"Ian Jackson" wrote
People keep saying that they use 4:1 or 9:1 baluns.
Often I can see no reason for this (such as when simply feeding a dipole
with coax, or on the output of an ATU).

I'm obviously missing the point. Why the impedance transformation?

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Nearly always there IS no point to be missed.

Reasoning seldom enters an argument.

Which of the infinite number of impedance ratios on one antenna are to be
favoured?

Personally, I have never used a balun except of the choke variety which can
be used between indeterminate impedances of any ratio to serve a
recognisable purpose.

But the right to free speech must be held.
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Reg, G4FGQ