Consistency Consequences

[Mike Ositoff]

What I was saying about consistent cycles seems to me to explain
Anderson's statement that any set of pairwise preference vote
totals has a set of rankings that will give those pairwise
preference vote totals:

If you have a given set of pairwise preference vote totals,
then, by making the number of voters sufficiently large, you
can make the pairwise preference vote totals in any cycle 
as small as you want, as a percentage of that total number
of votes. And, as I was saying the other day, a cycle is
inconsistent only if the percentages of the voters voting
the pair-orderings in the cycle are too large. So cycles
can be made consistent by increasing the number of voters.
So any set of pairwise preference vote totals can be achieved
with suffiently many voters.

***

Also, I asked earlier if a cycle can contain a unanimous defeat.
It can. A 3-candidate cycle can have one if there are truncations.
Larger cycles can have one, even if the other defeats are with
good-size majorities, even without any truncations.

***

Mike