no
ballot change
- the union of all strategies in S does not elect X (and thus, presumably,
is not favorable to all strategic voters).
- (optional criterion to prevent "cabal defensive overshoot protection";
with this criterion, it is harder to avoid overshoots) no proper subset of
any strategy in S elects X
Then, it is very hard for the "cabal" to actually be successful without
sophisticated vote management (and yes, calculating the best odds and acting
randomly counts as vote management, as the average voter lacks the capacity
to calculate the correct odds).

So I'd like to propose a slight extension of the Cabal equilibrium, the
"unanimous cabal equilibrium". In such an equilibrium, there is no cabal
strategy which does not have some working subset which is a member of some
"overshootable" set.

Jameson Quinn
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