Mr. Simmons wrote-

Whenever there is a bimodal (polar) distribution of voters on one divisive
issue and one of the factions has a clear majority, there will probably be
a majority first place winner from that faction which any common method
including IRV and all the Condorcet methods would pick.

Here's where I part company with the "majority rules" rhetoric:

If there is a candidate who has more approval than the "majority first
place vote winner" in this context, then I say that the Approval winner is
more likely to be a centrist, conciliatory candidate than the Condorcet
winner.

It's easy to prove: there are essentially only two factions. The first
place choice of the larger is the Condorcet winner. To have more approval
than the Condorcet winner, the Approval winner must have support from both
factions (otherwise she couldn't surpass the majority first place approval
count) but not 100% support in the larger faction (otherwise she would
share a tie as majority first place winner). 
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D-    I again have to mention the difference between legislative body 
elections (resulting in the making of laws) and executive/ judicial office 
elections (resulting in the enforcement of such laws).

51  AB
48  B
 1   C

100

If a choice is *near* to having a first choice majority, then he/she will 
obviously try to get his/her supporters NOT to make second choice votes.

To counter the above, I again suggest that executive/ judicial office 
candidates be required to get YES majorities.

If there is major political/ geographical split about some sort of 
super-issue, then the obvious solution is political separation (i.e. 
secession).

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