Physicist and dabbler in writing fantasy/science fiction.
Other agents are not random though. Many agents act in predictable ways. I certainly don't model the actions of people as random noise. In this sense I don't think other agents are different from any other physical system that might be more-or-less chaotic, unpredictable or difficult to control.
I think you are underselling the networking advantages of cities.
Most people are eventually part of a couple or family. Most couples make compromises in terms of one or the other taking not-the-best position for their career because they want to live in the same area as their spouse. In a big city (my experience is London) their are enough jobs in enough industries close together that a typical couple can both usually pursue their ideal careers (or close) without being in different places.
Add into this that your job might change. If you live in Boeing town: population - high, employers - one, then you work at Boeing, and if you stop working at Boeing you move house and your children change schools etc. If you live in a big city and you are a career-ist you can do the whole "monkey bars" thing where you keep jumping between companies as you think you can do better, all without moving home every 2-3 years.
This sounds like the opening premise of a fun TV show or film.
UFO believer makes big bet with (for the sake of TV) one very rich person. Then heads out on an epic road trip in a camper van to find the alien evidence. A reporter covers the story and she starts travelling with him sending updates back to her paper. Obviously they fall for eachother.
They have various fun adventures where they keep encountering unconvincing evidence, or occasionally super-convincing evidence (UFO flys by) that they comically fail to catch on camera. Meanwhile the rich person on the other side of the bet becomes a villain, sending a hench-person to cut the tires on their van, get them in trouble with the police and generally obstruct the process.
Yes, my position did indeed shift, as you changed my mind and I thought about it in more depth. My original position was very much pro-Kelly. On thinking about your points I now think it is the while my_money > 0 aspect where the problem really lies. I still stand by the difference between optimal global policy and optimal action at each step distinction, because at each step the optimal policy (for Kelly or not) is to shake the dice another time. But, if this is taken as a policy we arrive at the while my_money > 0 break condition being the only escape, which is clearly a bad policy. (It guarantees that in any world we walk away, we walk away with nothing.)
I understand your point, and I think I am sort of convinced. But its the sort of thing where minor details in the model can change things quite a lot. For example, I am sort of assuming that Bob gets no utility at all from his money until he walks out of the casino with his winnings - IE having the money and still being in the casino is worth nothing to him, because he can't buy stuff with it. Where as you seem to be comparing Bob with his counter-factual at each round number - while I am only interested in Bob at the very end of the process, when he walks away with his winnings to get all that utility. But your proposed Bob never walks away from the table with any winnings. (Assuming no round limit). If he still has winnings he doesn't walk away.
Lets put details on the scenario in two slightly different ways. (1) the "casino" is just a computer script where Bob can program in a strategy (bet it all every time), and then just type in the number of rounds (N). (Or, for your version of Bob, put the whole thing in a "while my_money > 0:" loop.) We could alternatively (2) imagine that Bob is in the casino playing each round one at a time, and that the time taken doing 1 round is a fixed utility cost of some small number (say 0.1). This doesn't change anything for utility-maximising-Bob, and in fact the time costs for 1 more round relative to his expected gains shrink over time as his money doubles up. (later rounds are a better deal in expectation).
With these models I just see a system where Bob deterministically looses all his money. The longer he goes before going bust, the more of his time he wastes as well (in (2)).
Kelly betting doesn't actually fix my complaint. A Kelly betting Bob with no point at which they say "Yes, that is enough money, time to leave." actually gets minus infinity utility in model (2) where doing a round costs a small but finite amount of utility in terms of the time spent. Because the money acquired doesn't pay off till they leave, which they never do.
I think maybe you are right that it comes down to the utility function. Any agent (even the Kelly one) will behave in a way that comes across as obviously insane if we allow their utility function to go to infinity. Although I still don't quite see how that infinity actually ever enters in this specific case. If we answer the infinite utility function with an infinite number of possible rounds then we can say with certainty that Bob never walks away with any winnings.
Yes, I completely agree that the main reason in real life we would recommend against that strategy is that we instinctively (and usually correctly) feel that the person's utility function is sub-linear in money. So that the dollars with probability is bad. Obviously if dollars is needed to cure some disease that will otherwise kill them immediately that changes things.
But, their is an objection that I think runs somewhat separately to that, which is the round limit. If we are operating under an optimal, reasonable policy, then (outside commitment tactic negotiations) I think it shouldn't really be possible for a new outside constraint to improve our performance. Because if the constraint does improve performance then we could have adopted that constraint voluntarily and our policy was therefore not optimal. And the N-round limit is doing a fairly important job at improving Bob's performance in this hypothetical. Otherwise Bob's strategy is equivalent to "I bet everything, every time, until I loose it all." Perhaps this second objection is just the old one in a new disguise (any agent with a finitely-bounded utility function would eventually reach a round number where they decide "actually I have enough now", and thus restore my sense of what should be), but I am not sure that it is exactly the same.
The problem with maximising expected utility is that Bob will sit their playing 1 more round, then another 1 more round again and again until he eventually looses everything. Each step maximised the expected utility, but the policy overall guarantees zero utility with certainty, assuming Bob never runs out of time.
But, even as utility-maximising-Bob is saved from self-destruction by the clock, he shall think to himself "dam it! Out of time. That is really annoying, I want to keep doing this bet".
At least to me Kelly betting fits in the same kind of space as the Newcomb paradox and (possibly) the prisoners dilemma. They all demonstrate that the optimal policy is not necessarily given by a sequence of optimal actions at every step.
I think that the situation of someone spamming all the "bad" reactions on a post they don't like is the upvote system that already exists. If a post has a fair amount of karma and then copy of 10 different negative reacts might not mean much.
That last bit was a mistake on my part. My comment origionally said that "If you are for some reason operating under the constraint that you have to send the same text to them all (maybe posting on a forum they all, and others, read then." I tried shortening it and ended up with the current nonsense.
You make a convincing case that their are forces that encourage very rich people to congregate relatively close together, I don't think its the main force behind what is going on but I can see that it exist. Other forces also exist, like those I outlined above. Mine is not a productivity argument, and you could if you wanted even lump my suggestion under "there were other rich people there to network with" where "network" here means "marry" and "rich people" here means "people with a career, not a job."