Runoff vs IRO

[Mike Ositoff]

I've recetnly posted an example where IRO defeats a Condorcet
winner who has a plurality of votes. IRO advocates insist that
it's ok to eliminate a Condorcet winner who is favorite of
the fewest, at least among whatever candidates remain. But
is it also ok to eliminate a Condorcet winner who is the
favorite of more people that any other alternative? :-)

Some days ago I said that it's difficult to say which is really
better, Runoff or IRO. But the more considerations we discuss,
the more it looks as if Runoff is clearly better than IRO,
if it means anything to elect a CW--or a CW that's a plurality
winner.

Here are some considerations:

1. Runoff, unlike IRO won't fail to elect a Condorcet winner
who is the favorite of more people than is any other alternative.

2. Runoff, unlike IRO, has a way in which it's obviously &
concretely better than Plurality: With Runoff, a Condorcet winner
can't lose if it comes in 2nd or 1st, in the 1st election. With
Plurality a Condorcet winner can't win unless it comes in 1st.
Neither that nor anything concrete can be said for IRO in
comparison to Plurality. As Dummett says, referring to IRO,
it is "...impossible to discern anything fair about it."
I'll post the full quote in a subsequent posting.

3. Runoff elects a CW when IRO doesn't in examples more general
and typical than the examples in which the reverse is true.
Let me re-copy the example I posted before, where IRO fails
badly but Runoff doesn't:

 60  70  100  83  75
  A   B    C   D   E
  B                D


When the candidate support tapers toward the extremes, as
it will be if the voters are distributed normally (in both
senses of the word), and when the smaller outer candidates
are still big enough to tip the scales among the inner candidates
when their transfers go inward after elimination, then
IRO will screw up in this way every time.

If elimination starts near the middle, and the biggest candidates
are more extreme, than in that special situation it's possible
to contrive an example where IRO elects a CW but Runoff doesn't.
It's necessary to have a candidate next to the CW who is
even smaller than the CW, who at the start gives his transfers
to the CW. Runoff fails to elect the CW in that example because
the biggest 2 candidates are extremes:

  100  40  70  103
    A   B   C    D
        C

(I've only included the 2nd choice that is relevant to
making IRO choose the CW).

This is, by comparison, a special trick example, which
makes IRO do better than Runoff at electing a CW.

4. IRO, but not Runoff, can fail to elect a CW who is everyone's
exclusive 1st or 2nd choice.

Runoff is better than IRO. Regrettably IRO is being proposed
in some communities to replace Runoff.

No on Measure F in Santa Clara.

Mike