Kevin said:
Hi,
I assume the definitions at http://www.barnsdle.demon.co.uk/vote/stfree.html are
correct.
I reply:
Yes. But I intend to update SDSC by adding wording that would answer the question that you ask later in the message that Iīm now replying to.
Also, the Approval strategy articles there will soon be updated. My approval strategy comments that Iīve just posted here are what someone should criticize if they want to criticize my Approval strategy statements before I do the updating at the website.
Kevin continued:
It seems to me that Mike's criteria aren't ambiguous, but it can be hard to decide
for certain whether methods satisfy them.
I reply:
You want it to always be easy, and no one can guarantee that for you. Some criteria, not just mine, can require some work to demonstrate compliance or noncompliance. But Iīve determined compliance or noncompliance for all the methods for which Iīve been stating it on EM. The criteria are useful in that sense.
Markus once asked me to show whether or not PC passes GSFC &/or SDSC. I replied that I didnīt have a demonstration of that. But those criteria are still useful, because pretty much all the other proposed methods have been shown to pass or fail them.
And please understand the difference between saying that thereīs a posted situation in which it isnīt possible to definitely say that a method passes or fails a criterion, versus saying that a failure example hasnīt been found yet, and nor has it been proven yet that there is no failure example.
Kevin continued:
WDSC:
If a majority of all the voters prefer A to B, then they should have a way of voting that will ensure that B won't win, without any member of that majority voting a less-liked candidate over a more-liked one.
So, a method would satisfy WDSC if the C>A>D>E>B>F>G voters, comprising a majority, could deny B the win by voting C=A>D=E>B=F>G. It isn't necessary that there be any other way for them to deny B the win.
I reply;
You got it. One is all it takes.
Kevin continued:
I think that's kind of a silly way to satisfy WDSC
I reply:
It was you who talked about a method in which it had to be done in that particular way. You must distinguish between silliness of WDSC and silliness of your hypothetical methods. A good way to make that distinction would be to find a silly way that needs to be voted in order to make an actual proposed method meet WDSC. Can you do that?
Additionally, if you believe that itīs silly to not want people to have to reverse a preference then youīre definitely not someone to whom Iīm talking when I offer my criteria.
Kevin continued:
, not to mention the fact that it could be very hard to spot the specific possibility that voting that way could keep B from winning.
I reply:
There are many combinations of a method and a criterion, such that the criterion isnīt one of my criteria, with which it is a lot of work to prove compliance or noncompliance. I canīt take credit for being the first to have those.
However, when you talk about compliance determination being difficult, it would be good if you could specify an actual example of a method and a criterion of mine. Iīve given you an example: PC and GSFC and SDSC. As I said, all other familiar proposed methods have been shown to pass those criteria or to fail them. No, donīt ask me what Kemmeny passes or fails. Iīll just let Mr. Kemmeny say whatīs good about his method, and then you can compare it to what I say is good about wv Condorcet, Approval, and CR.
Kevin continued:
So I think a criterion like WDSC could afford to be more precise.
I reply:
But you forgot to say in what way WDSC, or a criterion like it, is imprecise. A criterion is imprecise if you can show that its wording could mean more than one thing, or that it isnīt possible to say what its wording means. But if you want to say that a criterion of mine is imprecise, then I invite you to post a situation (configuration of candidates, voters, and votersīpreferences) with which, for some method, it isnīt possible to definitely say that that method passes that criterion. For instance, if I say that the method doesnīt fail in that situation, you need to have a convincing argument that my claim isnīt valid. Likewised if I say that the method fails.
Kevin continued:
As a first guess, I suggest: "If a majority of all the voters vote A in first or equal first, and B in last or equal last, then B mustn't win." If that doesn't resemble Mike's intention
I reply:
...and it doesnīt resemble WDSC.
Kevin continued:
, I'm not sure what his intention is by WDSC.
I reply:
In particular, my intention with WDSC is that if a majority of the voters prefer X to Y, then they should have a way of ensuring that Y wonīt win, without any of those voters reversing a preference.
In general, my intention with WDSC is to avoid the need for voters falsifying their preferences for strategic reasons. To minimize the need for defensive strategy. I define defensive strategy as strategy that is intended to protect majority rule, or to protect the win of a CW.
But Iīve made those intentions abundantly clear for a long time, but recently too, on EM, so Iīm not sure what you mean when you say that youīre not sure what my intention is by WDSC.
Kevin continues:
I reply:
Fine, propose that criterion then, and use it to compare methods. Weīll call it Kevin-Non-WDSC, unless you have a more descriptive name for it.
Fortunately Plurality passes your criterion, so maybe we donīt need electoral reform after all :-)
Kevin continues:
SDSC:
(Same as WDSC, except that "over a more-liked candidate" is replaced by "...equal to or over a more-liked candidate") If a majority of all the voters prefer A to B, then they should have a way of voting that will ensure that B won't win, without any member of that majority voting a less-liked equal to or over a more-
liked candidate.
Actually, I think this is either mistaken or unclear. Is it permissible for
the majority to have to truncate B and all candidates ranked below B, or would
that be considered ranking those candidates equal?
I reply:
On EM Iīve been, for quite some time, posting this definition:
A voter votes X equal to Y, and votes Y equal to X, if s/he votes X over someone, and votes Y over someone, and doesnīt vote X over Y, and doesnīt vote Y over X.
[end of definition of voting X equal to Y]
This definition will soon be added to SDSC at the website.
Kevin continues:
FBC:
By voting a less-liked candidate over his/her favorite, a voter should never gain an outcome that he/she likes better than every outcome that he/she could get without voting a less-liked candidate over his/her favorite.
I think this is clear, but hard to use. Suppose if I vote B>A>C>D>E, when A is my
sincere favorite (that is, I like candidates who come earlier alphabetically), then
B is elected. Suppose we try 20 other ways of voting, all with A at the top or
equal top, and these all elect E. I want to conclude that this is an FBC failure.
I can't, though, because it might be the case that e.g. A=E>B=D>C will elect A.
I reply:
The way to demonstrate that a method fails a criterion is to find a situation in which, with that method, the criterionīs premise conditions are met, and the criterionīs requirement is not met.
But, again, youīre complaining that it isnīt easy enough for you, and I sympathize, but I have to say that Iīm sorry to say that, with many combinations of method and criterion, and not just my criteria, one could devise a method for which proving compliance or noncompliance would involve some work. Anyway, as I said, you havenīt given us an actual method and a situation in which it takes too much work to demonstate compliance or noncompliance. But, as I said, I told you that it hasnīt been shown that PC fails GSFC or that PC passes GSFC, and it hasnīt been shown that PC fails SDSC, or that PC passes SDSC. So GSFC and SDSC havenīt been useful for PC. So what? PC passes SFC and WDSC. BeatpathWinner/CSSD, SD, and RP pass GSFC and SDSC.
I reply:
Also, in general I have to check what results one could get from B>C>D>E>A, D>C>E>B>A,
C>B>E>D>A, etc., no matter how unlikely it is to occur to someone to vote in such
insincere ways.
You do that. But first find out what the method is, and the situation.
So I would say, not only is FBC hard to check, but it doesn't seem to be sensitive
enough to "bad behavior" of the method.
I reply:
I only know of one method that passes FBC: CR. Approval passes FBC, but Approval is a version of CR.
No, FBC isnīt "sensitive to" the ways in which Condorcet wv is better than Approval. But thatīs why we have more than one criterion. Because different criteria show different method failures.
Kevin continues:
Both of these could be addressed by making FBC apply to more specific scenarios.
I reply:
Good. Write such a criterion. I have no objection. WDSC is more specific in the sense that it only applies to voters who are in a majority that prefers some X to some Y, and who want a way to defeat Y. But thereīs a way in which WDSC is broader than FBC: WDSC requires that, when its premise conditions are met, the voters referred to in the premise not have to reverse any preference in order to defeat Y, whereas FBC is only about favorite-burial.
Mike Ossipoff
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