User:Andrewa/Condorcet and New York simplified

It has been suggested that the problem with the New York State/New York City naming controversy may be a Condorcet or Condorcet-like paradox. I have given a formal demonstration that this is not the case at User:Andrewa/Condorcet and New York. This is a more user-friendly approach. Even if you want the full discussion, it's probably best to read and try to understand this first.

Could this be a Condorcet

A Condorcet paradox occurs when there are three alternatives... say, three candidates X, Y and Z, and if X were to stand against Y in a two-way contest then X would win, if Y were to stand against Z then Y would win, but if X were to stand against Z, Z would win. This puzzling and in a sense unresolvable situation is named after the Marquis de Condorcet, who first demonstrated that such scenarios are possible.

The discussion regarding the naming of the New York articles bears a superficial resemblance to a Condorcet scenario, but on the evidence to date it is not one. To see why, we need only examine the two possible Condorcet scenarios.

The decision to be made is where the base name New York is to lead... what the destination of that name is to be. There are three possible options:

(1) An article on New York State.

(2) An article on New York City.

(3) A disambiguation page pointing to both articles.

There are only two possible Condorcet scenarios in any three-way poll, as all three arrows need to be in the same direction around the triangle

There are exactly two ways in which this could be a Condorcet. In two-way discussions, it could be the case that (1) is preferred to (2) which is preferred to (3) which is in turn preferred to (1), or it could be exactly the other way around, (1) is preferred to (3) which is preferred to (2) which is preferred to (1). There are no other Condorcet scenarios possible. These two are completely different scenarios, obviously so when you think about it; Every one of the three decisions has been reversed. But none of those who have suggested that a Condorcet is a possibility have said which of the two they have in mind. This to me indicates that quite frankly, they haven't thought it through.

Because a little thought shows that neither is likely. The evidence is overwhelming that New York City is both a more common search term and a more significant topic than New York State, so (1) cannot be preferred to (2), assuming that the closing instructions are followed, meaning that illogical arguments and those plainly contrary to policy are disregarded.

And the reverse case is even less likely. There has never been a case made for New York State to be the primary topic of the term New York. It was quite vigorously claimed, but no evidence was ever presented, and an RfC eventually settled the issue. So it can't be that (1) is preferred to (3) either.

So it's not a Condorcet at all. It's a puzzle, certainly. But not that sort.

Dealing with a possible Condorcet

There is some speculation above, as the only way to determine with certainty whether or not a Condorcet exists is to conduct the three two-way polls. This is equally true of the majoritarian systems which Condorcet himself investigated, and consensus-based systems such as our own.

Looking at how we would conduct these polls provides a more concrete way of looking at the situation we have here.

The first step in testing is to conduct one of the three polls. It's not currently easy to test (2) against (3), because an RfC on this would be hypothetical. But we can test (1) against either (2) or (3) by raising an RM. The RM being currently developed tests (1) against (3).

If this RM succeeds

If a Condorcet is still suspected, then the next step would be to test (2) against (3) by an RM to make the destination the NYC article. It has been foreshadowed that one is likely.

If that then fails, then this shows conclusively that no Condorcet exists. A Condorcet only exists if all three legs of it are in the same direction around the triangle.

But if that were to succeed, then the final step would be a third RM to point the base name back to NYS. If a Condorcet really does exist, then this third RM will succeed too, and we'll be back where we started but at least we'll know where we stand. I don't think that anyone really believes it would succeed, but cross that bridge when we come to it. If that third RM fails, then again no Condorcet exists.

I encourage you to think very carefully about how likely it is that all three of these RMs will succeed. Particularly consider the third, to move NYS back to the base name after the other two have succeeded. It makes the point very well I think that, while it's easy to drop the Condorcet name, such scenarios are in practice extremely rare and unlikely.

If this RM fails

On the other hand, if this RM fails and a Condorcet is still suspected, the next RM would again be to point the base name to NYC, but in this case this tests (1) against (2) as the first move did not take place.

If a Condorcet exists, then this second RM will succeed. Again, if the first RM is correctly closed but still fails (that is, if NYS is preferred to the DAB as the NY destination in a two-way poll), then I do not think that the second RM has any chance at all. And if it does fail, then again there is no Condorcet.

But if it did succeed, then again we could hold a third RM, to positively identify (or not) the situation as a Condorcet. Again, cross that bridge if and when we come to it.

And again, I ask, does that seem like the scenario we have here? We are talking about a situation where in two-way polls, it is preferred to have the base name point to NYS rather than to a DAB, and to a DAB rather than to NYC. That does not seem to be what we have here at all. Rather, those opposing the DAB will oppose it in either two-way poll.

Conclusion

It's not a Condorcet. It looks like one superficially, in that there are three options, none of which is a clear winner over the other two taken together. But on closer examination, it doesn't look like one at all.

The suggestion that it might be one is very attractive to those who wish NYS to remain at the base name. If it is a Condorcet then there is no solution and the status quo might as well remain. But on the other hand, if it is not, then there is no logical reason for this to occur.

To test it definitively requires three polls. This proposed RM is (and should be) structured to serve as the first of these, if they prove necessary. So if anyone seriously believes that a Condorcet exists, holding this RM is the first step in demonstrating it.