[EM] Successful unopposed offensive order-reversal is more difficult in MDDB

[MIKE OSSIPOFF]

First let me re-state the definition of MDDB.

It's the same as MDDA, except that it uses SR instead of Approval.

MDDB:

A candidate is disqualified if another candidate is ranked over him/her by a 
majority of the voters.

(Unless that would disqualify all the candidates, in which case no one is 
disqualified)

The winner is the undisqualified candidate who has fewest candidates ranked 
over him, as summed over all the ballots.

[end of MDDB definition]

What I say below in this posting refers to the 3-candidate case, where B is 
the middle candidate, and a majority rank B over A.

With 3 candidates, in MDDB, in order for unopposed offensive order-reversal 
to succeed, it's necessary for the 1st choice totals of the three candidates 
to be in one particular order: CAB, where B is the middle CW, and the A 
voters are insincerely ranking C over B.

Though that's a necessary condition, I don' t know if it's a sufficient 
condition.

I don't know if, with 3 candidates,  in MDDB, defensive truncation always 
thwarts and punishes offensive order-reversal, as it does in MDDA, DMC and 
wv Condorcet. But even if it doesn't, the fact that the candidates' 1st 
choice strengths have to be in one particular order for the offensive 
order-reversal to succeed means that it won't be a problem.

I don't know, with 3 candidates, for MDDB, what conditions are needed for 
unopposed offensive order-reversal to not be penalized.

Say B is the middle CW, and that the A voters are insincerely ranking C over 
B.

In wv, for unopposed offensive order-revesal to succeed, A must be the 
biggest candidate (by 1st choice votes).

In wv, for unopposed offensive order-reversal to not be penalized, C must 
not be the biggest candidate.

In MDDA, for unopposed offensive order-reversal to succeed, C must be the 
smallest candidate.

In MDDA, for unopposed offensive order-reversal to not be penalized, M must 
not be the smallest candidate.

The conditions in DMC are the same as in wv.

As I said the other day, with MDDA, DMC, and wv, defensive truncation always 
penalizes offensivse order-reversal, by electing the reversers' last  
choice.

With MDDA and WV, defensive equal ranking always thwarts offensive 
order-reversal. That isn't true of DMC.

With MDDA, DMC and wv, when a majority rank C over A, A can't win by 
offensive truncation.

MDDA, DMC, and wv, if it the 1st place strength ordering isn't know, there 
is one chance in 3 that offensive order-reversal will succeed. And an equal 
chance that it will be penalized.

So not only must one know that the success condition be true, or at least 
that the penalty condition not be true, but one must also be sure that 
defensive truncation isn't being used.

Defensive truncation is much more natural and likely on a large scale, than 
is offensive order-reversal.

In MDDB, if the candidates' 1st choice strengths aren't known, then there's 
only 1 chance in 6 that unopposed offensive order-reversal will succeed.

Mike Ossipoff

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