Not As Bad As It Sounds!

[Mike Ositoff]

Hi--

Yesterday I mentioned that I expect that, with any of the
best methods that we propose, those Condorcet versions, it would
be possible to make one's favorite win by truncating, under some
conditions. I also pointed out that that strategy can't violate
majority rule,  and that a Condorcet winner is still protected
from it.

I should add somethign that will really sound bad (because
someone else might say it): 

Because you showed up to vote, instead of staying home, that
could make your favorite lose. That follows from the situation
I described yesterday. 

But, again, that only applies the kind of chaotic no-winner
situation called a natural circular tie (sometimes called a
"paradox of voting"). As with the other problem I discussed,
the same protection of majority rule & Condorcet winner apply
here too. 

It can't happen if your favorite doesn't have a majority against
it and E does have a majority against it. And if A is Condorcet
winner (in fact if anything other than E is CW), then that
ensures that E has a majority against it, unless there's lots
of indifference. And therer's really nothing we can do to help
indifferent voters.

***

Lest IRO advocates get too talkative about that, I should point
out that, with IRO, the fact that you showed up to vote instead
of staying home could cause your last choice to win. 

The numbers below are the numbers of voters voting particular
rankings:

  40  30 29
   A   B  C
       A  B


B wins. Then you, and one friend who votes like you do, arrive
late and say "Hold it. Do another count after we vote." And
you vote like the 29 voters, voting sincerely, because A is
your last choice. Guess what. You make A win.

In fact, you'd make A win even if B voters  didn't vote a 2nd
choice.

Of course more elaborate examples could be written, but
look how easy it is to make it happen.

***

One difference beween this, and the Condorcet example, is that
with IRO there's no guarantee that this won't cause violation
of majority rule or defeat a Condorcet winner (It did both things
in that simple IRO example).

I should add that that same problem can happen, probably, with
our Condorcet versions too. Again, the difference is the majority
rule & CW guarantees. Condorcet has them; IRO doesn't have them.

***

Mike