[EM] Defense against order-reversal

[MIKE OSSIPOFF]

Steph--

This is a preliminary reply:

You wrote:

2)does wv protects from order-reversal as well, and if it does not,
does margin or relative margin do a better job?

I reply:

wv protects better against order-reversal than margins & relative
margins. Since truncation requires no defensive strategy to protect
against it in wv, offensive order-reversal is the only thing that can
create a need for defensive strategy in wv. And wv provides two defensive 
strategies against offensive order-reversal that aren't
available in margins or relative margins:

1. Defensive truncation: Mere truncation is enough to make offensive
order-reversers regret what they tried, when it causes the offensive
order-reversal to backfire badly. Defensive truncation of course is
the mildest possible defensive strategy, the least drastic.

2. Equal favorite ranking: Adam pointed out that another defensive
strategy against offensive order-reversal in wv is to rank the
perceived CW in 1st place, along with your favorite. It has the advantage 
that it actually improves your immediate outcome, whereas
defensive truncation, when it penalizes offensive order-reversal,
also sometimes gives the defenders a worse outcome than if they'd
allowed the offensive order-reversal to steal the election.

In other words, as Adam pointed out, defensive truncation is a
dominated strategy. But I replied that dominated deterrent strategy
is common in legal systems and in the animal kingdom; it's widely
used because it works.

Advantages of defensive truncation are that it's the least drastic
defensive strategy there is, and that it actually makes the order-reverer 
sorry that they tried their offensive order-reversal.

Defensive truncation protects the CW by deterring offensive order-reversal. 
And I claim that it deters it well: You yourself pointed
out that it would be difficult to organize strategy in an election without 
everyone knowing. You said that it isn't possible for a
cohort of voters to all meet in a room in private and agree on strategy.
You were quite right. That's why offensive order-reversal is very
unlikely to ever be a secret strategy. And when the intended victims
hear about it, they'll individually feel like defending against it
by defensive truncation, even without any organizing. But then why
shouldn't there be discussion and organizing too, for the defensive
strategy? Sure there would be, if there'd been an offensive order-reversal 
campaign.

The difference with truncation is that it isn't necessarily offensively
intended. People might be lazy or in a hurry if there are lots of
candidates. Offensive or not, truncation will often result in majority
rule violation in margins & relative margins. And I've observed
strategically-intended truncation in a rank-balloting, without any
organizing. A voter just said "I don't have to vote between those two",
because he knew that by not doing so he might be able to sabotage the
CW and could win the resuling circular tie.

Anyway, both of the anti-order-reversal defensive strategies that
I've named here are good ones, and both are better than the
defensive order-reversal that will be needed in margins and
relative margins.

Lastly, also in response to your question, I remind you that it's
margins and relative margins (along with IRV & Plurality) that have
situations where the only Nash equilibria are ones in which some voters
use defensive order-reversal.

Mike Ossipoff


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