[EM] BC, cycle definition

[MIKE OSSIPOFF]

EM list:

The Beatpath Criterion (BC) has been defined here. I'd like
to point out that it can be also defined in terms of cycles
instead of beatpaths:

No one should win who has a pairwise defeat that isn't the
weakest defeat in some cycle.

(The strength of B's defeat by A is measured by how many people
ranked A over B).

***

When BC is worded that way, it's immediately obvious that the cycle
Condorcet methdos meet BC. I've defined those methods as
methods that solve circular ties by dropping defeats, and which
won't drop a defeat unless it's the weakest defeat in some cycle.

***

I should add that BC was defined before the Cycle Condorcet
methods were defined. BC was defined because it is the
essence of the defensive strategy criteria. It's easy to show
why BC-compliance implies compliance with all 5 defensive
strategy criteria.

And it's also obvious why compliance with BC makes it easy
to ensure that a candidate won't win if a majority don't want
him to. Easy in the sense that they can do it without drastic
measures like voting someone less-liked over someone more-liked.

They can give him a majority defeat, and deny him a majority
victory, ensuring that his defeat isn't the weakest defeat in
any cycle. And if X majority-beats Y, and X is in the sincere Smith set,
and Y isn't, then any cycle containing X & Y has to include a
non-majority link, since no one outside the sincere Smith set
can majority-beat a member of the sincere Smith set if no one
votes unfelt preferences. So in that instance, Y's defeat
can't be dropped, and no one needs strategy to achieve that
result.

Mike Ossipoff








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