[EM] terms for strategies: compression and reversal

[James Green-Armytage]

Dear election methods fans,

	It seems to me like there might be room for a bit of clarification in the
language which we use to discuss strategy in voting methods. 

	I'd like to point out that there are at least two basic kinds of
strategic alterations which a voter can make to their preference rankings
when voting. The two kinds are "compression" and "reversal." That is, if I
prefer R to S but I strategically vote R=S, I'm using a compression
strategy. If I prefer R to S but I strategically vote S>R, then I'm using
a reversal strategy.

	Blake Cretney, at condorcet.org, defines "compromising" as "Insincerely
ranking an alternative higher in the hope of getting it elected." I find
this to be a useful term. I usually take it to mean that if there are
three candidates R, S and T, and my sincere preference ranking is R>S>T, I
might use the compromising strategy to raise S up on my ballot, to
decrease the probability that T is elected. The accepted drawback is that
this may decrease the probability that R is elected.

I would like to further clarify this concept by naming two distinct kinds
of compromising strategies, that is, 1. compromising:compression, and 2.
compromising:reversal. 
In the above example, a compromising:compression strategy would be to vote
R=S>T. A compromising:reversal strategy would be to vote S>R>T. These are
distinct kinds of strategic manipulation.

	Blake Cretney defines “burying” as “Insincerely ranking an alternative
lower in the hope of defeating it.” I find this term useful as well. I
usually take it to mean that if there are three candidates R, S and T, and
my sincere preference ranking is R>S>T, I might use the burying strategy
to lower S on my ballot, to increase the probability that R is elected.
The accepted drawback is that this may increase the probability that T is
elected.
	Again, I would say that there are two distinct kinds of burying
strategies. 1. burying:compression, and burying:reversal. 
In the above example, a burying:compression strategy would be to vote
R>S=T (which, in some cases, such as this one, amounts to truncation). A
burying:reversal strategy would be to vote R>T>S. 

	Mike Ossipoff has defined terms which bear some relation to Blake
Cretney’s “compromising” and “burying” terms.
	One term which is related to “compromising” is Mike Ossipoff’s “favorite
betrayal” strategy. This is the strategy of voting another candidate over
one’s favorite.
	In the terms I have defined above, Mike’s favorite betrayal strategy is
similar to the compromising:reversal strategy, but it is at once more and
less specific. 
It is more specific in that it requires that another candidate is ranked
ahead of one’s sincere preference. For example, if there are only three
candidates R, S, and T, my sincere preference order is R>S>T, but I vote
S>R>T, then this is an example of favorite betrayal. However, if there are
four candidates Q, R, S, and T, my sincere preference order is Q>R>S>T,
but I vote Q>S>R>T, this is an example of compromising:reversal which is
not favorite betrayal.
However, it is less specific in that, while compromising implies that I am
voting S>R>T instead of R>S>T in order to improve S’s chances of winning,
favorite betrayal does not make this implication. Instead, it is possible
that this maneuver could actually be intended to improve R’s chance of
winning. 
This is the strategy which Blake Cretney calls “push-over” (although I’m
not totally sure why), and which can only be successful in methods which
lack monotonicity. (I think that it might be useful to make a distinction
between push-over:compression and push-over:reversal as well.) 

	Mike Ossipoff’s “offensive order reversal” strategy also seems to bear
some relation to the burying:reversal strategy which I have defined. To my
knowledge it is a special case where the candidate whom one is insincerely
placing lower in one’s rankings is in fact a Condorcet winner with respect
to the sincere preferences of the electorate.
	For example, if my sincere preference ranking is R>S>T, and I vote R>T>S,
this only qualifies as offensive order reversal if S is a sincere
Condorcet winner. (I’m not totally sure if I have this definition right,
actually, so Mike may feel free to correct me.)

	So, I’m hoping that these terms will help to clarify our future
discussions about strategy.
	It is implied that for each of these strategies there are corresponding
questions as to whether a voting method encourages them, in what
situations a method encourages them, the risk-reward ratio of this
incentive, and so on. Thus a corresponding set of criteria are also
implied.
	For example, a method which rewards burying:reversal may be said to fail
a burying:reversal prevention criterion. A method which only rewards
compromising:compression when there is no Condorcet winner may be said to
pass a weak compromising:compression prevention criterion. And so on.
There is quite a bit more work to be done here; I’m just trying to clear
the ground somewhat to make it easier. 

Sincerely,
James Green-Armytage