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. 

There is a major debate within the countries about how to respond to the past. Many Byzantians argue that the views of the Alpagoans are irrelevant. The Alpagoans are "unbombed", this provides them with many systematic advantage over the Byzantians such as career opportunities, indeed most of the top companies in Byzantian still have Alpagoan CEOs since many of the senior management were hired before Byzantian had built anywhere near the number of colleges in Alpago.

Many Byzantians argue that the views of the unbombed deserve very little consideration. Of course the unbombed will want to preserve their advantages. How can the Byzantians ever have their voices heard when unbombed members of parliament are giving their opinions in the Alpago parliament on how much compensation is appropriate? Surely if Alpago was truly sorry, they would accept the demands of the Byzantian government without question.

The Byzantians are undoubtedly correct in their assumption that the Alpagoans have a very strong incentive to underestimate what is owed. They are also correct when they say that the Alpagoans are in a position of power that makes it very easy for them to ignore the issue of compensation, after all, it does not affect them very much if their government decides to pay compensation to the Byzantians, instead of the alternate plan of wasting it on a fleet of nuclear submarines. However, in other areas, the Alpagoans no longer have a power advantage. Many Alpagoan politicians used to say that the war was justified, if a politician said that these days, even the conservative party would demand that they resign because no reasonable person could come to such a conclusion.

In contrast, some of the more extreme Byzantians regularly declare the burning of their capital as a intentional war crime, while the evidence quite clearly shows that the Alpagoans had not targeted their civilian population, only their military base which had inadvertently led to the fire when it was destroyed. During the war, the intentional targetting theory was best supported by the evidence available to the Alpagoans, but advance in forensics have long ago disproven this theory. Many Byzantines consider this forensic technique discredited, because it was originally used to blame the war on the Byzantines. The reason why the Alpagoans did not burn the city was not altruistic. They did not want to burn the city merely because this would make it impossible for them to loot it. It is politically risky for an Alpagoan to point out that the burning was unintentional, since they might be mistaken for a member of the Alpagoan Pillorying Club. These are really legitimately horrible people (even the conservative party consider them to be bigots).

On the other hand, the Alpagoans almost universally insist that they never executed any Byzantine civilians in the brief period that they occupied the country. There are extensive interviews with numerous witnesses who saw this happen with their own eyes, but no hard evidence. The Alpagoans dismiss these accounts as it is impossible for them to conceive that criminals might be telling the truth when their own soldiers (whom they consider honorable - they blame politicians for the war) deny this ever happened. Any Byzantine who mentions this immediately gets dismissed as a "loony conspiracy nut".

If the Byzantians want to consider the incentives of the Alpagoans, they need to also consider their own incentives, as they would be construed by a hardened cynic. They might argue that their incentives are to fight for justice as this would earn them respect, but the cynic would not accept this. The cynic would argue that their incentives are to fight for the maximal amount of compensation, even if a perfectly impartial judge decided that it should be X, their incentive would be to claim that it should be at least X + 1. These incentives exist, even if the Alpagoan government would never offer even half of X.

Some of the Alpagoan are motivated by conscious self-interest to preserve their advantages, while many more who are convinced that they support fair compensation are affect by unconscious self-interest bias. But, the cynic will believe that the Byzantians will have an incentive to position the effect of self-interest on the Alpagoans as greater than it is. The cynic will believe that similarly, some of the Byzantians will be motivated by conscious self-interest, and others by unconscious bias, all while completely convinced that they are being fair.

The Alpagoans are in a position of power when it comes to compensation. The Byzantians lack the ability to force them to pay it, so the resolution will most likely be on the terms of the Alpagoans. The cynic will note that the Byzantians have the incentive to position themselves as being in a position of power for all issues, even when they are the ones in the position of power, such as in relation to the claim that the Alpagoans had intentionally burned their capital. Many Byzantians know that the Alpagoans didn't actually intentionally try to burn their capital, but they see this as a technicality (they started an illegitimate war which resulted in the capital burning) and they do not want to get into an argument with their fellow Byzantians who *really* strongly believe this. Further disagreeing with other Byzantians would undermine their cause which they see as just. The cynic would note that this is a very easy argument for the Byzantians to make. It does not harm them if the actions of the Alpagoans are misrepresented, in fact it helps them. Further, there are social incentives to agree with their fellow Byzantians.

Even though the Alpagoans are correct that they didn't intentionally burn the city, many of them have formed their viewpoint out of self-interest. There is convincing historical evidence, but very few of them have actually seen this, nor do most of them have interest in checking it out as it might disprove their beliefs. Most Alpagoans would be unwilling to acknowledge this, as it would harm their credibility and by used as ammunition by Byzantian activists who believe that they burned it intentionally.

We can see that considering the incentives of all the parties will help both the Byzantians come to a better understanding regarding the situation. The same will be true for the Alpagoans - the Byzantians are right in that the Alpagoans are often unaware of their bias. On the other hand, if either group only considers the incentives of one of the parties, they will most likely come to a more biased conclusion than if they had considered the incentives of neither of the parties. For these purposes, it is very important that the cynic be maximally cynical, without actually being a conspiracy theorist, in order to reduce room for bias.

In my last post, I wrote about how the anthropic principle was often misapplied, that it could not be used within a single model, but only for comparing two or more models. This post will explain why I think that the anthropic principle is valid in every case where we aren't making those mistakes.

There have been many probability problems discussed on this site and one popular viewpoint is that probabilities cannot be discussed as existing by themselves, but only as existing in relation to a series of bets. Imagine that there are two worlds: World A has 10 people and World B has 100. Both worlds have a prior probability of 50% of being correct. Is it the case that World B should instead be given a 10:1 odds due to there being ten times the number of people and the anthropic principle? This sounds surprising, but I would say yes as you’d have to be paid 10 times as much from each person in World A who is correct in order for you to be indifferent between the two worlds. What this means is that if there is a bet that gains or loses you money according to whether you are in world A or world B, you should bet as though the probability of you being in world B is 10 times as much. That doesn’t quite show that the probability is 10:1, but it is rather close. I can’t actually remember the exact process/theorem in order to determine probabilities from betting odds. Can anyone link it to me?

Another way to show that the anthropic principle is probably correct is to note that if world A had 0 people instead, then there would be 100% of observing world B rather than world A. This doesn’t prove much, but it does prove that anthropic effects exist on some level. 

Suppose now that world A has 1 person and world B has 1 million people. Maybe you aren’t convinced that you are more likely to observe world B. Let’s consider an equivalent formulation where world A has 1 person who is extremely unobservant and only has a 1 in a million chance of noticing the giant floating A in world A and the other world has a single person, but this time with a 100% chance of noticing the giant floating B in their world. I think it is clear that it is more likely for you to notice a giant floating B than an A.

One more formulation is to have world A have 10 humans and 90 cyborgs and world B to have 100 humans. We can then ask about the probability of being in world B given that you are a human observing the world. It seems clear here that you have 10 times the probability of being in world B than world A given that you are a human. It seems that this should be equivalent to the original problem since the cyborgs don’t change anything. 

I admit that none of this is fully rigorous philosophical reasoning, but I thought that I’d post it anyway a) to get feedback b) to see if anyone denied the use of the anthropic principle in this way (not the way described in my last post), which would provide me with more motivation to try making all of this more formal.

Update: I thought it was worth adding that applying the anthropic principle to two models is really very similar to null hypothesis testing to determine if it is likely that a coin is biased. If there are a million people in one possible world, but only one in another, it would seem to be an amazing coincidence for you to be that one.