[EM] PC error

[MIKE OSSIPOFF]

In my demonstration that PC is nonfalsifying, I said:

In PC, X has a majority defeat, and the CW never has a majority
defeat, and so X can't win in PC, since it always has a stronger
defeat than the CW does.

[end of quote]

Of course it isn't true that the CW never has a majority defeat,
if someone order-reverses against him. Here's what I should have said:

Because a majority prefer the CW to X, and vote the CW over him,
X has a majority defeat.

For any candidate Z, other than the CW, a majority of the voters
prefer the CW to him, and so they rank the CW, but not Z (because
I said that everyone ranks down to the CW, but no lower).

That means that a majority of the voters don't rank Z. That means
that Z doesn't beat anyone by majority. So only the CW beats other
candidates by majority. So, when the X>CW voters order-reversed by
voting Y over the CW, they removed the only majority defeat that Y
could have. Y now has no majority defeat.

X has a majority defeat. Y doesn't. X can't win in PC.

So order-reversal doesn't benefit anyone; it can't elect someone whom
the reversers prefer to the existing winner, the CW.

As I said before, if reversal won't do it, truncation won't either,
since, compared to reversal, it merely weakens a defeat of the
sincere CW. In the case of PC, the truncation means that now there
are 2 candidates without majority defeat instead of just 1--Y and
the CW. In the case of BeatpathWinner, the CW's submajority defeat is 
another reason why X can't have a majority beatpath to the CW.
In the case of RP & SSD, the CW's submajority defeat is one more reason
why his defeat of X can't be the weakest defeat in a cycle.

So no one benefits by order-reversal or truncation. Obviously no
one benefits by extending their ranking past the existing winner,
to people whom he likes less than the existing winner. So no
one benefits by a strategy change.

Mike Ossipoff




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