[EM] Mike: strategy

[James Green-Armytage]

>
>
James G-A replying to Mike, on the topic of voting strategy...
>
>You say that vulnerability to strategy is an important strategy 
>consideration, and that wv adds a whole new wrong that Plurality and IRV 
>doesn't have, because wv is "vulnerable to burying".  

	First of all, when I say that Condorcet methods are vulnerable to
burying, I don't focus on WV. All Condorcet methods are at least somewhat
vulnerable to burying, but it seems that some are less vulnerable than
others. 
	I consider margins methods to be extremely vulnerable to burying; because
of this, I could never recommend margins for contentious elections. Use of
the burying strategy in margins methods can lead to total strategic
disequilibrium where election of a candidate who is the last choice of 90%
or more of the voters takes on substantial probability. Margins is
particularly bad with regard to strategy in that it often does not allow
for stable counterstrategy.
	I consider WV methods to be less vulnerable to burying (perhaps mostly
because it allows for much more stable counterstrategy) than margins
methods, on the theory that, at least in Duvergian scenarios (scenarios
with two major contenders), supporters of one Duvergian candidate can
routinely truncate before ranking the other Duvergian candidate, making it
so that any beatpaths returning to the sincere CW will include a <50%
link. This counterstrategy should probably stave off the very worst
burying abuses, but its applications are somewhat limiting/distorting in
that they require widespread truncation.
	I consider the class of "strategy-resistant" voting methods to be
substantially less vulnerable again than WV, and to allow for
counterstrategy (aka "defensive strategy") that does not distort expressed
rankings. These are e.g. AWP, S/WPO, AERLO/ATLO, CWP. Even here,
successful burying remains as a possibility, but its impact and
probability are effectively minimized.
	But anyway, yes, Condorcet methods (including WV) do have a problem that
IRV doesn't have, because they fail LNH and are vulnerable to burying.
Please read the rest of my reply before responding piece-by-piece, because
there I reply to objections that you are otherwise likely to make once
again here (e.g. the question of whether burying really creates a "new
problem").

>I say that emphasis on vulnerability to strategy is missing the point and 
>barking up the wrong tree. That's because offensive strategy or what you 
>call "burying" is only part of a mechanism which is one way of causing 
>certain undesirable results that can happen with any method. You don't
>want 
>me to repeat it all again, do you? It's repeated in all my postings in
>the 
>discussion. Well, I'll repeat part of it:
>
>Let's talk of these undesirable results: Failure to elect a CW, and 
>violation of majorilty wishes (which I"ve defined on EM recently). 

	I call your "majority wishes" definition the "WV-defined immune set". The
"immune set" is a term that Jobst has used for the minimal set of
candidates such that every defeat against a candidate within the set faces
a chain of at-least-equally-strong defeats leading back to that candidate.
	I doubt that you care very much what I call it, but I let you know so
that you won't be confused by my usage.

>Those 
>things are what I mean by "undesirable results".

	There are results that could be said to be more grimly undesirable than
your definition. For example, choosing a Pareto-dominated candidate,
choosing a Condorcet loser, choosing a candidate who is the sincere last
choice of 90% of the electorate, choosing a candidate that 90% of the
voters have never heard of, and so on and so forth. If you assume that not
selecting from the WV-defined immune set is the worst thing that could
possibly happen, then of course it is difficult to argue for any other
method besides WV.
	In addition to saying that a result is particularly undesirable if it
elects a very unpopular candidate (as above), one might say that a result
is particularly undesirable if it fails to elect a very popular candidate.
For example, failing to elect a candidate who is the sincere first choice
of 90% of the voters, failing to elect a CW with nearly half of the first
choice votes, etc. 
	The bottom line is that your definition of "undesirable results" allows
for only one 'level' of undesirability, whereas I say that there are
multiple levels, and that there are greater offenses than not electing the
sincere CW.
>
>All methods can have undesirable results. Because different methods have 
>different balloting rules and/or different count rules, they can have
>their 
>undesirable results by different mechanisms, and they can have them in 
>different examples.

	Right. I agree with you here, but from here we seem to go off in
different directions.
	First of all: "different methods can have their undesirable results from
different mechanisms". Yes, exactly. IRV can fail to elect a sincere CW
given sincere voting, whereas Condorcet methods can fail to elect a
sincere CW because of a burying strategy. So far so good. 
	Second: "different methods can have them in different examples." Correct.
In Duvergian-type examples, IRV elects the CW with near-perfect certainty.
In examples with three or more strong candidates, IRV does not reliably
elect the CW. On the other hand, Condorcet methods, while they always
elect the CW given sincere voting, are liable to be vulnerable to strategy
(and liable to provide an undesirable result) in a wider range of
scenarios than IRV.
	Hence, if one expected that most election scenarios in the near future
would be Duvergian, one could argue that IRV might more reliably choose
the CW than some Condorcet methods (e.g. margins) would.	
 
>That leads you to say that wv has a problem that IRV doesn't have: 
>vulnerability to "burying", because what you call "burying" is what can 
>cause the undesirable results to happen in wv.
>I say that if the undesirable results happen, if a CW loses, or majority 
>wishes are violated, that's still the same undesirable results,
>regardless 
>of what method did it, and regardless of what the mechanism is. You call
>it 
>a new "problem", but I call it the same undesirable result.

	I don't see a substantiative disagreement here, really. I am happy to
call a new path to undesirable results a "new problem". If a path to such
a result opens in scenarios where no such path had previously existed
(e.g. Duvergian scenarios), I'm happy to call this a "new problem". If the
method isn't denying election to CW's but voter strategy is, then I'm
happy to say that we have traded one problem for another (though the new
one may be less severe than the old).
	You don't agree with this usage of the term "new problem", but you cannot
"prove" that my usage is incorrect, so there's no point in trying; your
objection is more an emotional one than a factual one.
>
>I've told of two differences between those undesirable results in
>Plurality 
>or IRV, and in wv:

	Again, if the only kind of "undesirable result" you recognize is not
choosing from the WV-defined immune set, then your analysis is already
biased towards WV, and Condorcet methods in general. While I agree that
the winner should come from the sincere Smith set (of which the immune set
is always a subset, or equivalent), I recognize that there are plenty of
results that can be said to be more severely undesirable than choosing an
candidate outside that set.
>
>1. In IRV or wv they happen automatically, without anyone using strategy, 
>while in wv they're the result of offensive order-reversal.

	Yes, I understand this.
>
>2. In IRV or wv they can be prevented only by favoritei-burial, while in
>wv 
>and Approval they can be prevented by mere equal-voting. And in wv the 
>offensive strategy that causes the undesirable results can be deterred by 
>truncation.

	Yes, I understand this, although I have to guess that when you say "In
IRV or wv", you probably mean "IRV or margins". Also, I guess that you are
assuming that we are using a version of IRV that doesn't allow equal
rankings.
>
>In a recent posting, you repeated 4 or 5 times that IRV isn't vulnerable
>to 
>"burying" or strategic manipulation. Sure, I understood that you get that 
>language from your professors, or their articles, but I suggest that you
>not 
>uncritically copy your professors.

	Once again, that IRV is never vulnerable to the burying strategy is a
fact. That IRV is never vulnerable to strategic manipulation is clearly
untrue. (Even if you don't consider the compromising strategy to be
something that methods should be called "vulnerable to", there is still
the "push-over" strategy.)
	But as to uncritically copying from professors, what are you talking
about? If Blake Cretney is a professor, I don't know about it, and I've
never read any journal articles by him. Nor do I embrace all of his
definitions. I embrace his definitions of "burying" and "compromising"
strategies because I find them to be useful. If you don't find them
useful, I suppose that's your business, but you're never going to prove
them to be "wrong", or force anyone to "kiss their paradigm goodbye". As
for the phrase "vulnerable to strategic manipulation", that's pretty
straightforward.
>
>Some take the even more ridiculous position that Plurality is
>"susceptible" 
>or "vulnerable" to strategy because it lets Nader-preferrers defeat Bush
>by 
>voting for Kerry instead of Nader. That's a completely backwards 
>description, because the problem isn't that Plurality is vulnerable to
>that 
>voting. The problem is that those voters need to do that. (Of course, if 
>Plurality were somehow not susceptible to favorite-burial strategy, I'd
>like 
>that fine. But the real problem is that voters need to do that, not that 
>they can).

	I understand your point here, and I agree with you. When I say that
Condorcet methods are good because they minimize the incentive for the
burying strategy, I mean what you mean above.
>
James:
>	In our  current discussion of voter strategy, we seem to be talking
>largely at cross-purposes. You accuse me of ignoring points of yours which
>I have actually read and tried to take into account in my reply.
Mike:
>
>It was necessary for me to repeat the same things again and again, to
>answer 
>the same repeated statements of yours. If you'd noticed what I'd said,
>you 
>didn't show any sign of it.

	As I see it, you seem to overestimate the effectiveness of your own
arguments. Because you have "answered" some point, you tend to assume that
the point has been obliterated, and any repetition of it is a foolishness.
By this, you exclude the possibility that your argument (your "answer")
did not actually defeat the point that you believe it to have defeated.
Overall, you seem to repeatedly underestimate my intelligence by
re-posting things that I have already understood, and assuming that my
arguments are defeated as soon as you reply to them.
>
>You said "briefly", so I'll try to summarize it briefly. 

	Much too late for that! Oh well; I suppose I'm not one to talk :-)
>
>Talk of methods' vulnerability to strategy is completely missing the
>point, 
>in regards to what a strategy problem is. A strategy problem consists of
>a 
>need for defensive strategy. That's the important thing, from the voter's 
>point of view, and it's what my criteria try to minimize.

	I understand that. You think that methods should minimize incentive/need
for the compromising strategy, but you ostensibly don't care what kind of
vulnerability they might have to the burying strategy. This is more or
less where we began. I said that burying can be bad if it succeeds, but
you don't yet admit that a burying strategy could do anything worse than
electing someone outside the WV-defined immune set, so burying strategies
don't scare you none. I've now replied that there are worse things than
choosing from outside the immune set, and burying strategies might be able
to give us some of those worse things, in some scenarios. 
	Perhaps one way to proceed would be to ask what are some of the limits of
"unpopularness" for candidates getting elected as a results of voter
strategy in different Condorcet methods, in contrast to similar limits
within IRV. Another possibility is to discuss the range of possible
scenarios in which burying strategy can be successful in different
Condorcet methods, the range of scenarios in which burying strategies are
more than minimally likely to succeed, and the range of scenarios in which
IRV is unlikely to choose the CW. These are just a few suggestions among
many possibilities for further inquiry.
	I'd like to write a few examples to illustrate some of the points that
I'm talking about, but this message is too long already, so I'd better
save that for later.

>I also define "undesirable results", and point out that when they happen, 
>they're just as undesirable regardless of the mechanism that led to those 
>results. 

	Again, I'm happy to call a different mechanism that leads to the land of
bad results a "new problem", and if "bad results" are possible in
Duvergian scenarios with Condorcet while they weren't possible in
Duvergian scenarios with IRV, I'm happy to call this a "new problem".

>But some methods are better than others in regards to what it takes 
>to make those undesirable results happen, and what it takes to protect
>against them.
>
	Yes, of course.

Sincerely,
James