The problems with this scenario is that it is at best incomplete as given, and the missing information is highly relevant.

Once upon a time the countries of Alpago and Byzantine had a war. Alpago was mostly undamaged during this war. Byzantine was severely damaged by this war, although they have caught up in some metrics such as education, their economy is still somewhat weaker. Alpago was the clear aggressor, and now, fifty years later, everyone who is reasonable now acknowledges that Alpago was in the wrong.

This is not the way things generally play out. Normally, after this kind of war everyone (at least outside Byzantine) acknowledges that Alpago was in the right (regardless of what an "objective" reading would suggest). While this is not always the case, your scenario failed to specify the reason.

Possible reasons:

1) While the Alpagoans were better at warfare, the Byzantines are better at education and culture and thus their version of history won out. In this case expect a lot of Alpagoans to present themselves as Byzantines.

2) Subsequently a stronger third power sided with the Byzantines and defeated the Alpagoans, without doing as much damage to them as the Alpagoans had done to Byzantine.

3) Following the war there was a revolution in Alpago and the new ruling class want's to portray their predecessors as warmongers to justify their revolution.

4) The Alpagoans are an extremely unusually fair minded people.

I agree with other commenters that this reads like an obfuscated version of some real-world issue (perhaps A and B are white and black people in the USA or men and women or something?), and it ends up (for me, at least) not working well either as an oblique commentary on any real-world issue or as an abstract discussion of how to think well: it feels like politics and therefore stirs up the same defensive reflexes, the obfuscation makes it hard to be sure what the actual point is, I'm wasting brainpower trying to "decode" what I'm reading, and it's full of incidental details that I can't tell whether I need to be keeping track of (because they're probably highly relevant if this is a coded discussion of some real-world issue, but not so relevant if they're just illustrations of a general principle or even just details added for verisimilitude).

I propose the following principle: the mind-killing-ness of politics can't be removed merely by light obfuscation, so if you want to talk about a hot-button issue (or to talk about a more general point for which the hot-button issue provides a good illustration) it's actually usually better to be explicit about what that issue is. Even if only to disavow it by saying something like "I stumbled onto this issue when arguing about correlations between race and abortion among transgender neoreactionaries, but I think it applies more generally. Please try not to be distracted by any political applications you may see -- they aren't the point and I promise I'm not trying to smuggle anything past your defences.".

As to the actual point the article is (explicitly) making: I agree but it seems kinda obvious. Of course considering the incentives on all sides may be difficult to do when you're in the middle of a political battle, but I'm not sure that having read an article like this will help much in that situation.

If this is supposed to be a name swap for an actual conflict its too mangled to get throught. On the otherhand it seems messy and unclear as a pure hypothetical. It is some kind abstraction over many such conflicts? Alpago and Byzantine also seem awfully integrated into a single economy and how a country membership now is an economic class. I would expect two countries economies to mainly funciton within their own context and mechanicsw and not so automatically lean to others.

Also such phrases as "everyone who is reasonable now acknowledges that" are very shaded. I don't know whether it was intended to be used in that capacity its not a automatic "beyond reasonable doubt" disclaimer. Somewhat recently when I thought there were such stances and they "didn't get shot down" made me doubt the objectiveness of such claims. After hell experiences a couple of winters "when hell freezes" no more means "never". Addtionally what is the difference between "you are saying X but you are not reasonable" and "you are saying X, but you are just biased"? Also it can be understood as an expression of closed mindedness. No matter what your reasons or evidence they must be wrong if that is the conclusion. Or that if you say X I am going to disbelieve you as a person.

Once upon a time ...

I'm curious. For those in their 20s, how were you taught to write essays?

Back in the Stone Age when I was growing up, we were taught to have a thesis statement early on so that our readers would know what we were going to be talking about. Here's where we're going with this. Is that entirely out of fashion?

My advisor in grad school expanded on this, to here's the issue, here's the thesis, here's how we're going to get there. A tidy map to let the reader know where we're going, to make it easier to know what to look for to follow along with the progress of the trip.

After a couple of paragraphs, I have no idea where this is going, Are we setting up some analogy to current events, or just setting up the context in which some thesis operates? I don't know, and I find I just don't care enough to continue reading.

I have often griped about essays here, suggesting that people start with an abstract. But here, I want to get get some information on how people are being taught to write. I'm often infuriated by journalists these days, as they write and write and write, and I wonder and I wonder and I wonder where the hell it's all going. Are people doing this on purpose?

Are they being taught to do this? If so, what are the specifics of the pedagogy involved?

The problem with that thought experiment is that actual observer can't have this information. We can't know how many being are in the universe, and there are probably infinitely many of them. But in your experiment you know how many of them exist and also that there is no infinitely many of them. So the experiment models completely impossible world and its results are non relevant.

But from the same logic we may claim that I belong to the biggest class of all actually exiting (if SSA is true https://en.wikipedia.org/wiki/Self-sampling_assumption) or possible observers (if SIA is true https://en.wikipedia.org/wiki/Self-indication_assumption). In infinitely big universe all possible observers exist, so there will not be difference between SIA and SSA.

alpha = 1/(p+1) because the driver is at Y p times for every 1 time the driver is at X; so times the driver is at X / (times the driver is at X or Y) = 1 / (p+1).

The problem with pengvado's calculation isn't double counting. It purports to give an expected payoff when made at X, which doesn't count the expected payoff at Y. The problem is that it doesn't really give an expected payoff. alpha purports to be the probability that you are at X; yet the calculation must be made at X, not at Y (where alpha will clearly be wrong). This means we can't speak of a "probability of being at X"; alpha simply is 1 if we use this equation and believe it gives us an expected value.

Or look at it this way: Before you introduce alpha into the equation, you can solve it and get the actual optimal value for p. Once you introduce alpha into the equation, you guarantee that the driver will have false beliefs some of the time, because alpha = 1/(p+1), and so the driver can't have the correct alpha both at X and at Y. You have added a source of error, and will not find the optimal solution.

Indeed, though it doesn't have to be a time loop, just a logical dependency. Your expected payoff is α[p^2+4(1-p)p] + (1-α)[p+4(1-p)]. Since you will make the same decision both times, the only coherent state is α=1/(p+1). Thus expected payoff is (8p-6p^2)/(p+1), whose maximum is at about p=0.53. What went wrong this time? Well, while this is what you should use to answer bets about your payoff (assuming such bets are offered independently at every intersection), it is not the quantity you should maximize: it double counts the path where you visit both X and Y, which involves two instances of the decision but pays off only once.

You'd want to defect, but you'd also happily trade away your ability to defect to both choose heads, but if you could, then you'd happily pretend to trade away your ability to defect, then actually defect.

I think that this is a really good approach. In terms of philosophy, I'd suggest starting with the philosophy of mathematics as sometimes being exposed to a mathematical proof will make you realise that what you previously believed was completely wrong.

If you are trying to calculate probability of X being true by using bets, then the way that is by seeing when you are indifferent between receiving $A if X is true and $B if X is false and then applying maths. You can't calculate probability by using a weird utility function. If you use a weird utility function then you end up calculating something completely different.