Winner = first correct solution, or winner = best / highest-quality solution over what time period?

the most persuasive lie is the one you believe yourself

If someone really believes it, then I don't think they're operating in "bad faith". If the hidden motive is hidden to the speaker, that hiding doesn't come with intent.

It doesn't matter whether you said it was red because you were consciously lying or because you're wearing rose-colored glasses

It definitely matters. It completely changes how you should be trying to convince that person or behave around them.

It's different to believe a dumb argument than to intentionally lie, and honestly, humans are pretty social and honest. We mostly operate in good faith.

Agreed. LLMs will make mass surveillance (literature, but also phone calls, e-mails, etc) possible for the first time ever. And mass simulation of false public beliefs (fake comments online, etc). And yet Meta still thinks it's cool to open source all of this.

It's quite concerning. Given that we can't really roll back ML progress... Best case is probably just to make well designed encryption the standard. And vote/demonstrate where you can, of course.
 

I suppose one thing you could do here is pretend you can fit infinite rounds of the game into a finite time. Then Linda has a choice to make: she can either maximize expected wealth at $t_n$ for all finite $n$, or she can maximize expected wealth at $t_{\omega }$, the timestep immediately after all finite timesteps. We can wave our hands a lot and say that making her own bets would do the former and making Logan's bets would do the latter, though I don't endorse the way we're treating infinties here.

If one strategy is best for $t_n$, it's still going to be best at  $t_{\omega }$ as t goes to infinity. Optimal strategies don't just change like that as n goes to infinity. Sure you can argue that p(won every time) --> 0, but also that number is being multiplied by an extremely large infinity, so you can't just say that it totals to zero (in fact, 1.2, which is her EV from a single game, raised to infinity is infinity, so I argue as n goes to infinity, her EV goes to infinity, not 0, and not a number less than the EV from Logan's strategy). 

Linda's strategy is always optimal with respect to her own utility function, even as n goes to infinity. She's not acting irrationally or incorrectly here.

The one world where she has won wins her $2**n, and that world exists with probability 0.6**n.

Her EV is always ($2**n)*(0.6**n), which is a larger EV (with any n) than a strategy where she doesn't bet everything every single time. Even as n goes to infinity, and even as probability approaches 1 that she has lost everything, it's still rational for her to have that strategy because the $2**n that she won in that one world is so massive that it balances out her EV. Some infinities are much larger than others, and ratios don't just flip when a large n goes to infinity.

Yes, losing worlds also branch, of course. But the one world where she has won wins her $2**n, and that world exists with probability 0.6**n.

So her EV is always ($2**n)*(0.6**n), which is a larger EV (with any n) than a strategy where she doesn't bet everything every single time. I argue that even as n goes to infinity, and even as probability approaches one that she has lost everything, it's still rational for her to have that strategy because the $2**n that she won in that one world is so massive that it balances out her EV. Some infinities are much larger than others.

I don't think it's correct to say that as n gets large her strategy is actually worse than Logan's under her own utility function. I think hers is always best under her own utility function.

it seems like the vast majority of people don't make their lives primarily about delicious food

That's true. There are built-in decreasing marginal returns to eating massive quantities of delicious food (you get full), but we don't see a huge number of - for example - bulimics who are bulimic for the core purpose of being able to eat more.

However, I'd mention that yummy food is only one of many things that are brains are hard-wired to mesa-optimize for. Social acceptance and social status (particularly within the circles we care about, i.e. usually the circles we are likely to succeed in and get benefit from) are very big examples that much of our behavior can be ascribed to.

reward optimization might be a convergent secondary goal, it probably won't be the agent's primary motivation.

So I guess, reflecting this to humans, would you argue that most human's primary motivations aren't motivated mostly by various mesa-objectives our brains are hardwired to have? In my mind this is a hard sell, as most things humans do you can trace back (sometimes incorrectly, sure) to some thing that was evolutionary advantageous (mesa-objective that led to genetic fitness). The whole area of evolutionary biology specializes in coming up with (hard to prove and sometimes convoluted) explanations here relating to both our behavior and physiology.

For example, you could argue that us posting hopefully smart things here is giving our brains happy juice relating to social status / intelligence signaling / social interaction, which in our evolutionary history increased the probability that we would find high quality partners to make lots of high quality babies with. I guess, if mesa-objectives aren't the primary drivers of us humans - what is, and how can you be sure?

"I'll give you £1 now and you give me £2 in a week". Will she accept?

In the universe where she's allowed to make the 60/40 doubled bet at least once a week, it seems like she's always say yes? I'm not seeing the universe in which she'd say no, unless she's using a non-zero discount rate that wasn't discussed here.

| I'm not sure I've ever seen a treatment of utility functions that deals with this problem?

Isn't this just discount rates?

the way we're treating infinties here

Yeah, that seems key. Even if the probability that Linda will eventually get 0 money approaches 1, that small slice of probability in the universe where she has always won is approaching an infinity far larger that Logan's infinity as the number of games approaches infinity. Some infinities are bigger than others. Linear utility functions and discount rates of zero necessarily deal with lots of infinities, especially in simplified scenarios. 

Linda can always argue that in every universe where she lost everything, there's more (6 vs 4) universes where her winnings were double what they would have been had she not taken that bet.
 

Why, exactly, would the AI seize^[6] the button?

If it is a advanced AI, it may have learned to prefer more generalizable approaches and strategies. Perhaps it has learned the following features:

1. a feature that is triggered when the button is pressed ('reward')
2. a feature that is triggered when trash goes in the trash can
3. a feature that is triggered when it does something else useful, like clean windows

If you have trained it to take out the trash and clean windows, it will have been (mechanistically) trained to favor situations in which all three of these features occur. And if button pressing wasn't a viable strategy during training, it will favor actions that lead specifically to 2 and 3.

However, I do think it's conceivable that:

1. It could realize that feature 1 is more general than feature 2 or feature 3 (it was always selected for across multiple good actions, as opposed to taking out the trash, which was only selected for when that was the stated goal), and so it may therefore prefer it to be triggered over others (although I think this is extremely unlikely in less capable models).  This wouldn't cause it to stop 'liking' (I use this word loosely) window-cleaning, though.
2. It may realize that pressing the button itself pretty easy compared to cleaning windows and taking out the trash, so it will include pressing the button in one of it's action-strategies. Specifically, if this wasn't possible during training, I think this kind of behavior only becomes likely with very complex models with strong generalization capabilities (which is becoming more of a thing lately). However if it can try to press the button in addition to performing its other activities, it might as well, because it could increase overall expected reward. This seems more likely the more capable (good at generalizing) an AI is.

In reality (at least initially in the timeline of current AI --> superintelligent AI) I think if the button isn't pressable during training:

• Initially you have models that just learn to clean windows and take out trash and that's good.
• Then you might get models that are very good at generalizing and will clean windows and take out trash and also maybe try and press the button, because it uses its critical reasoning skills to do something in production that it couldn't do during training, but that its training made it think is a good mesa-optimization goal (button pressing). After all, why not take out trash, clean windows, and press the button? More expected reward! As you mention later on, this button-pressing is not a primary motivator / goal.
• Later on, you might get a more intelligent AI that has even more logical and world-aware reasoning behind its actions, and that AI might reason that perhaps since button-pressing is the one feature that it feels (because it was trained to feel this way) is always good, the thing it should care about most is pressing the button. And because it is so advanced and capable and good at generalizing to new situations, it feels confident in performing some actions that may even go against some of its own trained instincts (e.g. don't kill humans, or don't go in that room, or don't extra work, or - gasp - don't rank window-washing as your number one goal) in order to achieve that button-pressing goal. Maybe it achieves that goal and just has its robot hand constantly pressing the button. It will probably also continue to clean windows and remove trash with the rest of its robot body, because it continues to 'feel' that those are also good things.
• (Past that level of intelligence, I give up at predicting what will happen)

Anyways, I think there are lots of reasons to think that an AI might eventually try and press (or seize) the button. But I do totally agree that reward isn't this instant-wireheading feedback mechanism, and even when a model is 'aware' of the potentially to hack that reward (via button-pressing or similar), it is likely to prefer sticking to its more traditional actions and goals for a good long while, at least.