[EM] Reversal's success & backfire probabilities same for all pairwise-count methods

[MIKE OSSIPOFF]

I'd previously said that, with MDDB, unopposed offensive order-reversal can 
only succeed if the candidates' 1st choice strengths are in one particular 
order. My hope was that the ratio of backfire-probability to 
success-probability was greater for MDDB (and maybe MDD,ER-Buckling(whole)  
than for MDDA, wv, & DMC.

Not so. This has probably been discussed here before: What I mean by 
"unopposed" is "uncountered". Maybe "uncountered" would be a better term, 
since it specifically says that anti-order-reversal counterstategy isn't 
being used.

The usual assumption in order-reversal examples is that a majority rank 
someone over the reversers' candidate. Otherwise why would we care if s/he 
wins?  And the reversers insincerely raise someone over the middle CW, 
creating an artificial majority against him/her.

"Uncountered" means that no one is strategizing to thwart the offensive 
order-reversal. In particular, if the middle CW's voters prefer the 
reversers' candidate to the insincerely-raised candidate, they voter 
accordingly. The usual assumption in the example, of course, should be that 
that is what happens.

That's what I, and most of us, mean by an uncountered offensive 
order-reversal example.

In that example, each candidate in the cycle is majority-beaten, and each 
candidate in the cycle has the supporters of the candidate ahead of him in 
the beat-cycle ranking over him/her the candidate behind him/her in the 
beat-cycle. So it's symmetrical. So, if the favoriteness-strengths are 
unknown, then the 3 candidates must have the same probabilties of winning. 
So success, backfire, and neither must have the same probability for all 
pairwise-count methods in an uncountered offensive order-reversal example.

Before I realized that, I was calculating the probabilities, and MDDB gives 
plenty of opportunity for errors, hence my incorrect statement in MDDB's 
favor.

Really, the only practical difference I know of between MDDA and MDDB is 
that MDDB doesn't strictly meet SDSC (though it probably would fail it only 
when there's a majority subcycle--I don't know).

But there are at least two other differences between MDDA and MDDB that 
could be important:

1. MDDA is simpler, with an even briefer definition.

2. MDDB might be more pleasing to the person who doesn't like Approval, the 
person who wants ranking counts used throughout the count.

So I claim that MDDB is still a candidate. So is MDD,ER-Bucklin(whole), 
which I'll abbreviate as MDDERBW.

Maybe its less brief definition won't prevent it from being accepted, though 
I'm inclined to try the simpler MDD methods.

MDDERBW is more briefly defined if ERBW can be defined in terms of mean 
ranks. But mean ranks is a lot less obvious and natural than summed ranks, 
which are what MDDB uses.

That's a similar complication issue between RV that just adds up each 
candiates rating, vs the RV that calculates each candidate's mean rating. If 
RV is going to propoed, we should get its full simplicity and brevity 
advantage by just adding up each candidate's ratings, and declaring as winne 
the candidate with greatest sum.

It may well be that, though mean ranks is briefer, the traditional 
Bucklin-style definition of ERBW would be better accepted by people than its 
mean ranks definition.

Mike Ossipoff

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