[EM] C//A (was: Remember Toby)

[Juho Laatu]

On 12.6.2011, at 2.07, Kevin Venzke wrote:

> Hi Juho,
> 
> --- En date de : Ven 10.6.11, Juho Laatu <juho4880 at yahoo.co.uk> a écrit :
>>> 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 are taking about simple explanations to regular
>> voters then maybe all the strategy related aspects should be
>> considered not-simple.
>> 
>> C//A's counting process is quite simple (to explain)
>> although its counting process has two phases that differ
>> from each others. I don't think e.g. the "elect the
>> candidate that needs least number of additional votes to
>> beat all others" would be more complex.
> 
> The explanation may not be not much more complex. It is the strategy where
> I say MinMax is more complicated and, more importantly, hard to grasp.

I recommend sincere voting. Teaching multiple strategies to regular voters is far too difficult.

> If
> you teach someone how C//A works, I think you get the strategy
> understanding almost for free.

What is the general guidance? Maybe to rank those candidates that the voter approves.

> I don't see any way to go from the terse
> MinMax definition to an instinctive understanding of the strategy (or,
> if you wanted to suggest it, the reasoning why you wouldn't need a
> strategy).
> 
> It may be undesirable that C//A has an approval strategy component at
> all, but that is a different question to my mind.
> 
>>>> 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.
>> 
>> Not necessarily, but that need might pop up. For example in
>> the MinMax(margins) explanation above ("elect the candidate
>> that needs least number of additional votes to beat all
>> others") CW is not mentioned. Some voters might however
>> start wondering in what kind of situations the winner does
>> not win all others. In that case that individual voter might
>> need someone to explain that sometimes there is a CW and
>> sometimes not.
> 
> This feels like a shell game to me. The concept of "beat all others" is
> what you need to explain. I don't care whether you call it CW or avoid
> the term.

Ok, that explanation could be called also an extended CW rule (nothing more needed).

> 
>>>> 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?
>> 
>> I believe most people are not interested in the vote
>> counting process. The voting procedure and general idea of
>> the method must be easy to understand (but no mathematically
>> exact description is needed). People are happy enough if the
>> method seems good enough and experts and their own party are
>> not complaining about its possible problems.
>> 
>> If we take for example a country that uses D'Hondt to
>> allocate seats, only some voters are able to explain how the
>> D'Hondt allocation is actually counted. Most voters vote
>> happily despite of this and have considerable trust on the
>> method.
>> 
>> It is possible that the complexity of a method will be used
>> against it in some reform campaigns but maybe that's a
>> different story. This is not really a problem of the regular
>> voters but just a campaign strategy. Defendability in
>> campaigns is a valid separate topic for discussions though.
> 
> Sorry, I thought that was part of this topic. It is a great part of my
> concern here.

Ok, also that is a major concern if there are people who want to use all the propaganda that they can get in their hands against you.

> 
>>>>> 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'm living in the hope that strategic voting would not be
>> widely spread in Condorcet methods. If strategic voting
>> (offensive and defensive) becomes the norm, Condorcet
>> methods might well lose their attractiveness. If regular
>> voters have to start thinking about offensive and defensive
>> strategies instead of just indicating their preferences they
>> might get fed up pretty quickly.
> 
> Ok, but you appeared to say that you don't know why there should 
> theoretically be a difference among any of the methods. Maybe I didn't
> understand what you meant.

I don't know where my explanations went wrong. I only wanted to say that a simple and possibly sincere voting procedure is ok, and all complex strategies are too complex to the voters.

> 
>>>> 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.
>> 
>> Maybe e.g. the fact that they lack some of the weaknesses
>> of winning votes.
> 
> Oh? Maybe I should read lower.
> 
>>> So it wants to make equality of ranking
>> unattractive...
>> 
>> In what sense? I guess the basic assumption is that voters
>> will cast sincere votes.
> 
> In the sense that your problem with WV is that it is supposedly
> dissuading people from voting sincerely, because equality is useful.
> No?

If truncation is considered to be a strategic tool and not just ranking last ones equal, then that difference may be difficult to understand to the voters.

> 
>>> 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.
> 
> ...nothing else?
> 
> Ok, well if your basic assumption is that voters will be sincere, *no
> matter* what strategic problems margins could have that might encourage
> insincerity, why oh why does that not apply equally to WV? Does WV have
> a special power to make voters lie?

I hope that all typical Condorcet methods are good enough to usually avoid strategy related problems. The vulnerabilities (burial scenarios) of margins and winning votes are a bit different. Their behaviour is somewhat different also with sincere votes. I don't think winning votes would make voters lie (possible interest to truncate could be considered sincere and intentional way of hiding some rankings but giving a cutoff line).

> 
>>> 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.
>> 
>> If we want the majority side (A+B) to win, the voters
>> should be given strict advice not to truncate. In that sense
>> they should forget the approval part. And voters should be
>> warned that although there is a potentially successful
>> strategy available they should not use it.
> 
> They should, but this is so risky it seems clearly better to avert the
> scenario another way.
> 
>> (It is very easy to make the strategy work (only few
>> strategic voters needed) but the risks are quite high if the
>> A+B camp hates C. Voters that feel e.g. A>>>B>C
>> would be more tempted to use the strategy. This set-up is
>> thus quite unstable and therefore not a nice situation to be
>> in.)
> 
> Yes.
> 
>>>> 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.
>> 
>> Yes, simulations offer good support. They of course show
>> only what is written in their parameters. Often they are
>> theoretical in the sense that they observe the situation
>> after knowing the votes accurately and asking a question,
>> what if someone had voted in a different way. In practical
>> elections the situation looks quite different from an
>> individual voter's point of view. Maybe one could model also
>> that situation and run simulations that tell more facts on
>> how regular voters see the game. I'm not sure what
>> parameters you had in the simulations. I'm thinking about
>> parameters like uncertainty of the polls, risk of
>> backfiring, need to coordinate the behaviour of the similar
>> minded voters.
> 
> I tried to be clear that my point is not about the simulations themselves
> and what they say. Otherwise I would go into more detail and run a lot
> more of them. One can easily argue against simulations.
> 
>>>>> 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 have many things to say on this topic but maybe nothing
>> that would be very useful to others. I believe you have at
>> least done your homework well (existence of ICA as an answer
>> or discussion point that addresses some of the key problems
>> demonstrates that).
> 
> Thank you.
> 
>>> I mean, this is a fairly obscure issue that is a
>> *downside* to the method
>>> I am advocating here.
>> 
>> I see this area as a game where one needs to find a good
>> balance between various vulnerabilities and various positive
>> targets. ICA is one rather complex point in this space. That
>> makes it more difficult to give stable and meaningful
>> comments on it - when compared to the ease of commenting
>> some very basic stuff like Approval and Condorcet. ICA puts
>> some special emphasis on equal ranking with the first
>> preference candidate. On the other hand typical voters often
>> have strongly "patriotic" feelings like
>> A>>>B>C>D. I mean that all this complexity
>> makes it hard to find comments that would address the method
>> as a whole. ICA is to me actually a theoretical point in
>> space, demonstrating how one can develop methods that meet
>> some selected target criteria. I tend to like methods that
>> are simple and sincere voting oriented. From that point of
>> view ICA and other more complex approaches set the limits on
>> what one can do if one needs to patch the simpler methods
>> somehow.
> 
> I like simple methods as well.
> 
> I feel that my current simulation is rather effective in eliminating 
> the problems caused by complex method rules. Voters don't know the rules
> and I don't program any method-specific AI. The voters simply figure
> out how the method best works for them, in that particular configuration
> of voters and candidates.
> 
>>> 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.
>> 
>> My interest in explicit cutoffs comes from the interest to
>> get full sincere rankings (that implicit approval /
>> truncation may easily erase). If we assume that strategies
>> are not a problem, then explicit approvals could be sincere,
>> and sincere cyclic opinions could be solved in a way that
>> could be even better (?) than what plain rankings can offer.
>> The question is thus if use of strategies is so marginal
>> that also explicit approval would work.
> 
> If people want an explicit cutoff then please use the Approval-Weighted
> Pairwise methods, not C//A. AWP and CWP appear to be very good.
> 
> Of course I understand why you want an explicit cutoff.

I'd be quite happy to collect any additional sincere information (maybe only for polling purposes or whatever) if that is not too complex to the voters.

> 
>>> Maybe you want to say that any disincentive is good
>> enough. I'm not sure
>>> why that would surprise me.
>> 
>> I'm studying also the possibility that no additional
>> disincentive is needed. At least some societies could work
>> this way.
>> 
>>> 
>>> 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.
>> 
>> Maybe Condorcet methods are good in general. One could look
>> at this problem also from the point of view that in some
>> societies with tendency to resort to strategies some
>> defensive add-ons might be needed.
> 
> This makes me want to ask again whether you think I could make a Condorcet
> method that is actually bad.

If we assume that cycles are rare, then you could spoil Condorcet methods only partially. The psychological negative impact might be more serious though if you invent something really terrible.

> 
>> Well, I think we should be prepared for both approaches.
>> Time will tell us how people will react to use of Condorcet
>> methods in real elections.
> 
> I think if you are pessimistic you cover the optimistic bases too.

Yes, but one should be careful not to introduce unnecessary complexity and not to spoil the performance of the method with sincere votes.

> 
>>>>> 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.
>> 
>> I'm interested in getting definitions on which candidate
>> should be elected if we can assume 100% sincere votes. Would
>> it be someone with lots of first preference support, someone
>> that would have smallest opposition while in power, or would
>> we maybe like to measure the level of happiness of all
>> voters and then try to find a solution that gives highest
>> average happiness or maybe highest minimum happiness. There
>> are many alternatives. And different elections have
>> different needs. We might measure the quality of single
>> candidates one by one, or we might try to establish a linear
>> order among the candidates (maybe to demonstrate to the
>> audience that the electorate had a rational will). I'm thus
>> talking about performance with sincere votes. And my claim
>> was that there are viewpoints to this question where Smith
>> set is not a valid way to measure the quality of the
>> candidates.
> 
> Do we start from the assumption that this is a rankings method?

Rankings are close to ideal for competitive elections, so by default, yes.

> 
> If people voted sincerely and were informed about the candidates, I
> would not expect to see equal ranking or truncation. I have trouble
> imagining the argument that a lot of people have exactly equal utilities
> for certain candidates.

It would not be a big problem to require them to decide, or flip a coin if nothing else helps. Leaving some candidates unranked should be allowed if there are very many candidates. Ties and truncation could be allowed also to avoid losing ballots that were filled somehow wrong (error types depend on what kind of ballots / voting machines are in use).

> 
> So, with no equal ranking, the question seems to be whether you want
> Smith, and if so, are any of the methods better than others.
> 
> I am unsure whether utility-based arguments can touch this question.
> I don't think you should assume normalized utilities, which means you
> would never really have any idea what the utilities probably are.

It is probably too difficult to collect sincere utilities (or normalized utilities) in competitive elections. Therefore rankings may be the best we can do. Ranked methods are not able to see e.g. which Condorcet winners are strong and which ones weak (if measured as average utility), but one can not help that. Some time ago I tried to develop also methods where voters could use preference relations of different strength (e.g. A>B>>>C>D>>E). Also they may be too complex when compared to the additional information that they could give. It may be possible to collect other additional information in the rankings, like "none of the above" or "approved". This information may often be additional and not really indicating utility levels to be used to determine the winner.

> 
> If we're assuming voters to be sincere, the concept of "controversiality"
> loses all importance to me. I find the concept very weak but it at least
> could be tied to a voter regret issue. If there is no voter insincerity 
> to deter, I need to have something different to think about. Hopefully
> there is something else.

Some facts remain after the election. If the winner (X) won candidate Y 55-45, then there could be 45 voters working against X's proposals if they differ from what Y had proposed. If there is a top loop, then we will have an opposition (supporting some Y) that is bigger than number of voters that prefer X to Y. That's some kind of controversy leftover from the elections (sincere votes assumed).

> 
>>> 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.
>> 
>> Let's say there is a top loop of 3 (A, B, C) and D outside
>> the loop. Defeats between A, B and C are strong. All defeats
>> of D are weak.
>> 
>> If we elect A, then there are (say) B supporters that say
>> that there was a strong opinion that B is better than A.
>> 
>> If we elect D, then there are B supporters that say that
>> there was a marginal opinion that B is better than D. In
>> this case there is also a marginal opinion in favour of A,
>> and a marginal opinion in favour of C. We can say that in
>> many elections D is a good choice since there would be only
>> marginal forces of opposition against him.
>> 
>> Probably you should not draw a picture with Smith set drawn
>> above the D candidate. That could give the audience false
>> impression that all the candidates in the Smith set are
>> clearly better than D. And they might think that candidates
>> in the Smith set must be clones (in which case two of them
>> could have withdrawn and donated the victory to the
>> remaining one).
>> 
>> I must also add that of course this kind of situations
>> where someone outside the Smith set wins in MinMax are very
>> rare and probably will "never" happen in real elections. But
>> if they do happen, then there are also explanations why this
>> choice was correct.
>> 
>> Unfortunately cyclic group opinions are not an easy task to
>> explain to anyone, not even to experts. I personally am not
>> too much fond of the Smith set as a philosophy to explain
>> cyclic opinions since, as I said already earlier, it looks
>> to me like an artificial attempt to establish a linear order
>> and thereby explain the cyclic group opinions using
>> terminology that is valid only for linear/transitive
>> opinions. Explanations to regular voters are of course
>> another game.
> 
> Yes, I understand your stance.
> 
>>>> (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.
>> 
>> My thinking is such that since we can not make a fault free
>> system, it is possible that the ideal method for our needs
>> (in some particular single case) may well be a method that
>> violates numerous criteria, but each criterion is violated
>> only so little that it does not have any practical meaning.
>> As an end result the method with many marginal
>> vulnerabilities may not have any major vulnerabilities, and
>> in real life elections that could mean "fault free". In
>> addition to this the method should also achieve the intended
>> targets with sincere votes (and these targets may again be
>> in conflict with other criteria).
>> 
>> In this particular case I don't expect MinMax to violate
>> clone independence so seriously that it would stop people
>> nominating candidates (nor nominate numerous candidates).
>> There are MinMax strategies that attack on known sets of
>> clones, but also those strategies may be just theoretical
>> threats, not practical ones.
> 
> Well, I see what you are saying, that Smith tends to be justified using
> clone independence. And clone independence is normally justified due to
> problems with candidate nominations. But I wonder whether there is any
> room to use the clone concept to argue that clones are comparably "good"
> to elect

I don't know why clones would be better than others, except that since politicians try to become centrists there might be lots of clone like candidates around the centre point. Immunity of clones is a good think from nomination point of view. I guess real nominated clones are however rare. It is more typical that each party nominates just one candidate. or if two, then maybe two different kind of candidates.

(I also note that methods that use the pairwise matrix for deciding the winner and are strictly clone proof must sometimes make decisions as if there were clones although there are not (to make sure that the clone rule is not violated). That is because one can get equal matrix from ballots that have a clone and ballots that do not contain clone candidates (candidates that are always next to each others).)

Juho


> , and that if we use Smith to enforce this, we will be more
> right than wrong.
> 
> I don't disagree that MinMax doesn't really need clone independence.
> It wouldn't add much.
> 
> Kevin Venzke
> 
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