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

[Juho Laatu]

On 15.6.2011, at 14.46, Kevin Venzke wrote:

> It's better if explaining the method's
> rules is enough (or close) to understand the strategy.
...

> No, I am (almost) saying that if you have to explain the strategy
> separately then that's bad. I think people will want to understand the
> strategy in the sense that they can understand *how* they come to that
> conclusion.

Ok, my thinking was that in some cases it is enough to tell how to vote sincerely (=never mind the vote counting process, it is good enough to do the job). The next level would be to tell how the method works (and let people draw whatever simple conclusions they need to draw from that). The third level would be to teach them also how to vote strategically. The fourth level could be to tell them to vote as told by the trusted strategy experts that plan optimal strategy for their party.

>> 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.
> 
> If you're going to say that last sentence then your idea that truncation
> shouldn't mean more than a split vote makes no sense to me. If voters
> that you consider *sincere* may use truncation for a special reason,
> why can't that phenomenon be reflected in the method? Just due to the
> simplicity of the explanation when it isn't reflected?

My thinking was the the voters may well have some preferences between the remaining 100 candidates but they are so small and those candidates are so likely not to win that filling the ballot with complete rankings would be a too big task when compared to the expected benefits. For similar reasons voters might use equal ranking also elsewhere in the ballot.

So, in this case the voters were approximately / very close to sincere. Using truncation for some explicit strategic purpose would be different. But on the other hand, if truncation has an agreed sincere meaning, then voters could use also truncation in that meaning (e.g. approval) (losing rankings of the remaining candidates could be seen as just the way that the method works, and voters would thus rank sincerely only those candidates that they approve).

(I remind that in my terminology here "sincere" refers to use of some natural language description on what the ballot means and how one should vote (without voters having to worry about how the vote counting process works), and "strategic" means casting an efficient vote based on knowledge on how the vote counting process will work.)

>>>>> 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'm thinking this is something you might be able to argue either way.
> If they are clones, we guess they are comparably good.

Yes. If some candidates are next to each others in every ballot, then at least statistically those candidates are likely to be about as good (especially if we assume that in addition to being next to each others they form a sincere loop).

> If decloning the
> election means you would elect one of the clones, because he's good,
> then in the original election you should elect a clone.

Being able to declone in real life assumes that those candidates are friendly to each others or come from a group with strong internal discipline. In this case they (or the party) would be unhappy if none of them won because all of them were beaten by some of them. Technical clones may also be non-friendly in the sense that they can not agree on someone giving up to help one of the others, and when in office supporters of those candidates that beat the winner could form a nasty majority opposition. Statistically being a technical clone however increases the probability of being a "friendly loser". It is a good target not to punish (nor reward) friendly clones. (Note that MinMax meets this requirement almost always (assuming sincere votes).)

(Reminder: Forming a loop does not mean that the looped candidates are clones or even near clones. Ballots contain thus more information than the matrix.)

> 
> Your argument assumes inherent unhappiness when voters are overruled,
> and measures this as the quantity of voters. But I am tempted to see
> my argument above as more concrete... We already know something about
> the candidates' comparability and might want to assume that the clone
> supporters don't have a strong preference.

We are both talking about the impact that electing one particular candidate has on the society. I think this is a good viewpoint when comparing the performance of different methods with sincere votes (better than technical arguments alone). I note that all usual Condorcet methods are quite good in both aspects. For example in MinMax violation of clone independence (or "violation of the top cycle") is a very rare event and occurs only when the requirements of the worst pairwise loss criterion get strong. And the same in the other direction. Methods that are 100% clone proof (or "cycle proof") violate the opposition strength criterion only rarely.

We were discussing about clones (not top cycles). I wonder if it would be worth the trouble to measure (from the ballots) how strongly a top cycle is based on (near) clones and how strongly the cycle is between candidates that are not clones. If one does not want to make the decision either simpler way, this additional information could give some additional justification to making some more fine-tuned decisions. Decisions would be approximate / heuristic since it is hard to tell where the line between clones and non-clones exactly 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.
> 
> Yes. And my response again is that that doesn't tell us whether we
> still gain more than lose by having this protection. You can argue it
> case by case if you want, but I don't think that will give you a method
> definition.

Yes, as I already wrote above, trying to be accurately or asymptotically clone proof and not protect all cycles would be a heuristic / approximate / statistical estimate.

> 
>>> 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.
> 
> I was sort of expecting you to argue "no, clone independence gives
> you *nothing* other than the freedom from nomination problems."

The nomination problems may lead to nomination regret after the election. I also wrote above that clones are not always "friendly clones". So, protecting them always from each others may not make 100% sense either. And technical clones could in principle be also not clones in the sense of having similar opinions and same uniform group of supporters.

One approach that I have addressed sometimes is the possibility of naming clones explicitly. If parties nominate multiple candidates they could thus indicate that those candidates are indeed clones and the vote counting procedure should treat them as such. This kind of relations could be also hierarchical. Note that in the extreme case we end up having a binary tree of candidates where no loops are possible. This is one solution to the problem of cyclic preferences (and one possible response to Arrow). Even when candidates form a full binary three this method meets the Condorcet criterion since we must now assume that all binary branches represent just one candidate (and the one (out of each pair of candidates) with more votes wins). The voters can not determine which candidates are clones, but the nomination process takes care of this. (Note that this line of arguments started from the complexity of reliably detecting clones from the ballots, and problems of protecting the whole top loop instead of clones only. Explicit clones would make things clear. Probably we would not have a full binary tree but just protection of few candidate groups, if any. This could thus be one more trick in the list of defensive strategies.)

Juho