Hugh: Order-reversal

[Mike Ossipoff]

Order-reversal isn't a problem in a 3-candidate race, because
in such a race there's no reason for Middle voters to list
a 2nd choice; and if they don't list a 2nd choice, then it's
a sure thing that order-reversal will backfire badly every time.

When I talk about Middle voters not listing a 2nd choice, someone
will accuse the method of having a truncation "problem". What's
the problem? Defensive trunctation happens to be the defensive
strategy in Condorcet, when completely devious conditions exist.

For whom is the truncation of Middle voters a "problem"? For
the extreme voters who therefore know they can't get away
with order-reversal? For the Middle voters who thereby assure
their candidate's win if he's Universal winner? If no one
has a problem with it except the would-be order-reversers,
the I suggest that it isn't a problem.

And the fact that, under the worst conditions, a defensive
strategy is called for shouldn't be counted against Condorcet.
IRO also requires defensive strategy. The difference is that
Condorcet requires it only with a devious electorate who'd
at least like to steal vicotory from the universal winner
if they though they could get away with it. And IRO requires
defensive strategy even if no one's inclined to attempt
offensive strategy. IRO does its own offensive strategy.

Now, someone might point out that, with more than 3 candidates,
and when there's doubt about which one is the middle universal
winner, then there's strategy dilemma, when there's a devious
electorate. But as I showed a long time ago, it would then
merely be a matter of using the defensive strategy of not
extending one's ranking any farther than the likely needed
compromise. If would-be order-reversers know that's being done,
and if everyone has the same polling information, then
a would-be order-reverser can expect that his prospecive
victims will likely be limiting their rankings as described
above, and that the order-reversal can't be expected to
succeed, and that its success would require luck. Besides,
the fact that thwarted order-reversal elects someone
less-liked than the intended victim, who is between
that candidate & the perpetrators, means that that
in-between candidate's voters have less to lose if
both players defect, in that game of chicken. So the prospective
victims of the order-reversal have the upper hand in that game
of chicken.

Before criticizing Condorcet because these considerations can
even come up, under devious conditions, consider that there's
no such thing as a completely perfect method. As I said, Condorcet's
need for strategy occurs only under devious voting conditions
that would be especialy unlikely in a public election. These
problems need to be put into perspective by comparing them to
those of other methods. 

Anyway, to return to the subject, Condorcet has no strategy
problems in a 3-candidate race, for the reasons that I
gave earlier. I had to say something about bigger elections
because someone else might. Truncation due to laziness or
disinclination to study many candidates would be common. Truncation,
as I said, isn't a problem in Condorcet. Order-reversal would
be quite improbable in public elections, & if it became a
real threat, then if voters are that sophisticated, then they
either won't mind the use of defensive strategy, or else
they'll be open to added features to thwart order-reversal,
such as Iterative-Condorcet, Stepwise-Condorcet, or, probably]
better yet, Iternative-Stepwise-Condorcet. Things we needn't
concern outselves about any time soon, if ever.

By the way, when, a few months ago, I said that Stepwise Condorcet
appealed to me more than Iterative Condorcet, I just meant that
that was my impression at that time; I didn't mean that it's
objectively better. I don't know which is better, but the
combination of both procedures would, it seems, give better
protection.

Other anti-order-reversal measures for devious electorates
would involve a 2nd balloting. Methods like BeatsAll//Approval,
or Condorcet///Approval, which I defined a long time ago
here.

If order-reversal is ever a problem, such a sophisticated
electorate would be willing to adopt a refinement against
it, unless they were willing to just rely on defensive
strategy, which would be well-understood & effective by
such sophisticated voters.


Oh, one other refinement that I forgot to mention is the
"circular tie option", whereby a voter could indicate that
in the event of a circular tie containing candidates above
& below a certain point in hir ranking, the candidates
below that point shall be dropped. This would allow
the benefits of defensive trunction while still voting a
complete ranking of all the candidates. Less deluxe than
the other refinements mentioned above, but could be used
in combination with them.

Excuse this long discussion, but if I didn't bring up
elections with more than 3 candidates, someone else would,
and it would still become necessary to say this. The fact
that I've already said it doesn't mean much, because
people have a way of waiting a while, then bringing
up the same objections again. So this is a pre-emptive
re-statement of things that I've said a long time ago. 
Most likely it won't be necessary to re-state it again
for the Condorcet vs IRO debate.

But the discussion of "ideal voting methods" is an interesting
topic in its own right, and none of us knows what the most
ideal one is, even among the refinements we've discussed.

The ideal method criteria named by Steve & Rob appear to
be un-meetable, too demanding. But the naming of those
criteria led to finding a few more nearly ideal methods:
Iterative Condorcet, Stepwise Condorcet, Iterative Stepwise
Condorcet.


Mike








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