[EM] Better answer to WS's example

[Michael Ossipoff]

WS--

Let me word my answer better, now that I've had a more thorough look at the 
example.

Your objection was that if the Blues order-reverse against Red, and if the 
Reds do defensive truncation, that will elect Hitler. In my most recent 
posting, I correctly pointed out that Hitler doesn't win then. I'll get to 
that again, but disregard it for now.

Effectively, your claim, that offensive order-reversal countered by 
defensive truncation will elect Hitler in the example, is correct for wv 
Condorcet, and I'll tell why in a minute. The claim is literally true for 
MDDA and MAMPO. By the way, I was incorrect when I said that MAMPO elects 
Hitler when both the Reds and Blues truncate against eachother. WV, MDDA and 
MAMPO all return an R, B tie then.

But that's a good thing. It means that when the Reds announce that they're 
going to truncate, or when numerous articles, ads and letters to the editor, 
etc. advise them to, then the Blues would be very foolish to order-reverse.

In fact I claim that it isn't a problem at all. If the Blues vote that they 
like Hitler better than Red, doing so even after someone has told them what 
the result will be, then they shouldn't be surprised if they get Hitler. It 
won't happen. There may be two nuttys, but the electorate isn't 51% nuttys.

What about the fact that, strictly speaking, with the numbers exactly as you 
wrote them, Hitler doesen't win? If it were likely for Hitler to lose then, 
the Reds would have no threat or deterrence against the offensive 
order-reversal. But it only happens if Red and Blue are really in a pairwise 
tie. Pairwise ties are vanishingly rare in public elections. If Red has even 
one more vote than Blue, then Hitler wins, when the Blues order-reverse and 
the Reds defensively truncate.

If Blue is bigger than Red, then the Blues don't need strategy to win. Only 
if there's a pairwise tie between Red and Blue do the Blues gain by the 
offensive order-reversal. And, if Blue and Red look about equal, then of 
course it's many times more likely that Red pair-beats Blue than that Red 
and Blue are in an exact pairwise tie. Therefore, offensive order-reversal 
by the Blues would be a big mistake.

So that's my answer. The example won't happen, because the Blues will be 
deterred, with MDDA, MAMPO, and with wv Condorcet.

The Reds, when announcing their truncation, could invite the Blues to do the 
same. With any of the 3 abovementioned rank methods, the result will be a 
Blue-Red tie.

With MDDA and MAMPO, the Reds would also want to truncate if they felt that 
the Blues might do so.

Mike Ossipoff