sen

Karma: 171

sen Jul 13, 2020, 12:27 AM
8 points
on: What counts as defection?
I think your focus on payoffs is diluting your point. In all of your scenarios, the thing enabling a defection is the inability to view another player’s strategy before committing to a strategy. Perhaps you can simplify your definition to the following:
- “A defect is when someone (or some sub-coalition) benefits from violating their expected coalition strategy.”
You can define a function that assigns a strategy to every possible coalition. Given an expected coalition strategy C, if the payoff for any sub-coalition strategy SC is greater than their payoff in C, then the sub-coalition SC is incentivized to defect. (Whether that means SC joins a different coalition or forms their own is irrelevant.)
This makes a few things clear that are hidden in your formalization. Specifically:
- The main difference between this framing and the framing for Nash Equilibrium is the notion of an expected coalition strategy. Where there is an expected coalition strategy, one should aim to follow a “defection-proof” strategy. Where there is no expected coalition strategy, one should aim to follow a Nash Equilibrium strategy.
- Your Proposition 3 is false. You would need a variant that takes coalitions into account.
I believe all of your other theorems and propositions follow from the definition as well.
This has other benefits as well.
- It factors the payoff table into two tables that are easier to understand: coalition selection and coalition strategy selection.
- It’s better-aligned with intuition. Defection in the colloquial sense is when someone deserts “their” group (i.e., joins a new coalition in violation of the expectation). Coalition selection encodes that notion cleanly. The payoff tables for coalitions cleanly encodes the more generalized notion of “rational action” in scenarios where such defection is possible.

sen Jul 12, 2020, 12:40 AM
6 points
1
on: Lurking More Before Joining Complex Conversations
“That’s a good point, but I think you’re behind on some of the context on what we were discussing. Can you try to get more of a feel for the conversation before joining it?”
- It gives the person an understandable reason for their misstep. (“Sorry, I must have misunderstood what you were talking about.”)
- It gives the person a reason to stick around. (“I messed up. If I want to correct this, I need to listen and get more context.”)
- It adjusts the person’s behavior in future interactions. (“I should get a feel for the conversation before joining it to avoid messing up in the future.”)
- It’s no more aggressive than it needs to be to allow you to disregard what the person said and continue your conversation.
- What little aggression is there is reasoned and grounded in something easily understood, so it doesn’t come off as rude.
The above sounds better in text than it does in an actual conversation, but the same principles should apply in an actual conversation. “Name, hold on. I think you’re missing some context. Can you listen for a few minutes to catch up?”

sen Jul 8, 2017, 8:49 PM
0 points
in reply to: ChristianKl’s comment on: Epistemic Laws of Motion
I don’t see how your comment contradicts the part you quoted. More pressure doesn’t lead to more change (in strategy) if resistance increases as well. That’s consistent with what /u/SquirrelInHell stated.

sen Jul 8, 2017, 8:29 AM
0 points
on: Epistemic Laws of Motion
That mass corresponds to “resistance to change” seems fairly natural, as does the correspondence between “pressure to change” and impulse. The strange part seems to be the correspondence between “strategy” and velocity.″ Distance would be something like strategy * time.

Does a symmetry in time correspond to a conservation of energy? Is energy supposed to correspond to resistance? Maybe, though that’s a little hard to interpret, so it’s a little difficult to apply Lagrangian or Hamiltonian mechanics. The interpretation of energy is important. Without that, the interpretation of time is incomplete and possibly incoherent.

Is there an inverse correspondence between optimal certainty in resistance strategy (momentum) and optimal certainty in strategy time (distance)? I guess, so findings from quantum uncertainty principles and information geometry may apply.

Does strategy impact one’s perception of “distances” (strategy * time) and timescales? Maybe, so maybe findings from special relativity would apply. A universally-observable distance isn’t defined though, and that precludes a more coherent application of special/general relativity. Some universal observables should be stated. Other than the obvious objectivity benefits, this could help more clearly define relationships between variables of different dimensions. This one isn’t that important, but it would enable much more interesting uses of the theory.

sen Jul 5, 2017, 4:55 AM
0 points
on: The Unreasonable Effectiveness of Certain Questions
The process you went through is known in other contexts as decategorification. You attempted to reduce the level of abstraction, noticed a potential problem in doing so, and concluded that the more abstract notion was not as well-conceived as you imagined.

If you try to enumerate questions related to a topic (Evil), you will quickly find that you (1) repeatedly tread the same ground, (2) are often are unable to combine findings from multiple questions in useful ways, and (3) are often unable to identify questions worth answering, let alone a hierarchy that suggests which questions might be more worth answering than others.

What you are trying to identify are the properties and structure of evil. A property of Evil is a thing that must be preserved in order for Evil to be Evil. The structure of Evil is the relationship between Evil and other (Evil or non-Evil) entities.

You should start by trying to identify the shape of Evil by identifying its border, where things transition from Evil to non-Evil and vice versa. This will give you an indication of which properties are important. From there, you can start looking at how Evil relates to other things, especially in regards to its properties. This will give you some indication of its structure. Properties are important for identifying Evil clearly. Structure is important for identifying things that are equivalent to Evil in all ways that matter. It is often the case that the two are not the same.

If you want to understand this better, I recommend looking into category theory. The general process of identifying ambiguities, characterizing problems in the right way, applying prior knowledge, and gluing together findings into a coherent whole is fairly well-worn. You don’t have to start from scratch.

sen Jul 5, 2017, 12:08 AM
2 points
on: We need a better theory of happiness and suffering

“But hold up”, you say. “Maybe that’s true for special cases involving competing subagents, …”

I don’t see how the existence of subagents complicates things in any substantial way. If the existence of competing subagents is a hindrance to optimality, then one should aim to align or eliminate subagents. (Isn’t this one of the functions of meditation?) Obviously this isn’t always easy, but the goal is at least clear in this case.

It is nonsensical to treat animal welfare as a special case of happiness and suffering. This is because animal happiness and suffering can be only be understood through analogical reasoning, not through logical reasoning. A logical framework of welfare can only be derived through subjects capable of conveying results since results are subjective. The vast majority of animals, at least so far, cannot convey results, so we need to infer results on animals based on similarities between animal observables and human observables. Such inference is analogical and necessarily based entirely on human welfare.

If you want a theory of happiness and suffering in the intellectual sense (where physical pleasure and suffering are ignored), I suspect what you want is a theory of the ideals towards which people strive. For such an endeavor, I recommend looking into category theory, in which ideals are easily recognizable, and whose ideals seem to very closely (if not perfectly) align with intuitive notions.

sen Jul 2, 2017, 1:05 PM
0 points
in reply to: Adam Zerner’s comment on: Idea for LessWrong: Video Tutoring
I meant it as “This seems like a clear starting point.” You’re correct that I think it’s easy to not get lost with those two starting points.

I’m my experience with other fields, it’s easy to get frustrated and give up. Getting lost is quite a bit more rare. You’ll have to click through a hundred dense links to understand your first paper in machine learning, as with any other field. If you can trudge through that, you’ll be fine. If you can’t, you’ll at least know what to ask.

Also, are you not curious about how much initiative people have regarding the topics they want to learn?

sen Jul 2, 2017, 8:38 AM
0 points
on: Idea for LessWrong: Video Tutoring
A question for people asking for machine learning tutors: have you tried just reading through OpenAI blog posts and running the code examples they embed or link? Or going through the TensorFlow tutorials?

sen Jul 2, 2017, 1:12 AM
0 points
in reply to: username2’s comment on: Open thread, June 26 - July 2, 2017
Yes. I follow authors, I ask avid readers similar to me for recommendations, I observe best-of-category polls, I scan through collections of categorized stories for topics that interest me, I click through “Also Liked” and “Similar” links for stories I like. My backlog of things to read is effectively infinite.

sen Jul 2, 2017, 12:28 AM
1 point
in reply to: TezlaKoil’s comment on: What useless things did you understand recently?
I see. Thanks for the explanation.

sen Jul 1, 2017, 8:55 PM
0 points
in reply to: cousin_it’s comment on: What useless things did you understand recently?
How so? I thought removing the border on each negation was the right way.

I gave an example of where removing the border gives the wrong result. Are you asking why “A is a subset of Not Not A” is true in a Heyting algebra? I think the proof goes like this:
- (1) (a and not(a)) = 0
- (2) By #1, (a and not(a)) is a subset of 0
- (3) For all c,x,b, ((c and x) is a subset of b) = (c is a subset of (x implies b))
- (4) By #2 and #4, a is a subset of (not(a) implies 0)
- (5) For all c, not(c) = (c implies 0)
- (6) By #4 and #5, a is a subset of not(not(a))
Maybe your method is workable when you interpret a Heyting subset to be a topological superset? Then 1 is the initial (empty) set and 0 is the terminal set. That doesn’t work with intersections though. “A and Not A” must yield 0, but the intersection of two non-terminal sets cannot possibly yield a terminal set. The union can though, so I guess that means you’d have to represent And with a union. That still doesn’t work though because “Not A and Not Not A” must yield 0 in a Heyting algebra, but it’s missing the border of A in the topological method, so it again isn’t terminal.

I don’t see how the topological method is workable for this.

sen Jul 1, 2017, 7:48 AM
0 points
in reply to: cousin_it’s comment on: What useless things did you understand recently?
I guess today I’m learning about Heyting algebras too.

I don’t think that circle method works. “Not Not A” isn’t necessarily the same thing as “A” in a Heyting algebra, though your method suggests that they are the same. You can try to fix this by adding or removing the circle borders through negation operations, but even that yields inconsistent results. For example, if you add the border on each negation, “A or Not A” yields 1 under your method, though it should not in a Heyting algebra. If you remove the border on each negation “A is a subset of Not Not A” is false under your method, though it should yield true.

I think it’s easier to think of Heyting algebra in terms of functions and arguments. “A implies B” is a function that takes an argument of type A and produces an argument of type B. 0 is null. “A and B” is the set of arguments a,b where a is of type A and b is of type B. If null is in the argument list, then the whole argument list becomes null. “Not A” is a function that takes an argument of type A and produces 0. “Not Not A” can be thought of in two ways: (1) it takes an argument of type Not A and produces 0, or (2) it takes an argument of type [a function that takes an argument of type A and produces 0] and produces 0.

If “(A and B and C and …) → 0” then “A → (B → (C → … → 0))”. If you’ve worked with programming languages where lambda functions are common, it’s like taking a function of 2 arguments and turning it into a function of 1 argument by fixing one of the arguments.

I don’t see it on the Wikipedia page, but I’d guess that “A or B” means “(Not B implies A) and (Not A implies B)”.

If you don’t already, I highly recommend studying category theory. Most abstract mathematical concepts have simple definitions in category theory. The category theoretic definition of Heyting algebras on Wikipedia consists of 6 lines, and it’s enough to understand all of the above except the Or relation.

sen Jun 30, 2017, 8:12 AM
0 points
in reply to: cousin_it’s comment on: Kelly and the Beast
I am, and thanks for answering. Keep in mind that there are ways to make your intuition more reliable, if that’s a thing you want.

sen Jun 30, 2017, 7:40 AM
0 points
in reply to: cousin_it’s comment on: Kelly and the Beast
Fair enough. I have a question then. Do you personally agree with Bob?

sen Jun 30, 2017, 7:38 AM
0 points
in reply to: cousin_it’s comment on: Kelly and the Beast
Algebraic reasoning is independent of the number system used. If you are reasoning about utility functions in the abstract and if your reasoning does not make use of any properties of numbers, then it doesn’t matter what numbers you use. You’re not using any properties of finite numbers to define anything, so the fact of whether or not these numbers are finite is irrelevant.

sen Jun 30, 2017, 7:25 AM
0 points
in reply to: cousin_it’s comment on: Kelly and the Beast
The original post doesn’t require arbitrarily fine distinctions, just 2^trillion distinctions. That’s perfectly finite.

Your comment about Bob not assigning a high utility value to anything is equivalent to a comment stating that Bob’s utility function is bounded.

sen Jun 30, 2017, 7:01 AM
0 points
in reply to: cousin_it’s comment on: Kelly and the Beast
It can make sense to say that a utility function is bounded, but that implies certain other restrictions. For example, bounded utility functions cannot be decomposed into independent (additive or multiplicative, these are the only two options) subcomponents if the number of subcomponents is unknown. Any utility function that is summed or multiplied over an unknown number of independent (e.g.) societies must be unbounded*. Does that mean you believe that utility functions can’t be aggregated over independent societies or that no two societies can contribute independently to the utility function? That latter implies that a utility function cannot be determined without knowing about all societies, which would make the concept useless. Do you believe that utility functions can be aggregated at all beyond the individual level?
- Keep in mind that “unbounded” here means “arbitrarily additive”. In the multiplicative case, even if a utility function is always less than 1, if an individual’s utility can be made arbitrarily close to 0, then it’s still unbounded. Such an individual still has enough to gain by betting on a trillion coin tosses.
You mentioned that a utility function should be seen as a proxy to decision making. If decisions can be independent, then their contributions to the definition of a utility function must be independent*. If the utility function is bounded, then the number of independent decisions something can decide between must also be bounded. Maybe that makes sense for individuals since you distinguished a utility function as a summary of “current” decision-making, and any individual is presumably limited in their ability to decide between independent outcomes at any given point in time. Again, though, this causes problems for aggregate utility functions.
- Consider the functor F that takes any set of decisions (with inclusion maps between them) to the least-assuming utility function consistent with them. There exists a functor G that takes any utility function to the maximal set of decisions derivable from it. F,G together form a contravariant adjunction between set of decisions and utility functions. F is then left-adjoint to G. Therefore F preserves finite coproducts as finite products. Therefore for any disjoint union of decisions A,B, the least-assuming utility function defined over them exists and is F(A+B)=F(A)*F(B). The proof is nearly identical for covariant adjunctions.
It seems like nonsense to say that utility functions can’t be aggregated. A model of arbitrary decision making shouldn’t suddenly become impossible just because you’re trying to model, say, three individuals rather than one. The aggregate has preferential decision making just like the individual.

sen Jun 29, 2017, 5:34 PM
0 points
in reply to: MrMind’s comment on: Kelly and the Beast

Also it’s unclear to me what the connection is between this part and the second.

My bad, I did a poor job explaining that. The first part is about the problems of using generic words (evolution) with fuzzy decompositions (mates, predators, etc) to come to conclusions, which can often be incorrect. The second part is about decomposing those generic words into their implied structure, and matching that structure to problems in order to get a more reliable fit.

I don’t believe that “I don’t know” is a good answer, even if it’s often the correct one. People have vague intuitions regarding phenomena, and wouldn’t it be nice if they could apply those intuitions reliably? That requires a mapping from the intuition (evolution is responsible) to the problem, and the mapping can only be made reliable once the intuition has been properly decomposed into its implied structure, and even then, only if the mapping is based on the decomposition.

I started off by trying to explain all of that, but realized that there is far too much when starting from scratch. Maybe someday I’ll be able to write that post...

sen Jun 29, 2017, 5:25 PM
0 points
in reply to: MrMind’s comment on: Kelly and the Beast
The cell example is an example of evolution being used to justify contradictory phenomena. The exact same justification is used for two opposing conclusions. If you thought there was nothing wrong with those two examples being used as they were, then there is something wrong with your model. They literally use the exact same justification to come to opposing conclusions.

The second set of explanations have fewer, more reliably-determinable dependencies, and their reasoning is more generally applicable.

That is correct, they have zero prediction and compression power. I would argue that the same can be said of many cases where people misuse evolution as an explanation.

When people falsely pretend to have knowledge of some underlying structure or correlate, they are (1) lying and (2) increasing noise, which by various definition is negative information. When people use evolution as an explanation in cases where it does not align with the implications of evolution, they are doing so under a false pretense. My suggested approach (1) is honest and (2) conveys information about the lack of known underlying structure or correlate.

I don’t know what you mean by “sensible definition”. I have a model for that phrase, and yours doesn’t seem to align with mine.

sen Jun 29, 2017, 5:17 AM
1 point
in reply to: cousin_it’s comment on: Kelly and the Beast
Would your answer change if I let you flip the coin until you lost? Based on your reasoning, it should not. Despite it being an effectively-guaranteed extinction, the infinitesimal chance is overwhelmed by the gains in the case of infinitely many good coin flips.

I would not call the Kelly strategy risk-averse. I imagine that word to mean “grounded in a fantasy where risk is exaggerated”. I would call the second strategy risk-prone. The difference is that the Kelly strategy ends up being the better choice in realistic cases, whereas the second strategy ends up being the better choice in the extraordinarily rare wishful cases. In that sense, I see this question as one that differentiates people that prefer to make decisions grounded in reality from those that prefer to make decisions grounded in wishful thinking. The utilitarian approach then is prone to wishful thinking.

Still, I get your point. There may exist a low-chance scenario for which I would, with near certainty, trade the Kelly-heaven world for a second-hell world. To me, that means there exists a scenario that could lull me into gambling on wildly-improbable wishful thinking. Though such scenarios may exist, and though I may bet on such scenarios when presented with them, I don’t believe it’s reasonable to bet on them. I can’t tell if you literally believe that it’s reasonable to bet on such scenarios or if you’re imagining something wholly different from me.