[EM] Markus: Demonstration that Benham & Woodall meet CD

Thu Jan 9 12:29:07 PST 2014

Hi Juho--

On Thu, Jan 9, 2014 at 2:21 PM, Juho Laatu <juho4880 at yahoo.co.uk> wrote:

> Few requests to make the definition precise.
>
> 1) You should define what "falsifying a preference" means.
>

Good point. I was going for brevity. A voter falsifies a preference if s/he
votes X over Y and doesn't prefer X to Y,.

You're right: That should be included in my definition of sincere voting.

I left it out for brevity. After all, if you tell someone that you reside
at a certain adress, but it isn't true, then we'd all agree that you're
falsifying your address. But are you falsifying your address if you live at
a certain addres, but don't mention your address in a conversation?  To be
a falsification, a statement must be an untrue positive statement.

That's why, for brevity, I didn't include a definition of falsifying a
preference. But now I will add that definition, to my definition of sincere
voting, in my CD definition.

Thanks for mentioning that.

> I have seen different uses on that term on the EM list. If the voter feels
> "A>B" but votes "A=B" or if the voter feels "A=B" but votes "A>B" a
> falsification
>

Obviously the latter isn't a falsificaton. But  I wouldn't call the former
a falsification. Still, when you put it that way, as a positive statement
that you don't have a preference among A and B, then of course it could be
argued that you're falsifyig, because you're making a false statement that
you don't have a preference. Good point--It's better that I include, in my
sincere voting definition, a definition of falsifying a preference.

But I'll just add that when you feel A>B, and vote A=B, you aren't really
falsifying a preference. You're only falsifying a lack of preference, and
that is an entirey different thing. So, though I agree that I should
include a definition of falsifying  preference, I don't agree that it's
really needed. I'll include it because I want my definition to be as clear
as possible.

You could still argue that you're falsifying _about_ a matter of
preference. But that's fudging the meaning of "a preference", and, strictly
speaking, I don't believe that that argument holds up. The right
interpretation is the literal interpretation.

> , or are all differences in preferences and voted rankings falsifications?
>

Yes and no. Voting A=B, when you feel A>B can be said to be a
falsification, but, strictly speaking it is not a falsification of a
preferences. It's a falsification of a non-preference. It's a fasification
regarding the matter of a preference. But it isn't a falsification of a
preference.

But i agree that I should include, for clarity, a definition of falsifying
a preference.

> I note that you excluded the case where the elecion does not allow the
> voter to express all hies/her preferences. Here I thus mean the case where
> the voter can express all his/her preferences.
>
>

Yes. In Approval, say you prefer X to Y, and you prefer Z to X.

You approve X, and you don't vote for Y, because you want to vote your
preference for X over Y.

But, so doing, it isn't possible for you to vote your preference for Z
over X.

Therefore, by my definition of sincere voting, you aren't failing to vote
sincerely, when you fail to vote your Z>X preference.

>
>
> 2) What does "B voters refuse to vote A over anyone" mean?
>
>

I posted to EM, two complete, precise, ballotinig-indpendent and
count-independent definitions of voting X over Y.

It was a few years ago. I'm guessing that it was around the beginning of
2011.

But, just saying imprecisely what occurs to me now, without looking up my
posted definitions, I'd say that it voting X over Y means what one would
intuitively expect it to mean. If X and Y were the only candidates in the
election, your ballot would be more likely to make X win than to make Y
win. i.e., the number of examples in which it would make X win is greater
than the number of examples in which it would make Y win.

I don't know if that likelihood clause is needed, because I don't know if
nonmotonic methods, in practice, can exhibit nonmonotonicity with only 2
candidates.

Maybe the definition should say "...;using a method that is being used
somewhere for governmental elections.", in order to rule out unproposable
methods that would let Y beat X, when no actually-used method would.

Another variation: You're voting X over Y if you vote in  way that would
make X win if X and Y were the only canddates and you were the only voter.
Maybe it, too, should have the "with a method actually in governmental use
somewhere" clause.

I like that one. If these two definitions are different from the ones that
I posted before, then I'll add these two to those two.

That's the best I can do for right now. Maybe that's one of my posted
definitions of voting X over Y. Maybe not.

> Does that mean not ranking A at all
>

Yes. That would satisfy all of my definitions of not voting A over anyone.

> (=not mentioning A in the ballot) if that possibility exists, and
> otherwise ranking A last (on the ballot)?
>

Yes, that, too, would satisfy my definitons of not voting A over anyone.

But I emphasize that all of my definitions of voting X over Y are
completely independent of balloting. None of them speak of rankings or
cardinal ratings, etc.

> Is it ok to rank A tied last (on the ballot) when it would be possible to
> rank also A last alone (on the ballot)?
>

Yes. If you rank A and C both in last place, then you aren't voting A over
C, by any of my definitions.

...and that agrees with everyone's intuition too.

> Is it ok to rank A last (on the ballot) even if one could leave A unranked
> (=not mentioned in the ballot)?
>
>

Certainly, by any of my definitions of voting X over Y, and by anyone's
intuitive judgement.

You know that if you leave A out of your ranking, or if you rank A alone in
last place (without leaving anyone unranked), or if you rank A and C alone
n last place (without leaving anyone unranked, then, in all 3 instances,
you aren't votiing A over anyone,. All of my definitions of voting X over
Y agree with you about that.

>
>
> 3) What does "C voters are indifferent between A and B, and vote neither
> over the other" mean?
>

It means that the C voters don't have a preference between A and B. It
means that the C voters don't prefer A to B, and that the C voters don't
prefer B to A.

And it means that the C voters don't vote A over B, or vote B over A.

> Does that allow e.g. votes 100: C>A>B, 100: C>B>A?
>
>

Ok, good point. In your example, they could be said to be _collectively_
not voting either A or B over the other, even though individually they all
are.

But the answer to your question is: Certainly not, because all of my
definitions of voting X over Y refer only to an individual voter's vote,
not to a collective pairwise decision or defeat. My definitions of voting X
over Y are entirely explicit about that.

Nevertheless,  for clarity, I should specify "No C voter votes A over B, or
B over A".

So, thanks for pointing out those two ways in which my definition of CD
could be made clearer.

Michael Ossipoff

>
>
> Juho
>
>
> On 9.1.2014, at 18.39, Michael Ossipoff <email9648742 at gmail.com> wrote:
>
> Kevin and Markus--
>
> Kevin--
>
> The definition below is what I now mean by CD.
>
> Markus--
>
> You asked me to precisely define the chicken dilemma, and to demonstrate
> that Benham and Woodall don't have the chicken dilemma.
>
> I've defined a criterion that I call the Chicken Dilemma Criterion. It's
> intended as a precisely-defined criterion. I'll state it below in this
> post. But, if it isn't precise, then you should feel free to say so.
>
> In a subsequent post, I'll tell why Benham and Woodall pass CD.
>
> *Supporting definitions:*
>
> 1. The A voters are the voters who prefer candidate A to everyone else.
> The B voters are the voters who prefer candidate B to everyone else. The C
> voters are the voters who prefer C to everyone else.
>
> 2. A particular voter votes sincerely if s/he doesn't falsify a
> preference, or fail to vote a felt preference that the balloting system in
> use would have allowed hir to vote in addition to the preferences that s/he
> actually votes.
>
> *Premise:*
>
> 1. There are 3 candidates: A, B, and C.
>
> 2. The A voters and the B voters, combined, add up to more than half of
> the voters in the election.
>
> 3. The A voters and the B voters all prefer both A and B to C.
>
> 4. The A voters are more numerous than are the B voters.
>
> 5. Voting is sincere, except that the B voters refuse to vote A over
> anyone.
>
> 6. Candidate A would be the unique winner under sincere voting (...in
> other words, if the B voters voted sincerely, as do all the other voters).
>
> 7. The C voters are indifferent between A and B, and vote neither over the
> other.
>
> *Requirement:*
>
> B doesn't win.
>
> [end of CD definition]
>
>
> ------------------------------
>
> In the chicken dilemma scenario described in the premise of the Chicken
> Dilemma Criterion (CD) defined above, if B won, then the B voters would
> have successfully taken advantage of the A voters' co-operativeness. The A
> voters wanted to vote both A and B over the candidates disliked by both the
> A voters and B voters. Thereby they helped {A,B} against worse candidates.
> But, with methods that fail CD, the message is "You help, you lose".
> ------------------------------
>
> *Some methods that pass the Chicken Dilemma Criterion:*
>
> ICT, Symmetrical ICT <http://wiki.electorama.com/wiki/Symmetrical_ICT>,
> MMPO <http://wiki.electorama.com/wiki/MMPO>, MDDTR, IRV<http://wiki.electorama.com/wiki/IRV>,
> Benham's method<http://wiki.electorama.com/w/index.php?title=Benham%27s_method&action=edit&redlink=1>,
> Woodall's method <http://wiki.electorama.com/wiki/Woodall%27s_method>
>  ----
>
> Election-Methods mailing list - see http://electorama.com/em for list info
>
>
>
> ----
> Election-Methods mailing list - see http://electorama.com/em for list info
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20140109/e023f0e3/attachment-0004.htm>