[EM] Remember Toby

[Kevin Venzke]

Hi Juho,

--- En date de : Mer 8.6.11, Juho Laatu <juho.laatu at gmail.com> a écrit :
> I was busy with other activities for a while but here are
> some comments.
> 
> > 
> > --- En date de : Mer 1.6.11, Juho Laatu <juho4880 at yahoo.co.uk>
> a écrit :
> >>> I agree with Kevin that "elect the CW if there
> is one,
> >> else elect the 
> >>> candidate ranked (or ranked above last) on
> the
> >> greatest number of ballots" is plenty simple, and
> is much 
> >>> more satisfactory than MinMax or Copeland in
> other
> >> respects.
> >> 
> >> In what sense is the above mentioned "implicit
> approval
> >> cutoff" + Approval to resolve is the best "simple"
> method?
> >> If compared to MinMax, is it maybe easier to
> explain to the
> >> voters, more strategy free, or yields better
> winners? Would
> >> an explicit approval cutoff be fine (to allow full
> rankings
> >> to be given)?
> > 
> > It is surely easier to explain than MinMax,
> 
> If we talk about the sincere voting procedure, then MinMax
> voter only needs to rank candidates, but if loops are
> resolved using implicit Approval, then the voter should know
> in addition to the idea of ranking that truncation means
> that the remaining candidates are not approved. The voter
> needs to decide where to truncate. Or alternatively one
> could let the voters vote without knowing that truncation
> means disapproval. That would give more power to those that
> have the knowledge (although not very much if approvals are
> expected to come into play only seldom). I note also that if
> we don't tell to the voters how their ballots will be
> interpreted, then all Condorcet methods become very similar
> from the sincere voting procedure point of view (just rank
> the candidates sincerely and that's it).
> 
> If explanation to regular voters should contain strategic
> voting aspects, then the methods become more complex to the
> regular voter. I don't know if voters should be trained to
> use of approval as a tie breaker or if those properties
> should be hidden from the voters as discussed above. Burial
> would be even more difficult to explain (but maybe not
> recommended to the voters). In Approval all voters are
> expected to vote strategically (=decide where to put the
> cutoff), but if one uses approval only for tie breaking then
> one need not be as careful as with normal Approval.

I don't recommend that voters not be instructed on how the method is
supposed to work.

I think with C//A it is easier to explain how to find the winner, and
the strategy becomes obvious. No defeat strengths are involved. MinMax
has its strategy too, and this is harder to perceive because the method
rules are harder to understand.

> If we talk about the vote counting process (with sincere
> votes) and how to explain it, then we have a two phase
> explanation (=Condorcet winner, and alternatively sum of all
> the ticks in the ballots if there is no Condorcet winner)
> vs. a one or two phase MinMax explanation (elect the
> candidate worst worst defeat is least bad. MinMax(margins)
> is quite simple since it is enough to refer to the number of
> additional votes each candidate would need to win all others
> (if doesn't already). None of the explanations is quite
> obvious to average voters if one has to explain the
> difference between having a Condorcet winner and not having
> a Condorcet winner. The MinMax(margins) specific explanation
> is maybe easiest (and still fair, clear and exact enough) to
> present without talking about the probabilities of having or
> not having a top cycle.

You have to explain CW either way.

> If we seek simplicity, I'd be happiest to explain the
> voting procedure simply "just rank the candidates" and use
> the MinMax(margins) "additional votes" explanation if the
> voters need to know how the votes are counted.

When I think of "simplicity" I mean that the voters would actually 
understand how the method works.

I don't think you will have much luck proposing methods if you don't
think voters need to understand them. Can you find an angle / sales 
pitch that dodges this?

> > has more obvious burial 
> > disincentive (especially if the comparison is to
> margins),
> 
> All Condorcet methods have a burial incentive with some
> variation between different methods. I don't know why
> margins would be more problematic than winning votes. 

The theoretical reason is that the offensive and defensive strategies
look exactly the same. It's analogous to Borda. You cannot tell whether
somebody is trying to steal an election or just cover themselves.

> I mean
> that they have different kind of vulnerabilities and
> disincentives, and it is not straight forward to say which
> ones are more problematic. 

It is not straightforward but one can certainly make an effort. It is
not clear to me what strategic benefit margins is even supposed to have.
So it wants to make equality of ranking unattractive... where does this 
get us? It isn't IRV, there is no guarantee that the truncations turn 
into sincere rankings. If someone wanted to tell you a half-truth why 
would you guess that they won't decide to just lie now instead? You 
would have to presume that all would-be truncators are just lazy.

> Also Condorcet with approval as a
> tie-breaker has its own burial problems, although the
> approval cutoff introduces also some risk to the burying
> strategy. I'll give one example of a burying strategy when
> approval is used for tie-breaking.
> 
> 49: A>B
> 02: B>A
> 49: C
> 
> A wins. But if the two B supporters vote B>C, then there
> is a cycle, implicit approvals will be used, and B wins.
> 
> One possible comment to this strategy problem is that A
> supporters could truncate and not approve B (that seems to
> come from the same party or the same coalition at least). In
> that case all the big groupings could simply bullet vote and
> only the small ones would rank their second favourites. That
> approach could kill the chances centrists that are not the
> first candidates of one of the major groupings as potential
> compromise candidates and Condorcet winners.

This last scenario doesn't seem to be a problem experimentally. I have
usually found that Approval over-selects the centrist. That is, the
centrist will be one of the two winners during the pre-election polling,
and the third candidate who lost out then can't win the election even if
they turn out to be sincere majority favorite.

If the centrist is seen as worse than expectation, then sure, they won't
get many votes.

Anyway, I know that C//A is not immune to burial.

> It seems I have to give one more example to cover also
> cases where the difference between major an minor candidates
> is not that clear.
> 
> 26: A>B
> 25: B>A
> 49: C
> 
> Again, if two of the B supporters vote B>C, then B wins.
> If some A and B supporters truncate in order to defend
> against burying or as a general safety measure against the
> other competing grouping (A and B supporters may not guess
> right which one of them will have more votes), then C wins.
> Before the election A and B groupings could both claim that
> they are bigger and therefore they should truncate, and all
> the voters of the other grouping should rank also the
> candidate of the other grouping.
> 
> This second example comes close to the traditional Approval
> strategy related problems where near clone
> parties/candidates fight about who must approve whom. The
> strategic problems of approval as a tie-breaker and winning
> votes are also quite closely related.

The method isn't perfect, no.

I don't believe this kind of scenario has a good resolution. I think in
practice one of those candidates will drop out, and while that's bad,
I don't think we can do much about it.

> Although use of approval as the tie-breaker has some
> disincentive against burial in the sense that approving some
> unwanted candidate increases the risk of electing that
> candidate, in these examples burial works anyway. Plain
> Approval method is free of the burial strategy but that does
> not mean that this property can be carried also to Condorcet
> methods that use approval for tie-breaking.

Maybe so, but it appears to be true anyway. I ran a few simulations
recently, on a 1D spectrum. I don't expect anyone to take it as gospel
or even as fully explained, I just offer it as evidence that I'm not a
total fool when I make claims. In these simulations, here were the
percentage of voters that wanted (after learning the method and playing
against the other voters) to use burial strategy on average:
WV 3.3%. Margins 3.4%. C//A (implicit) 1.9%. C//A (explicit) 7.0%.

I also explained on EM why C//A might have better resistance than WV,
years before I wrote and ran these sims.

Voters wanting to compromise?
WV 0.1%. Margins 1.6%. C//A (implicit) 0.3%. C//A (explicit) 1.2%.

My point? I am actually trying to learn things, and to some extent I
guess I'm probably succeeding. I don't view EM as purely an art project.

> > and, in my
> > view, gives comparably good winners to WV,
> 
> Did you mean "when compared to WV"?

No, I meant I think it's about the same. Though in the sims above it
was the best of those methods according to sincere Condorcet efficiency.

> The approval
> tie-breaker version clearly assumes an implicit approval
> cutoff, so in that sense it may collect more information
> than basic ranking based Condorcet methods. But on the other
> hand an implicit approval cutoff cuts away some ranking
> information that could have been useful. Since approvals are
> used only when there is a top cycle, that approach may lose
> more ranking information (due to truncation) than it gives
> additional approval information. Picking good winners would
> benefit of collecting lots of sincere information. (There
> may also be different opinions on what kind of candidates
> would be good winners.)

Yes. Lots of theory in that paragraph. May be right, may be not, may
vary based on the circumstances. It often happens with election methods
that things don't work the way one would expect. Regarding the last
parenthetical I'm willing to go with sincere Condorcet efficiency.

> > but more attention may need to
> > be placed on where to stop ranking than under WV. (In
> practice, I would
> > not plan to rank any lower than could possibly help me
> in WV, so I would
> > probably vote the same under both methods.)
> 
> This sounds like voters would need to use some (cutoff
> placing) strategy while voting. That does not make the
> methods simpler to the voters.

I didn't say it did. I say it's unfortunate but still simpler on the
whole.

> > The favorite betrayal incentive is worse than WV
> though. (This is where
> > I should plug my ICA method, which satisfies FBC. But
> it's more
> > complicated.)
> 
> I'll skip this part since the mail is about to become so
> long (and this one would require more work from me :-).

I am sure that is true; what I find myself wondering is whether and why
you might be confident that you would have an argument on this topic. 
Have you thought about it? Or you think I haven't done any homework?

I mean, this is a fairly obscure issue that is a *downside* to the method
I am advocating here.

> > An explicit approval cutoff in this method is not fine
> at all: You will
> > lose the burial disincentive. You would be able to try
> to stop your
> > opponents from winning as CW without hurting your own
> candidate's odds
> > to win that way, and then in the approval count you
> would not have to
> > stand by the pawn candidates you voted for. This
> strategy would only
> > backfire when too many voters try it and make a pawn
> candidate the CW.
> 
> Yes, some of the disincentive is lost. But there are also
> other reasons why burial may backfire. You may not manage to
> create a loop and the pawn candidate might win.

Yep, I said that one. That's the scenario where multiple factions are
trying to cheat on the first phase.

> If voters manage to create a cycle, the end result could be
> a quite sincere Approval election, i.e. not an outright
> victory to the ones who created the cycle (=some
> disincentive). In that election those voters that falsified
> their preferences e.g. from A>B>C to A>C>B would
> still have a dilemma of being forced to (explicitly) approve
> also C if they want to (explicitly) approve B (in addition
> to the obvious A) (=some disincentive).

I'm not sure I follow that. Since nobody's going to be approving the
pawn candidates in phase 2, who can win other than a frontrunner? You're
not going to pairwise beat your own candidate by burying, you can only
sink the other guy. If he wins on approval, that's just the same outcome
you were going to get anyway.

But sure, yes, there is "some" disincentive. What I meant was, the
disincentive is no longer very good. It's no longer something to brag
about. It's *vastly* worse than margins in my opinion. In margins it is 
at least confusing to think through the burial issues. To my eye the
brokenness of C//A (explicit) is hard to miss.

Maybe you want to say that any disincentive is good enough. I'm not sure
why that would surprise me.

You may as well consider me to be in agreement with statements like "X
might be good enough in some situations." Why not. Can't really argue
about that.

> > Also, the reason I don't need to see Smith in this
> method is that unlike
> > MinMax, where there isn't an obvious justification for
> failing Smith,
> 
> I think there is an obvious justification for failing
> Smith. If one of the candidates outside the Smith set is
> less controversial (in terms of number of votes needed to
> become a Condorcet winner, or in terms of size of opposition
> planning to work against the elected candidate in favour of
> some other candidate vs. number of supporters) then why not
> elect that candidate. This is one very rational way of
> measuring which candidate should be elected. There may be
> other criteria too, but not necessarily any better than this
> one.

For me "controversial" is an art project term. So is "rational." I wish I
could get it in practical terms. The first one is so close to being one,
too.

If you look at a standard 4-candidate Smith failure example I see
remorseful voters. I can count them, and your argument still works. I
have to ask how I should differentiate different "degrees" of remorse,
if I want to say that sometimes more remorseful voters is OK, if Smith
is involved. I'm not sure how to do that.

> (Actually I think the popularity of Smith set comes
> partially from the temptation of forcing the circular
> preferences to a linear order. In that case the natural
> position of the top cycle may appear to be ahead of the
> other candidates. This approach can however be considered
> irrational since it completely hides away the defeats within
> the cycle. Forcing cyclic preferences to linear ones is thus
> the dangerous (and irrational) part. The opinions are cyclic
> and there is no need to establish a linear order. Other
> criteria may work better, like e.g. the the opposition
> against the elected candidate. Another reason behind the
> popularity of Smith set is the interest to make a method
> clone proof. That is a positive target. But it may violate
> other criteria, like making the least controversial
> candidate win. In the case of MinMax and possibility of
> electing outside the top cycle, violation of the clone
> criterion is not very critical, i.e. the number of
> candidates that parties nominate may not change despite of
> not meeting this criterion 100%.)

The question I have is, is the *only reason* that clone independence is
desirable, that it may prevent aberrations in the candidate nominations?
Maybe Smith has a justification here. I don't have an answer.

Kevin Venzke