Id said:
WV is much more strategy-free. The difference is unidirectional.
Juho replies:
I doubt the unidirectionality. I think the example I gave (Sincere votes:
49:A, 49:BC, 1:CB. Strategic votes: 49:A, 49:BC, 1:CA.) was an example of a
situation where WV is vulnerable to a strategy and margins is not.
I reply:
Its always possible to contrive an example that affects one method but not
another.
But margins has a much worse problem with offensive order-reversal than wv
does. As I said, in wv, offensive order-reversal can always be thwarted by
merely not ranking the perpetrators candidate.
The criterion SDSC describes wvs advantage in that regard. In margins, to
prevent the offensive order-reversal from succeeding, drastic defensive
strategy is often necessary, such as defensive favorite-burial.
I was answering on these matters well before the EM mailing list began.
Another thing: A few years ago, a margins advocate kept making references to
game theory. So I finally said, If were going to invoke game theory, then
lets apply it. I pointed out that, when theres a CW, in wv elections,
theres always a Nash equilibrium in which the CW wins and no one reverses a
preference. But in margins there are situations in which the only Nash
equilibria involve order-reversal, even when theres a CW.
Juho continues:
Quoting me:
> But Minmax only scores the candidate according to his worst defeat. >
That doesnt tell what it would take to get rid of all of his > defeats and
make him the CW.
Juho replies:
I think minmax(margins) does give information on how many votes a candidates
needs to become a Condorcet winner. I'll use an example to visualize what I
meant. A loses to B 40-50. A loses to C 30-45. A wins all the other
candidates. If there would be 16 additional voters that would rank A first
the 30-45 defeat would change to a 46-45 win and the 40-50 defeat would
change to a 56-50 win. 15 additional voters would be too little and 17th
additional voter is not needed. One thus needs to add one to the worst
margins defeat of a candidate to get the number of additional voters that
the candidate needs to become a Condorcet winner.
I reply:
But it wont do to only talk about when that candidate could be first-ranked
by those people. In general the CW might not be first ranked by them. That
someone ranks A over one candidate, in general doesnt mean that s/he will
rank A over another candidate. So to find out what it would take to make A
the CW, in general, would be to add up how many pair-wise preference votes
would have to be changed, summed over all the voters, to make A the CW.
Thats Dodgson, or something very similar.
In general, looking at As worse pair-wise defeat isnt enough.
Id said:
One of the advantages of wv over margins is that, in wv, offensive >
order-reversal is easily thwarted by simply not ranking the > reversers
candidate.
Juho replies:
Does this mean that voters that are not sure what strategies other voters
will use but who believe that strategies will be used should bullet vote
their own favourite? :-)
I reply:
<smiley> In margins, to protect the CW from offensive order-reversal, its
often necessary for people to whom the CW isnt favorite to rank the CW
alone in 1st place, above their own favorite, so that someone worse wont
win by offensive order-reversal.
Quite so, with wv, if they believe that their favorite is CW, and if they
expect others to offensively order-reverse, then yes, they should only rank
their putative CW. An advantage here is they they neednt know which
direction the offensive order-reversal will come from, from which end of the
political spectrum. They dont have to know who will reverse. Merely knowing
that its a very devious electorate and that someone is likely to
offensively order-reverse is all they need to know.
In general, in a devious electorate, try not to rank below the likely CW,
especially if it is your favorite. Better yet, of course, use ARLO and
power truncation, to all but eliminate the problem.
But the penalty for unsuccessful offensive order-reversal is such that it
probably wont be happening, and wont be a problem.
Juho continues:
As I said, I'd prefer sincere ballots to strategic defences.
I reply:
So do I. Thats why I wrote the defensive strategy criteria, to show which
methods best allow sincere voting. SSD(wv) passes all of the majority
defensive strategy criteria. Margins methods fail all of them.
Id said:
> Offensive order-reversal, the only thing that could cause a > strategy
problem in wv (truncation causes a strategy problem in > margins), requires
lots of co-ordination, many strategic voters and > has great risk of
failure--especially in wv, where its so easily > thwarted, merely by not
ranking the perpetrators candidate. > > In margins, a CW could be defeated
by truncation even if it is > inadvertent, lazy, hurried, or otherwise
non-strategic. But of > course the election could be stolen from the CW by
strategically- > intended truncation too, in margins.
Juho replies:
I think the best way forward would be to give practical examples of
situations where the methods fail due to strategic voting. This would
demonstrate that the theoretic vulnerabilities are also practical
vulnerabilities. And this gives us the opportunity to estimate the
probabilities too. Maybe you can provide an example that demonstrates some
really bad case where margins fail.
I reply:
Id be glad to. Ive posted those examples many times since the EM list
began. Ive posted them for every generation of EM membership. Ill post
them again in a subsequent posting.
Juho continues:
I'll try to do the same for winning votes. I have no intention to prove that
winning votes would be worse than margins in all scenarios. I'd like to see
them roughly at the same level with respect to vulnerability to strategies.
I reply:
Youll find that it isnt like that.
Juho continues:
In addition to that I hope that the strategy related problems would stay at
levels where they are not a probable threat in typical large scale public
elections.
I reply:
You know that, in countries that use Plurality strategy is rampant. Its
discussed and recommended, virtually coerced, by the media. As people find
out about margins strategy needs, theyll publicize and recommend them.
I was once conducting a pair-wise-count vote in an organizational meeting.
(It was a group that liked IRV, and the better Condorcet versions hadnt
been proposed yet, and IRV was going to be the circular tie solution).
It was evident that the compromise was going to be the CW. One participant,
when it was his turn to vote, truncated his ranking, leaving the CW out,
saying, I dont have to vote between that pair. (referring to the CW and
the candidate he liked less). He knew that he could keep the compromise, the
CW, from winning as CW. He wanted to throw it into a circular tie so that
his favorite would have a chance of winning.
That was explicit intentional offensive truncation, a strategy that would be
a major problem with any Condorcet version except for the wv methods.
What, you ask, was the outcome of the vote? I believe that that voter wasnt
sufficient to make a circular tie. The CW was going to win as CW in spite of
his offensive truncation. So the supporters of his alternative walked out of
the meeting. There were two of them. On their way home from the meeting they
stopped at a café and wrote a proposal of their own, which they promoted,
since they didnt like what the coalition was choosing.
Juho continues:
Since US presidential elections are a well known study item on this list I
propose to use that framework (nation wide Condorcet election).
I reply:
Well, you know, we just happen to have a presidential poll posted to EM
<smiley>
Juho continues:
Here's my example. It is in principle the same one I already used but now
presented as a bit more realistic scenario. We have three candidates:
D=Democrat, C=CentristRepublican, R=RightWingRepublican. I don't have any
small party candidates, and that's maybe a deviation from realism, but let's
do this simple scenario first. Sincere votes: 21: D 21: DC 03: DR 03: CD 26:
CR 26: RC Many Democratic voters truncated since they were not interested in
the Republican party internal battle between R and C. The R supporters note
that they could vote RD and get R elected (with winning votes). They spread
the word among the R supporters and press too to reach the required number
of voters. 6 out of the 26 R supporters follow the recommended strategy (=>
20: RC, 06: RD). R wins (with winning votes). Is this scenario a credible
real life scenario?
I reply:
In wv, I doubt it. Notice that the only reason why the R can succeed at that
is because the C are helping R. As I said, the only way you can succeed in
stealing the election by offensive order-reversal is if your victims are
trying to help you. Hows that for something to be proud of?
Juho continued:
Do you expect 6 out of the 26 R supporters to vote strategically? Opinions
will be different in the poll that was used for planning the strategy and in
the actual election. Does that make the strategy less credible?
I reply:
Yes. Offensive order-reversal isnt a natural way of voting, and it would
require organization and public discussion. It would be impossible to
conceal it from its intended victims, whod then be unlikely to rank R.
With margins, the defense is much more drastic--defensive favorite-burial.
Juho continued:
Is there a risk that this strategy would backfire?
I reply:
Certainly. If the intend victims dont try to help the perpetrators, helping
with their own victimization, the offensive order-reversal will fail, and
will result in an outcome worse for the reversers than the CW.
With margins: Truncation, whether strategic, lazy, hurried, or whatever,
will often defeat C.W.s. To avoid that, voters will be advised to use
insincere defensive strategies instead of ranking sincerely.
Mike Ossipoff
----
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