Yes, that's a valid point. This is precisely why I introduced the concept of a small, constant probability ?, representing the chance for the hostage ...
The analysis you provide would hold true if the hostage was guaranteed in advance to have exactly one opportunity to escape during the entirety of the...
The original Sleeping Beauty problem does indeed hinge on a single coin toss, but it's crucial to understand the unique nature of this coin toss withi...
It's worth noting that your provided sequence converges on 1/3. If the captive is not keeping track of the date, their credence should indeed be exact...
Yes, my first sentence was wrong. There is a new coin flip every day when the captor must decided on a new (or the same) safehouse. In the case where ...
Suppose you've been kidnapped. Each morning, your captor flips a coin. If it lands on heads, you're blindfolded and taken to safehouse #1 (or simply w...
Let us stick with the normal Sleeping Beauty scenario for now, if you don't mind, as I think the lessons drawn will generalize even to your extreme va...
Before the experiment begins, neither John Doe nor the sitter can rule out a possible future in which we are on Day2 of the experiment and John Doe re...
So, as they await the interviewer, John Doe and the sitter contemplate the probability that the coin landed tails. The coin might be right there on a ...
In that case, the probability that my chosen door contains a car remains 1/2. The probabilities that a car is behind door 3 or behind door 4 get updat...
The halfer and thirder responses, as you frame them here, correspond to different questions answered from different epistemic perspectives. Consider t...
Your variation of the problem indeed appears to me to contain elements reminiscent of the Monty Hall problem, but with a key difference in the selecti...
From the external point of view of the experimenter, it makes sense that the tree probabilities add up to more than one since the three outcomes are n...
I agree with the idea that Sleeping Beauty's credence in H is updated to 1/2 after she learns that her current awakening is occurring on a Monday. The...
I now realize that in the OP's stipulation of the problem, and in line with most discussions of it, it is when the fair coin lands tails that Sleeping...
I appreciate your viewpoint, but I can modify my analogies to meet the condition in your first scenario. Scenario 3 (Lottery study) Imagine that ticke...
For sure, but your new variation doesn't mirror the Sleeping Beauty problem anymore. You earlier version was better. We must rather imagine that in th...
She does recognize that for the coin to land 100 times in a row is unconditionally unlikely. But why would it not be rational for her to condition her...
I can easily adjust my lottery study example such that I am guaranteed to be selected but, once selected, the very (unconditionally) low event that le...
I'm not sure why you think this is absurd. Compare again my lottery study example. Suppose there are one billion people on the waiting list. If a coin...
There is a space of possible awakening/interview events A that are being characterised by the day in which they occur ((M)onday or (T)uesday) and by t...
One clue to this is to let SB bet on the outcome that her credence is about and see if her betting behavior leads her to realize the EV she is anticip...
I would rather say that the experience works by ensuring that Sleeping Beauty finds herself being awoken in circumstances that she knows to be twice a...
If you mean P(Awake) to refer to the probability of your being awakened at all (on at least one day) then P(Awake) is indeed 0.5. But in that case P(A...
But I'm not saying that. What I'm saying is that she is being awoken every Mondays and she is awoken half the time on Tuesdays. So, on average, on a r...
(I woke up early) P(Tuesday|Awoken) = (P(Awoken|Tuesday) / P(Awoken)) * P(Tuesday) Sleeping Beauty is awoken with probability 3/4 on an average day (M...
In the quoted post you say: "P(Awake|Heads) is just the prior probability that she will be woken up if the coin lands heads" I think my lottery study ...
This is not a probability. It's a ratio of probabilities that I have expressed as a ratio of corresponding frequencies. The updated probability P(Head...
It makes it twice as likely that individual bets are winning bets. Right? Likewise in Sleeping Beauty's problem, the fact that she is being awoken twi...
This is a follow-up to my previous post. In the case of Sue's selection to participate in the lottery study, we have P(Heads|Selected)=P(Selected|Head...
Wasn't that rather the Cinderella problem? You're inviting us to imagine ourselves in Sleeping Beauty's shoes to support the halfer position. However,...
In the Wikipedia article, the problem is set up thus: "Imagine you are given two identical envelopes, each containing money. One contains twice as muc...
If we assume that all results are equally likely, the EV of switching given that the chosen envelope was seen to contain n is (2n + n/2)/2 - n = 1.5n....
Your assertion that 'only two values are possible' for the contents of the envelopes in the two-envelope paradox deserves further exploration. If we c...
There is nothing there that I disagree with. But I don't think the paradox arises if the values of the two envelopes are stipulated in advance ($10 an...
Indeed, I concur that the paradox can also manifest when the option to switch envelopes is offered prior to opening the initially chosen one. The reso...
Unless you are subscribing to ChatGPT Plus (for $20 per month), it's GPT-3.5 you have access to. When you subscribe to ChatGPT Plus, you can then sele...
In my experience, GPT-3.5 is much more liable to make up references whenever there is any sort of gap in its knowledge. GPT-4 very seldom does so when...
My understanding and resolution of the paradox is somewhat aligned with this perspective. The paradox was first introduced to me about 30 years ago by...
In his paper, 'Truth and Rule Following', John Haugeland artfully fuses Kant's concept of 'synthetic a priori' and the phenomenological/existential id...
The nativist view posits that individuals are born either biological women or men, with the expectation that their gender expressions naturally align ...
Comments