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timtyler comments on Explicit Optimization of Global Strategy (Fixing a Bug in UDT1) - Less Wrong
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Set aside different preferences, because I have no idea how to deal with that. It seems like just having different source codes makes things very difficult.
You used "1" and "2" as your indexical labels, which come with a very obvious order. But suppose that Omega labeled one agent ♠ and the other agent ♣. If you and your opposite have different source codes, you have no idea how your opposite internally represents the symbol that they received. For example, you certainly have no guarantee that the two of you order these in lexicographically the same way. So how could you possibly coordinate on a tie-breaking strategy?
Conventionally, spades comes before clubs:
Bridge: spades, hearts, diamonds, clubs;
Poker (generally) spades, hearts, clubs, diamonds.
Except that generally you list them going up - clubs, diamonds, hearts, spades.
Reference? They are not generally listed that way on the internet:
Google "spades, hearts, diamonds, clubs" - 4,090
Google "clubs, diamonds, hearts, spades" - 2,950
Huh, that surprises me. I was going purely by personal experience, plus the fact that bidding goes from low to high in Bridge; that's the order I would expect people to list the suits in, because that's the order they occur in.
Those numbers are not hugely different - it might be more accurate to say that "there is no reliable consensus on order".
To deal with this kind of problem, you want the best ordering you can find.
Not everyone has to agree on it.
The other agent, who has different source code to you, has to agree on it. If it were you and Sniffnoy playing the game ...
In the post, it said:
"Suppose Omega appears and tells you that you have just been copied".
Oh, I see the problem. I was talking about Tyrrell_McAllister's question upthread, in which the assumption of identical source code (i.e. copying) is dropped.
If you don't know much about the other agent - except that it is also trying to win - I figure you should also probably just do the best you can to pick the most mutually-obvious ordering, hoping that they will be doing much the same. Sometimes, it won't work out - but that is doing as well as you can.
That's assuming linear utility. If the most important thing is to consistently get at least a few points, then randomness may be a better strategy.