I see it often taken for granted that a 'fair' komi for perfect play should be an integer, so that the game can end in a draw.

I came up with a counterexample in which only a non-integer komi will lead to a 'fair' outcome under Japanese rules. See my post on nordicgodojo.eu for more.

So basically B can choose between board result B+6, or offering W a choice between B+7 and repetition.

This means B would only choose the first line with komi 5.5, right? Either with komi 6 or 7 he could choose the second line.

I don't think things like this need any complicated example though. We can just blindly assume on the empty board that such choces will turn up throughout the game/tree, B+5, B+6 etc. - and repetition is among them a few places. The phenomenon simply comes from the fact that the relation/preference (thus perfect play) between "repetition" and B+n depends on komi.

It is even possible to have a position involving ko and seki that theoretically could be scored as N + ½ pt. (for Black) by territory scoring. I.e., whichever player resolves the position to an integer loses ½ pt. That is to say, if Black plays first with gote the result is N, while if White plays first with gote the result is N + 1. OC, the current Japanese rules do not recognize a board score that is not an integer, so will score it as N or N + 1, anyway. I constructed such a position many years ago, and Bernd Gramlich did too.

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A related simpler example for the Japanese 1989 Rules I showed again here in 2006: http://home.snafu.de/jasiek/mistakes.html

A player has to make a decision between a score (for a double ko seki) and the result "no result" (for a triple ko), which are incomparable so he cannot know which result is better. This is first of all a mistake of rules design rather than a matter of komi, although Antti's komi study is also interesting indeed.

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As long as the rules allow repetition, the players will need to weight it against other outcomes like B+6 etc, which will inevitably depend on komi AND on actual tournament rules, tournament standings and other possible factors.

Calling this a rules design mistake seems pointless, because even if some text expicitly declares that repetition must be treated exactly as jigo for example, the actual environment in which the game is played can override this anytime (mandating a rematch, treating it as 0.4 pts each etc.). So the choice will remain complicated.

It is a rules design mistake because rules of play can always provide a score as a result so that there need not be any tournament rules for exceptional results. Trivial example: superko.

Ah ok, that way you have a score, but don't have the same game (as played by most players and pros) anymore. Also that score comes at the cost of robbing players from freedom of legal moves. Imagine "fixing" chess like this.

Not the same game any more? Ok, every ca. 5,000th game is slightly different. But if that is your concern, Japanese 1989 Rules ought to be prohibited, e.g., because of dame preventing ordinary territory (relevant in each game).

More freedom of legal moves does not equate greater tactical/strategic complexity, which increases with superko compared to no-result, or decreases with Basic-Fixed-Ko-Rules compared to no-result. If maximum of tactical/strategic complexity were the concern, first of all dame must be valuable (relevant in every second game for greater tactical/strategic complexity for who gets the last dame and in every ca. 20th game for who wins the dame ko fight). Next, suicide would have to be allowed because it is slightly more frequent than strategically interesting long cycle ko fights.

Assume that positional super ko is used. There is a case in which, if white cannot win without komi, he can neither win with komi.

Matti, I believe you but can you please support your statement by theory or an example?

Have a molasses ko, which would decide the game. After a cycle in molasses ko a player must play tenuki. If he passes he would lose the ko. The game becames effectively no pass go. After finishing the yose the players continue inside the territories. The player who has less territory usually runs out of moves and has to pass and loses. One cannot play inside the komi. We assume that in this game there are no tesujis in the post yose stage.