[EM] Juho reply, 22 Feb., 1548 GMT

[Michael Ossipoff]

I’d 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:

It’s 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 wv’s 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 we’re going to invoke game theory, then 
let’s apply it.” I pointed out that, when there’s a CW, in wv elections, 
there’s 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 there’s a CW.

Juho continues:

Quoting me:

 > But Minmax only scores the candidate according to his worst defeat. > 
That doesn’t 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 won’t 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 doesn’t 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. 
That’s Dodgson, or something very similar.

In general, looking at A’s worse pair-wise defeat isn’t enough.

I’d 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, it’s 
often necessary for people to whom the CW isn’t favorite to rank the CW 
alone in 1st place, above their own favorite, so that someone worse won’t 
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 needn’t know which 
direction the offensive order-reversal will come from, from which end of the 
political spectrum. They don’t have to know who will reverse. Merely knowing 
that it’s 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 won’t be happening, and won’t be a problem.




Juho continues:

As I said, I'd prefer sincere ballots to strategic defences.

I reply:

So do I. That’s 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.

I’d 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 it’s 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:

I’d be glad to. I’ve posted those examples many times since the EM list 
began. I’ve posted them for every “generation” of EM membership. I’ll 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:

You’ll find that it isn’t 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. It’s 
discussed and recommended, virtually coerced, by the media. As people find 
out about margins’ strategy needs, they’ll 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 hadn’t 
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 don’t 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 wasn’t 
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 didn’t 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. How’s 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 isn’t a natural way of voting, and it would 
require organization and public discussion. It would be impossible to 
conceal it from its intended victims, who’d 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 don’t 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