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

[Juho Laatu]

On 13.6.2011, at 5.37, Kevin Venzke wrote:

> Hi Juho,
> 
> --- En date de : Sam 11.6.11, Juho Laatu <juho4880 at yahoo.co.uk> a écrit :
>>> --- 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.
> 
> I'm not sure this is the same question. You can recommend whatever you
> want, but this is not what I think is sought at the stage where you are
> trying to propose something.

Do you mean that MinMax without strategic guidance would be a strategic mess, or what?

> 
>>> 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.
> 
> Do we even need general guidance? I guess "vote for who you approve" is
> ok, even though "approve" is too vague for my own tastes. Personally, I 
> am going to use something similar to "better than expectation" strategy.

Ok, it could then be close to normal Approval strategy, with sincere rankings added for the "approved" candidates.

> 
>>>>> 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).
> 
> I didn't understand what that sentence is referring to.

I referred to the MinMax(margins) explanation "elect the candidate that needs least number of additional votes to beat all others" that can be seen to refer to CW since it actually is an extended CW definition itself (it counts required additional votes instead of just requiring that the number of required additional votes should be 0).

> 
> This is how I see it, as far as explanations.
> 
> MinMax(margins): we want the candidate who beats all others. If we don't
> have one we take the candidate who needs the fewest addditional votes.
> (You can combine this into one sentence but I am unsure you get a lot of
> points for that.)

Ok, see the short MinMax(margins) definition above.

> 
> C//A: we want the candidate who beats all others. If we don't have one,
> we take the candidate with the most votes in total.

votes = explicit rankings (or alternatively: votes = higher tan last place rankings)

> 
> With both methods we have to explain the same concept to start with. I
> think the difficulty of explanation is about the same. The difference is
> that the strategy implications of Minmax's "part two" are much more
> opaque.

Ok, you seem to refer also to strategic implications that maybe (?) should be explained and included as part of the general definition of the method. Or maybe the idea is that otherwise strategies will confuse the voters after they start wondering about them (?).

> The theory that this opacity makes it harder to strategize under
> Minmax is not obvious to your audience either. All that's obvious is
> "I'm not sure I get it." That is what I see as a liability.
> 
>>>> 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.
> 
> I think this should be expected. When I see all the anti-IRV arguments
> that people manage to come up with it makes me believe that no method
> will have an easy route to adoption.

Yes, but still the questions which method is best and which method can be attacked easily using also irrational and exaggerating arguments could be addressed also separately.

> 
>>>> 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).
> 
> I'm just saying, if people could use equal ranking, I don't believe they
> normally would, if they are being *totally* sincere. Therefore I don't
> need to consider the possibility that there is going to be equal ranking
> on these ballots.

Yes, sincere voters could be expected to be able generate a preference between any two candidates, and not many have a need to explicitly indicate their exactly equal preference between some candidates. Truncation (to equal last position) of unknown and irrelevant candidates could be a natural thing to do to most sincere voters if the number of candidates is high.

> 
>>> 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.
> 
> I'm not suggesting the collection of ratings. I'm trying to investigate
> from what angle we can try to answer your question. If we knew or could
> make assumptions about utilities from rankings (which doesn't really
> seem promising) it would help.

Yes, sincere utilities would help deriving more information from the ballots. In many elections one may however consider determination of plain majorities (with no weight on how strong the preferences are) to be the key goal and key criterion in determining the winner. We are very used to that idea since in competitive environments that has proven to be a stable approach. One could also assume that to some extent the utilities are already included in the rankings. I could for example rank X higher that Y although I personally like Y more but I think that election of X would be anyway better for most and therefor also to me (because I want the society to be peaceful). Maybe some day in some small societies also pure ratings will be used (maybe in "well integrated" societies like families already today, and in sports events).

> 
>>> 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).
> 
> It is unfortunate that the 55-45 don't represent members in an assembly
> or something, since then you could turn the controversy concept into
> a practical issue.

Yes, from this point of view we could move from electing single winners to electing assemblies (or why not use direct democracy too). This is an interesting topic. When an we break questions to smaller questions? When are cycles a result of different weights on different topics that all candidates support? When should decisions be made based on bigger compromises (like a program of a coalition government, or maybe just using regular political horse trading)? I'll however skip this line of discussion due to space and time and tolerance restrictions :-).

> 
>>>>> 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, 
> 
> No no. I'm saying, can we propose that if candidate A is 86% "good" to
> elect, then his clones are also about 86% good, and when Smith allows
> us to satisfy clone independence, we are getting something good more 
> often than we are losing something?

I think clones are about as good and therefore should typically be about as far from being elected.

There are however different kind of clones. If all clones are ranked equal with each others then they are very much like "one candidate", and their "distance from being elected" should be the same. But if those clones form a strong cycle, then we could assume that opinions within that clone cycle must be weak (since the clones are anyway close to equal), or we could assume that those clones are no good because there is so much controversy among them. If one of them would be elected, voters would be unhappy. They would strongly feel that another one of the clones should have been elected. From this latter point of view independence of clones is not a positive feature. Of course in a ranked ballot based method it is difficult to tell which indicated preferences between the clones were strong and which ones just "flips of a coin". MinMax can be said to follow the latter philosophy, and therefore it does not protect clones that are badly cyclic (being so cyclic that someone outside of the clone set will be elected is a very rare situation, but possible, and in some sense indicates what the philosophy of the methods is).

I also note (second time) that methods that use the pairwise matrix to count the results may give clone protection also to non-clones. And of course (this is also just a reminder) members of the Smith set need not be clones.

> 
> The question is does clone independence give us *anything* other than
> reduced nomination problems, and could this be enough to justify Smith.

If one wants the method to be 100% clone proof, and the method uses the pairwise matrix for making the decisions, then one should elect from the Smith set since Smith set may sometimes consist of clones. But despite of not necessarily electing from the Smith set methods like MinMax may not have any major nomination problems. One must thus balance between different criteria and how well to meet each one of them.

> 
>> 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 am a little unsure whether it matters whether there technically are
> ever any clones. It might though.

The definition of the independence of clone criterion is very strict. Maybe no large real life election will ever have any clones according to that definition. But of course meeting that criterion quite typically (but not necessarily) means that the method treats also near clones nearly the same way.

Juho



> 
>> (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).)
> 
> Yes, that's true. But that just means that Smith *doesn't necessarily*
> provide us with a clone-related benefit.
> 
> Kevin Venzke
> 
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