Well, it was a given that it wasn't a linear equation, because ten minutes playing Devil Survivor can't yield one-fourth of a battle finished. I was fairly confident that it was a polynomial expression, however, since in matters like writing and reading eventually there's only so much you can take. Roleplaying is an activity that's definitely better than quadratic - if I spend two hours straight on it at the right time, my companions and may well get six dozen responses in, while distributing that activity randomly over three days is more likely to yield about a dozen responses. So I picked cubic. I haven't actually done any regression on it yet (it was midnight my time when I submitted this).
The Volunteer's Dilemma (http://en.wikipedia.org/wiki/Volunteer's_dilemma) is in essence the Prisoner's Dilemma with more players - which means that defection is an even more dominant strategy. The problem is that the decision whether to do unpleasant tasks becomes a Volunteer's Dilemma with multiple future selves as my competition
Ah, interesting; I was recently trying to think about procrastination in terms of defecting against your future self in an iterated Prisoner's Dilemma, but this makes more sense.
Of course the standard causal reasoning would say to defect (actually, if you have a sufficiently low estimate of the probability that anyone else will cooperate, I guess it would say to cooperate), but TDT-like reasoning should allow acausal coordination to get an average of one cooperator (or however many are needed). At a Bay Area LW meetup last year, I was in a discussion (well, mostly just listening to a discussion) about the Luring Lottery. Someone, I think it was Nick Tarleton, concluded that in a Luring Lottery of n TDT agents each trying to maximize its own winnings, assuming each one knows how many other players there are and that the others are also TDT agents, each would pseudorandomly choose with probability 1/n to submit one entry, or to submit zero otherwise. (I may be misremembering the details, but it was along those lines.) A similar strategy would probably apply in a Volunteer's Dilemma among TDT agents.
So perhaps we could reduce procrastination by taking TDT sufficiently seriously! If there's one situation that merits the assumption that multiple agents are strongly correlated (and/or can very reliably predict each other), it's where all the agents are slightly delayed versions of yourself. (That was the original context in which I was thinking about this; real-world results pending.)
And 8am tenshiko forms coalitions with 8:15am tenshiko to sleep just a bit longer, causing 9am tenshiko to curse the laziness of her sleeping peers.
Edit: Dang it! I was just thinking about gender pronouns like an hour before writing this, and I still did the default male!
If you don't know the gender, the polite thing to do is to use a gender-neutral pronoun like "they". In this case, it was readily apparent to me that it was a Japanese name with the feminine suffix "-ko", but your mileage may vary.
Thanks, I normally do that, more because it is cognitively easier than being polite. I honestly think it has more to do with my learning Spanish gender suffixes long ago, as this issue crops up in my daily life at times. If the word ends in 'o', I just gravitate to thinking of it as male.
I shall try to think of "-ko" as a feminine suffix. I'm looking at you, Kinko's.
I shall try to think of "-ko" as a feminine suffix. I'm looking at you, Kinko's.
Parsing it that way makes me think of "Kinko" as an incredibly cute name, especially if I interpret "kin" as a word - so "kinko" would mean something like "little female cousin" or "little sister" or something.
I'm obligated to point out the intrinsic risk of this way of thinking, as the uneducated can mistake the less common masculine suffix -hiko for a regular -ko. This is really the reason why romanization is such a travesty; none of this would have happened in beautiful kanji...
Fortunately 7:00am tenshiko is playing on a completely different team; the competition only really starts with 4:30 tenshiko, the first of the doubles to come home from school. To my frustration, 10:30 tenshiko, 10:45 tenshiko, and 11:00 tenshiko have now become regular players. I'm trying to figure out how to dissuade them, but they tell me that feeling tired in the morning is something I should blame on 7:00am tenshiko because teenagers are designed to go to bed at midnight and wake up at ten. (7:00am tenshiko has tried to defend herself with the allegation that waking up with an alarm clock is intrinsically less restful than waking up naturally, but nobody really cares.)
Don't sweat about it, although I have to say this is the first time that's actually happened to me personally on the Internet, sticking mostly to venues where there's a genre field or areas that are female-dominated, like FF.net and Livejournal.
The funny thing is that tenshiko is a distinctly feminine name in Moonspeak, meaning most literally heaven-messenger-child, more figuratively "angel girl" (the suffix for child is used in the modern era exclusively for girls). I figured if beizutsukai is thrown around here with its ridiculous claimed pronunciation of "beiztskai", I can justify using a trendily translated version of my name as an alias.
You could set a policy that a tenshiko at any particular time is allowed to obligate any of its successors to complete some action only if she has completed an action of similar magnitude assigned to her by a previous tenshiko. Like a Ponzi scheme. The pro: this gives each tenshiko-instance an incentive to complete the task. The con: the consequences of one tenshiko-instance defecting are high, since her successors will be released from pressure to complete tenshiko's long-term goals.
If you ignore the temporal aspect, I wonder if there is any connection to the http://en.wikipedia.org/wiki/Stag_hunt
No, this problem is completely different from the stag hunt. This is because any individual tenshiko would prefer to spend her time doing something else and will only regret her decision if she can't convince any of the later tenshikos to make up for her. A stag hunt would be deciding to participate in a high-reward extracurricular activity, like the drama club - if one tenshiko defects, there's a significant cost, but if everyone defected then at least there'd be a uniform gain among all selves of more free time.
This has been bothering me ever since I started trying to use rationalist techniques to make better decisions (like anti-akrasia ones). The only field related to rationality I knew much about was game theory, but to my disappointment basic game theory has only increased my problems due to a certain formulation I can't abandon.
The Volunteer's Dilemma (http://en.wikipedia.org/wiki/Volunteer's_dilemma) is in essence the Prisoner's Dilemma with more players - which means that defection is an even more dominant strategy. The problem is that the decision whether to do unpleasant tasks becomes a Volunteer's Dilemma with multiple future selves as my competition - 4:00 tenshiko, 4:15 tenshiko, 4:30 tenshiko, and so on. Although the incentive to defect should decrease as time goes on, there's the problem of how 9:00 tenshiko can easily defect in an even more effective fashion and bring in 11:00 tenshiko and 11:15 tenshiko to further level the playing field. There is the further problem that, given how many of my current hobbies convert time to reward in an approximately cubic function, the incentive is high for 6:00 tenshiko, 7:00 tenshiko, and 8:00 tenshiko to form coalitions.
I guess what I'm really asking for is a more advanced matrix that represents the diminishing returns of bringing in other future selves, such as went-to-bed-at-1:00 tenshiko and completely-bombed-that-test-at-10:00 tenshiko, or at least the diminishing probability over time that "it doesn't matter, 9:45 tenshiko can take care of it".
If this goes well, I will probably try to flesh out the material received in responses with what I already know and produce a post in main discussing time management and its relation to game theory.