On December 6, the Defendant and Co-Conspirator 2 called the Chairwoman of the Republican National Committee to ensure that the plan was in motion. During the call, CoConspirator 2 told the Chairwoman that it was important for the RNC to help the Defendant's Campaign gather electors in targeted states, and falsely represented to her that such electors' votes would be used only if ongoing litigation in one of the states changed the results in the Defendant's favor. After the RNC Chairwoman consulted the Campaign and heard that work on gathering electors was underway, she called and reported this information to the Defendant, who responded approvingly.

...

On [December 14], at the direction of the Defendant and Co-Conspirator 1, fraudulent
electors convened sham proceedings in the seven targeted states to cast fraudulent electoral ballots in favor of the Defendant. In some states, in order to satisfy legal requirements set forth for legitimate electors under state law, state officials were enlisted to provide the fraudulent electors access to state capitol buildings so that they could gather and vote there. In many cases, however, as Co-Conspirator 5 had predicted in the Fraudulent Elector Instructions, the fraudulent electors were unable to satisfy the legal requirements.

Nonetheless, as directed in the Fraudulent Elector Instructions, shortly after the fraudulent electors met on December 14, the targeted states' fraudulent elector certificates were mailed to the President of the Senate, the Archivist of the United States, and others. The Defendant and co-conspirators ultimately used the certificates of these fraudulent electors to deceitfully target the government function, and did so contrary to how fraudulent electors were told they would be used.

...

That evening, at 6:26 p.m., the RNC Chairwoman forwarded to the Defendant, through his executive assistant, an email titled, "Electors Recap - Final," which represented that in "Six Contested States"—Arizona, Georgia, Michigan, Nevada, Pennsylvania, and Wisconsin— the Defendant's electors had voted in parallel to Biden's electors. The Defendant's executive assistant responded, "It's in front of him!"

I'm not going to quote all 45 pages for you. Read it yourself. The above was simply an example of them having evidence of a criminal conspiracy of which Trump was a party.

What it’s doing is criminalizing Trump’s beliefs and his legal counsel, so now the first amendment is thrown under the bus. — NOS4A2

They're not criminalising his beliefs and legal counsel. His conspiracy to use fraudulent electors is a crime:

The Defendant and co-conspirators organized fraudulent slates of electors in seven targeted states ... attempting to mimic the procedures that the legitimate electors were supposed to follow under the Constitution and other federal and state laws. This included causing the fraudulent electors to meet on the day appointed by federal law on which legitimate electors were to gather and cast their votes; cast fraudulent votes for the Defendant; and sign certificates falsely representing that they were legitimate electors.

The claims that he did so knowingly and fraudulently are without evidence and therefor bullshit. — NOS4A2

Some of the evidence is described in the indictment. For example:

On December 13, the Defendant asked the Senior Campaign Advisor for an update on "what was going on" with the elector plan and directed him to "put out [a] statement on electors." As a result, Co-Conspirator 1 directed the Senior Campaign Advisor to join a conference call with him, Co-Conspirator 6, and others. When the Senior Campaign Advisor related these developments in text messages to the Deputy Campaign Manager, a Senior Advisor to the Defendant, and a Campaign staffer, the Deputy Campaign Manager responded, "Here's the thing the way this has morphed it's a crazy play so I don't know who wants to put their name on it." The Senior Advisor wrote, "Certifying illegal votes." In turn, the participants in the group text message refused to have a statement regarding electors attributed to their names because none of them could "stand by it."

The actual evidence itself will be presented at trial.

The Defendant's conspiracy to impair, obstruct, and defeat the federal government function through dishonesty, fraud, and deceit included the following manner and means:

a. The Defendant and co-conspirators used knowingly false claims of election fraud to get state legislators and election officials to subvert the legitimate election results and change electoral votes for the Defendant's opponent, Joseph R. Biden, Jr., to electoral votes for the Defendant. That is, on the pretext of baseless fraud claims, the Defendant pushed officials in certain states to ignore the popular vote; disenfranchise millions of voters; dismiss legitimate electors; and ultimately, cause the ascertainment of and voting by illegitimate electors in favor of the Defendant.

b. The Defendant and co-conspirators organized fraudulent slates of electors in seven targeted states (Arizona, Georgia, Michigan, Nevada, New Mexico, Pennsylvania, and Wisconsin), attempting to mimic the procedures that the legitimate electors were supposed to follow under the Constitution and other federal and state laws. This included causing the fraudulent electors to meet on the day appointed by federal law on which legitimate electors were to gather and cast their votes; cast fraudulent votes for the Defendant; and sign certificates falsely representing that they were legitimate electors. Some fraudulent electors were tricked into participating based on the understanding that their votes would be used only if the Defendant succeeded in outcome-determinative lawsuits within their state, which the Defendant never did. The Defendant and co-conspirators then caused these fraudulent electors to transmit their false certificates to the Vice President and other government officials to be counted at the certification proceeding on January 6.

c. The Defendant and co-conspirators attempted to use the power and authority of the Justice Department to conduct sham election crime investigations and to send a letter to the targeted states that falsely claimed that the Justice Department had identified significant concerns that may have impacted the election outcome; that sought to advance the Defendant's fraudulent elector plan by using the Justice Department's authority to falsely present the fraudulent electors as a valid alternative to the legitimate electors; and that urged, on behalf of the Justice Department, the targeted states' legislatures to convene to create the opportunity to choose the fraudulent electors over the legitimate electors.

d. The Defendant and co-conspirators attempted to enlist the Vice President to use his ceremonial role at the January 6 certification proceeding to fraudulently alter the election results. First, using knowingly false claims of election fraud, the Defendant and co-conspirators attempted to convince the Vice President to use the Defendant's fraudulent electors, reject legitimate electoral votes, or send legitimate electoral votes to state legislatures for review rather than counting them. When that failed, on the morning of January 6, the Defendant and co-conspirators repeated knowingly false claims of election fraud to gathered supporters, falsely told them that the Vice President had the authority to and might alter the election results, and directed them to the Capitol to obstruct the certification proceeding and exert pressure on the Vice President to take the fraudulent actions he had previously refused.

e. After it became public on the afternoon of January 6 that the Vice President would not fraudulently alter the election results, a large and angry crowd— including many individuals whom the Defendant had deceived into believing the Vice President could and might change the election results— violently attacked the Capitol and halted the proceeding. As violence ensued, the Defendant and co-conspirators exploited the disruption by redoubling efforts to levy false claims of election fraud and convince Members of Congress to further delay the certification based on those claims.

Are you saying that he didn't do these things or that these things aren't crimes?

Now we’re on the road to criminalizing political speech because a man dared to doubt the results of an election. — NOS4A2

These are the actual laws he's alleged to have broken:

18 U.S. Code § 371 - Conspiracy to defraud the United States

18 U.S. Code § 1512(k) - Conspiracy to obstruct an official proceeding

18 U.S. Code § 1512(c)(2) - Obstruction of and attempt to obstruct an official proceeding

18 U.S. Code § 241 - Conspiracy against rights

He's not being prosecuted for doubting the results of the election. He's being prosecuted for conspiring to overturn the results of the election.

To quote Bill Barr from here:

"As the indictment says, they're not attacking his First Amendment right. He can say whatever he wants. He can even lie. He can even tell people that the election was stolen when he knew better.

"But that does not protect you from entering into a conspiracy," he added. "All conspiracies involve speech, and all fraud involves speech. Free speech doesn't give you the right to engage in a fraudulent conspiracy."

You, like Smith, are trying to read Trump’s mind. You in fact do not know that he knowingly made false claims. You know you don’t know because you in fact cannot read minds. — NOS4A2

You do not know that Relativist does not know that Trump knowingly made false claims. You know you don't know because you in fact cannot read minds.

More fake word crimes — NOS4A2

What does this mean? That he didn’t commit the crimes he’s been indicted for or that the criminal statutes cited in the indictment don’t exist?

Indictment

Conspiracy to Defraud the United States
Conspiracy to Obstruct an Official Proceeding
Obstruction of and Attempt to Obstruct an Official Proceeding
Conspiracy Against Rights

Whereas https://www.nytimes.com/2023/06/15/us/politics/trump-indictment-justice-department.html

When Donald J. Trump responded to his latest indictment by promising to appoint a special prosecutor if he’s re-elected to “go after” President Biden and his family, he signaled that a second Trump term would fully jettison the post-Watergate norm of Justice Department independence.

“I will appoint a real special prosecutor to go after the most corrupt president in the history of the United States of America, Joe Biden, and the entire Biden crime family,” Mr. Trump said at his golf club in Bedminster, N.J., on Tuesday night after his arraignment earlier that day in Miami. “I will totally obliterate the Deep State.”

Such a hypocrite.

It will be interesting to see what this latest indictment is for. — NOS4A2

https://www.nbcnews.com/politics/donald-trump/special-counsels-target-letter-trump-2020-election-probe-cites-three-f-rcna95096

The letter that former President Donald Trump received from special counsel Jack Smith informing him that he is a target of the federal investigation into efforts to overturn the 2020 presidential election mentions three federal statutes related to the deprivation of rights, conspiracy to defraud the U.S., and tampering with a witness.

This indictement is the Big One. All the others are serious, for sure, but even being charged with attempting to prevent the transition of power must be seen as enormously consequential. I mean, really, how could someone under indictment for trying to subvert the Presidential election realistically run for President? 2024 is going to be one hell of a year in US politics. — Wayfarer

I'd say Georgia is more important. If Trump wins the next election then he's obviously going to pardon himself. Or if another Republican wins then they might pardon him.

Trump says he expects indictment in 2020 election probe

Former US President Donald Trump has said he expects to be arrested by a federal investigation into the January 6 riot at the Capitol and efforts to challenge the results of the 2020 election.

...

In a post on his Truth Social platform, Mr Trump claimed that he had been sent a letter "stating that I am a TARGET of the January 6th Grand Jury investigation, and giving me a very short 4 days to report to the Grand Jury, which almost always means an Arrest and Indictment."

So the case consists of an accusation by an unknown source, of unknown reliability. Fox News has reported:

“Sources said the Burisma executive appears to be at a "very, very high level" of the company. One source familiar suggested the confidential source could be referring to the head of Burisma, Mykola Zlochevsky, but said the name of the Burisma executive is redacted in the document.” — Relativist

GOP had evidence disproving Biden bribery claims in 2019, top Democrat says

But according to a transcript of an interview with Mr Zlochevsky which Giuliani associate Lev Parnas provided to Congress during the first impeachment of Mr Trump, the Burisma founder said years ago that his company never had any contact with the elder Mr Biden.

In his letter, Mr Raskin wrote that the Ukrainian executive “explicitly and unequivocally denied” the allegations of bribery. He said Mr Zlochevsky also “denied (1) that anyone at Burisma had “any contacts” with then former Vice President Biden or his representatives while Hunter Biden served on the Burisma board, and (2) that former Vice President Biden or his staff “in any way” assisted Mr. Zlochevsky or Burisma”.

‘Whistleblower’ who accused Bidens of corruption is charged with arms trafficking and violating Iran sanctions

A “whistleblower” who has repeatedly accused the Bidens of corruption has been charged by the Justice Department with arms trafficking, acting as a foreign agent for China and violating Iran sanctions.

Gal Luft, who is a citizen of both the United States and Israel, is accused of paying a former adviser to Donald Trump on behalf of principals in China in 2016 without registering as a foreign agent.

Prosecutors say that Mr Luft pushed the former government employee, who is not named, to push policies that were favourable to China.

They also allege that he set up meetings between officials of Iran and a Chinese energy company to discuss oil deals, which would violate US sanctions.

They also alleged that Mr Luft “conspired with others and attempted to broker illicit arms transactions with, among others, certain Chinese individuals and entities” by working as a middleman to find both buyers and sellers for “certain weapons and other materials” in violation of the US Arms Control Act.

Clearly this is just Biden getting revenge.

I appreciate the reply but I’ve run out of motivation and am going to end my involvement with this. I wouldn’t change my bet, so I’m a committed halfer. I don’t think any number of analogies are going to convince me to change my bet in that specific case.

If a die rolls a 6 then Sleeping Beauty is woken six times otherwise she is woken once. When woken what is her credence that the die rolled a 6?

Halfers have to say $1\over6$ and thirders have to say $6\over11$.

Before she is first put to sleep she is to bet on whether or not the die will roll a 6 – paid out at the end of the experiment – and each time she is woken she is allowed to change her bet.

If she bets according to her credence then both halfers and thirders have to say that before she is first put to sleep she will bet that the die will not roll a 6.

Thirders then have to say that when woken she will change her bet and bet that the die did roll a 6.

Are thirders willing to commit to their position and change their bet?

No, the prior probability that she will be woken on Tuesday, and the coin landed Heads, is 1/4. — JeffJo

The rules of the experiment say that she won’t be woken on Tuesday if the coin lands heads. That means that the prior probability that she will be woken on Tuesday and the coin lands heads is 0.

P(Heads, woken on Tuesday) = P(Heads) × P(woken on Tuesday|Heads) = 1/2 × 0 = 0.

Just look at how you calculated the probability of waking up in my experiment. It’s the same reasoning.

On each day in the range 1 to N, the prior probability that she will be woken on that day AND the coin landed on Heads is 1/N. — JeffJo

Pr(Heads & Day = D) = 1/2 * 1/N.

That aside, using your above reasoning, in the normal problem the prior probability that she will be woken on Tuesday and the coin landed on Heads is 0, and the prior probability that she will be woken on Monday and the coin landed on Heads is 1/2.

So when she "rules out" Pr(Heads & Day = Tuesday) she's "ruling out" some Pr = 0, not some Pr = 1/4. "Ruling out" some Pr = 0 after waking does nothing because it was already "ruled out".

Your claim that "The next enclosure is the toucan enclosure iff I first turned right at the fork (P = 1/2) and then passed the tiger enclosure," is an assumption that can't be put forward without begging the question against the Thirder. You need to substantiate, rather than presuppose, that when you're nearing an enclosure, there's a 1/2 chance the path you're on is a T-path. — Pierre-Normand

My wording may have been imprecise.

Both of these are true (note the tense):

1. To reach the toucon enclosure I must first turn right at the fork and then pass the tiger enclosure
2. The probability that I will turn right at the fork is $1\over2$

When I wake and consider my credence that the next enclosure is the toucon enclosure I consider what must have happened (or not happened) for the next enclosure to be the toucon enclosure. I know that I must have first turned right at the fork (A) and then passed the tiger enclosure (B).

P(A, B) = P(A) × P(B|A)

My claim is that the probability of having turned right at the fork is equal to the probability of turning right at the fork, i.e. $1\over2$.

Your claim is that the probability of having turned right at the fork is equal to the fraction of all encountered enclosures which are right-side enclosures, i.e. $2\over3$.

I don't think your claim makes any sense. The probability of the first event having happened isn't determined by what could happen after that first event happens. The probability of the first event having happened is determined only by the probability of that first event happening.¹

Your conclusion only applies if I'm dropped into an enclosure at random, perhaps via parachute. This is your so-called "episodic perspective" (where it’s not the case that I turned right at the fork; it’s only the case that I’m on the right-side path). But given that this isn't what happens to me, I shouldn't reason this way.

¹ _{Where no new relevant information is learned.}

I’m only considering one fork as only that is comparable to the Sleeping Beauty problem. What’s true of multiple forks isn’t true of one fork, as evidenced by (1):

1. The next enclosure is the toucon enclosure iff I first turned right at the fork (P = $1\over2$) and then passed the tiger enclosure.

This is only true if there is one fork.

So what is wrong about my analysis of one fork?

1. Conditionally on its being a first encounter on a path segment, P(Tiger) = P(Hippo)
2. Conditionally on Leonard being on a T-path segment, P(Tiger) = P(Toucan)
3. The three possible outcomes are exhaustive and mutually exclusive
4. Therefore, P(Tiger) = P(Hippo) = P(Toucan) = 1/3 — Pierre-Normand

As it stands your conclusion is a non sequitur. You need to justify this inference:

P(Hippo|Hippo or Tiger) = P(Tiger|Hippo or Tiger)
Therefore P(Hippo) = P(Tiger)

I just need you to agree that it is equivalent to your procedure first. — JeffJo

It's not. You say:

"If the coin landed on Heads, then an N-sided die is rolled, where N>=2. She is woken on day D1 - that is, D1 days after day 0 - where D1 is the result of this roll, and asked her credence. Then she is put back to sleep."

In my example she isn't put back to sleep. The experiment just ends. The same with her second tails interview. So we have no idea how many days the experiment will last. It could be anywhere between 1 and N days.

Something is indeed is ruled out when she wakes. — JeffJo

What is ruled out?

Now, let's look at a particular moment of Leonard's visit. As he walks, before reaching a new enclosure, he might reason this way: "Since each fork in the path gives an equal chance of leading to a T-path or an H-path, there is a 50% chance that the next enclosure I'll see will have a hippo." Thus, when he approaches an enclosure, he might conclude there is a 25% chance of it being a tiger enclosure, and a 25% chance of it being a toucan enclosure.

Is this reasoning accurate? — Pierre-Normand

1. The next enclosure is the toucon enclosure iff I first turned right at the fork (P = $1\over2$) and then passed the tiger enclosure.

2. My credence that the next enclosure is the toucon enclosure is equal to the probability that the first event happened multiplied by the probability that the second (dependent) event happened.

Having amnesia is no excuse to reject (2). Even with amnesia I know that (1) is true.

If my credence that the next enclosure is the toucon enclosure is $1\over3$ then the probability that I passed the tiger enclosure, if I turned right at the fork, is $2\over3$, but then my credence that the next enclosure is the tiger enclosure is $1\over6$.

If the probability that I passed the tiger enclosure, if I turned right at the fork, is $1\over2$, then my credence that the next enclosure is the toucon enclosure is $1\over4$ (as is my credence that the next enclosure is the tiger enclosure).

Either way my credence that the next enclosure is the hippo enclosure is $1\over2$.

From the episodic perspective, Sleeping Beauty knows that conditionally on her present awakening being the first, it is equally probable that it is a H-awakening (and that the coin will land heads) or that it is a T-first-awakening (and that the coin will land tails). She also knows that in the event the coin will land (or has landed) tails, it is equiprobable that she is experiencing a T-first-awakening or a T-second awakening. Since the three possible outcomes are exclusive from her episodic perspective, their probabilities must sum up to 1 and since P(H-awakening) = P(T-first-awakening) and P(T-first-awakening) = P(T-second awakening), all three possible outcomes must have probability 1/3. — Pierre-Normand

This appears to be repeating Elga's argument:

P(T₁|T₁ or T₂) = P(T₂|T₁ or T₂)
∴ P(T₁) = P(T₂)

P(H₁|H₁ or T₁) = P(T₁|H₁ or T₁)
∴ P(H₁) = P(T₁)

∴ P(H₁) = P(T₁) = P(T₂)

Those first two inferences need to be justified.

And again, you keep using circular logic. You deny that events with non-zero prior probability are "ruled out" in your solution. So you claim that my solution, which does "rule out," must be wrong. This is a fallacy; your presumption that you are right is your only defense. You have never argued for why you think they aren't events. — JeffJo

I can't prove a negative. If there is some prior probability that is ruled out when woken then tell me what it is.

If you can’t then I have every reason to accept that there isn’t one.

It's precisely because they mean different things that I've provided detailed arguments for deducing 1 from 2 (alongside with other premises). However, the truth of 2 certainly is relevant to the deduction of 1. Nobody would be a Thirder in a scenario where coins lading tails would generate as many awakenings as coins landing heads. — Pierre-Normand

If they mean different things then 4 and 5 are neither definitions nor true by definition, and given that 1, 2, and 3 are true (and that "the degree to which I believe that" means the same thing in 4 and 5), one or both of 4 and 5 are false.

The degree to which I believe that my current interview is my only interview is equal to the degree to which I believe that I have been assigned only one interview.

These mean two different things:

1. My credence favours this being a tails awakening rather than a heads awakening
2. There are more tails awakenings than heads awakenings

You can argue that 1 is true because I believe that 2 is true, but then my argument above shows that this is unreasonable.

The fraction of awakenings which are tails awakenings is the wrong fraction to base one’s credence that this is a tails awakening on.

This overlooks the issue that your credence can change over time when your epistemic perspective changes. — Pierre-Normand

It doesn’t. If my credence in A changes then my credence in B will change along with it (or my credence in A iff B will change).

4 and 5 aren't true by definition; rather, they are definitions. — Pierre-Normand

I have since changed the wording (although it makes no difference, this wording is just more exact).

4. The degree to which I believe that my current interview is a heads interview is equal to the fraction of interviews which are heads interviews
5. The degree to which I believe that I have been assigned one heads interview is equal to the fraction of experiments which have one heads interview

These are neither definitions nor true by definition.

One or both must be false given 1, 2, or 3.

When I previously addressed this inference of yours, I conceded that it is generally valid, but I also pointed out that it involved a possible conflation of two meanings of the predicate P(). The problem I identified wasn't with the validity of the inference (within the context of probability calculus), but rather with the conflation that could occur when the expression P(A) appears twice in your demonstration. — Pierre-Normand

There is only one meaning I'm using: "the degree to which I believe that the proposition is true". It's stated as much in P1.

If I am certain that A is true if and only if B is true then the degree to which I believe that A is true is equal to the degree to which I believe that B is true. This is true for all As and Bs.

It isn't rational for me to believe more strongly in one side of a biconditional that I am certain is true.

What makes you "pretty sure" that A is true is the expectation that A is much more likely to occur than not-A. As such, this probabilistic judgment is implicitly comparative. It is therefore dependent on how you individuate and count not only A events but also not-A events. As I've argued elsewhere, a shift in epistemic perspective can alter the way you count not-Heads events (i.e., Tails events), transforming them from non-exclusive to exclusive. For example, when you move from considering possible world timelines to specific awakening episodes, what were concurrent alternatives (not-H events) become exclusive possibilities. This change in perspective modifies the content of your comparative judgment "H is much more likely to occur than not-H," and consequently affects your credence. — Pierre-Normand

Given the above meaning, and as I said before, these cannot all be true:

1. My current interview is a heads interview iff I have been assigned one heads interview
2. The fraction of interviews which are heads interviews is $1\over3$
3. The fraction of experiments which have one heads interview is $1\over2$
4. The degree to which I believe that my current interview is a heads interview is equal to the fraction of interviews which are heads interviews
5. The degree to which I believe that I have been assigned one heads interview is equal to the fraction of experiments which have one heads interview

You seem to assert that 4 and 5 are true by definition, but they're not. Given the truth of 1, 2, and 3, it must be that one or both of 4 and 5 is false.

Your propositions P1 through P4 and C1 though C4 above frequently shift between those two perspectives, which vitiates the validity of some inferences. — Pierre-Normand

So which premises are false or which conclusions do not follow?

Therefore, when shifting to the episodic perspective, it would be a mistake is to divide the probability of the T-timeline (1/2) between the two T-awakenings, suggesting each has a probability of 1/4. This line of thinking presumes these awakenings to be exclusive events within the T-timeline — Pierre-Normand

My current interview being the first or the second T-awakening are exclusive events.

But I brought up something like this here:

1. Sleeping Beauty is given amnesia
2. She is asked her credence that a coin has been tossed
3. A coin is tossed
4. If the coin lands tails then:
4A. She is given amnesia
4B. She is asked her credence that a coin has been tossed

Thirder reasoning is that because step 2 is twice as likely to occur as step 4B then I am twice as likely to be in step 2 as step 4B.

Halfer reasoning is that because step 2 is twice as likely to occur as step 4B and that because if 4B will occur then I am equally likely to be in step 2 as step 4B then I am three times as likely to be in step 2 as step 4B.

I agree, with a caveat. The specific details of whether she is woken at a specific point ("day") in the experiment do matter. You can test this in Elga's solution. If she is told that the current day is Tuesday, then she knows Pr(Heads) must decrease to 0. If she is told that it is not Tuesday, the Law of Total Probability actually requires it to go up. It goes from 1/3 to 1/2 in the Thirder soluton, and from 1/2 to 2/3 in the Halfer solution. This is quite relevant, even if you think it is wrong AND CAN PROVIDE A VALID REASON

But it isn't the day name that matters, it is the details associated with that day name. And since these details are different on different "days," we can track them by naming the "days."

Now, you could argue about why those details might matter; but so far you have refused to. You have just asserted they don't (in spite of evidence like I just presented). But naming them cannot affect the correct answer, no matter how those details affect it. SO THERE IS NO REASON TO NOT NAME THE "DAYS." And even the possibility that they might have an effect makes them relevant.

In other words, you are proffering the red herring here. You are insisting that we must ignore a piece of potential information, because you think it has no affect. If so, there is no harm in including it. — JeffJo

When I said that the only things that matter are:

1. She has either one or two interviews determined by a fair coin toss and
2. She doesn’t know if she’s already had one

I was referring to her just waking up, not being told any further information.

If she's told that the coin landed tails then 1 is no longer relevant and she just considers 2. If she's told that this is now her first interview then 2 is no longer relevant and she just considers 1.

And I don't see why having to consider 2 affects her consideration of 1. Knowing or not knowing that this is now her first interview only affects her credence that this is now her first interview. It doesn't affect her credence that she will have two interviews.

This procedure creates what, in your words, are "the only things that matters." She has either one, or two, interviews and does not know if another will/did happen. The only thing that is different, is that your possible two interviews occur under different circumstances; one is mandatory, and one is optional. What we disagree about is whether the part that is missing - the non-interview when the option is not taken - matters.

Here they occur under identical circumstances. That is, either steps 2.1 thru 2.4, or steps 3.1 thru 3.4. And those circumstances can be used to answer the question. I did "name" the details by calling them state S1 or S2, but since they are identical to SB she can call them state S.

There are three possible combinations of the two coins in state S, and they are equally likely. Her credence in state S=(H,T) is 1/3.

This has nothing to do with what may or may not get "ruled out" in a solution to your version of the experiment. That difference is the red herring in the "most frequent" presentation of the problem. This is a self-contained experiment with a trivial answer.

But it's an answer you don't like. So you will either ignore it, or repeat the non sequitur that it includes the "ruling out of a 1/4 probability" that we are debating about above, which is circular logic. — JeffJo

In this example when woken she rules out the prior probability HH = $1\over4$.

No prior probability is ruled out here when woken so your example isn't equivalent.

The answer follows trivially from what I have said before - have you read it? — JeffJo

Nothing in your above post tells me what prior probability is ruled out when she's woken in this experiment.

In your experiment the prior probability HH = $1\over4$ is ruled out when woken.

If you cannot tell me what prior probability is ruled out when woken in my experiment then I have no reason to accept that your experiment is at all equivalent.

So tell me what prior probability is ruled out in my experiment above.

If there isn't one then there isn't one in the ordinary experiment either. You may have other reasons for believing that the answer to the problem is $1\over3$, but those reasons can't be that some prior probability of $1\over4$ is ruled out when woken.

While in each case the biconditionals "I am now in an H-awakening iff I am now (and will be) in an H-run" or (on Wednesday) "I was in an H-awakening iff I am now in an H-run" hold, the probabilities don't necessarily match due to the two-to-one mapping between T-awakenings and T-runs. — Pierre-Normand

I know I referred you to one of my previous posts, but I’ll respond to this directly too.

We’re discussing credence.

If I am certain that A is true if and only if B is true and if I am pretty sure that A is true then ipso facto I am pretty sure that B is true.

Given the biconditional one’s credence in the left hand side must match one’s credence in the right hand side, even if there is this “two-to-one mapping”.

I am certain that my hand is one of two hands I have if and only if I have two hands.

I am pretty sure that my hand is one of two hands I have.

Therefore I am pretty sure that I have two hands.

It doesn’t make sense to say that you’re pretty sure (P = 2/3) that your current interview is one of two but that you’re on the fence (P = 1/2) as to whether or not you have been assigned two interviews.

Either you are pretty sure that you have been assigned two interviews or you are on the fence as to whether or not your current interview is one of two.

But the time period after the coin is flipped still exists, and the coin can be Heads during that time. — JeffJo

She is put to sleep on day 0.

If the coin lands heads then a 14-sided dice is rolled. She is woken that many days later and asked her credence.

If the coin lands tails then a 7-sided dice is rolled. She is woken that many days later, asked her credence, and put back to sleep. The dice is rolled again. She is woken that many days later and asked her credence.

Whether heads or tails she can wake on any day between 1 and 14 days after she is first put to sleep.

Nothing is ruled out when she wakes. She doesn't rule out heads and day 1, she doesn't rule out heads and day 2, ... and she doesn't rule out heads and day 14.

The specific days she’s woken or kept asleep are irrelevant. The only things that matter are that she has either one or two interviews – determined by a fair coin toss – and that she doesn’t know if she’s already had one. Everything else is a red herring.

Since I now know that I will soon rationally infer that this note was written during an H-awakening with probability 1/3 (on the basis of no new information), I can already infer this right now. — Pierre-Normand

Then before the experiment starts the thirder will say "since I now know that I will soon rationally infer that the coin will have landed heads with probability 1/3 (on the basis of no new information), I can already infer this right now, before the coin is tossed."

But I think this is wrong.

Making n large makes Sleeping Beauty's epistemic situation on Wednesday, when she receives a note, nearly identical to her situation when she wrote the note, since the Bayesian updating she can perform on the basis of the note being unique is negligible. — Pierre-Normand

They're not nearly identical. On Wednesday she knows that she only had the opportunity once. When she wrote the note she didn't know that it was her only opportunity. So contrary to the above, there is new information on Wednesday.

Note that when Sleeping Beauty doesn't receive a note on Wednesday, her credence P(H) = 1/2 doesn't merely differ in value from her credence P(H) = 1/3 during awakenings; the predicates P() also have different meanings. During awakenings, P(H) refers to the odds that her current awakening episode is occurring during a coin toss that landed heads. On Wednesday, P(H) refers to the odds that the experimental run she is exiting from was an H-run. While in each case the biconditionals "I am now in an H-awakening iff I am now (and will be) in an H-run" or (on Wednesday) "I was in an H-awakening iff I am now in an H-run" hold, the probabilities don't necessarily match due to the two-to-one mapping between T-awakenings and T-runs. — Pierre-Normand

I address this here.

the prior probability for any event is based set of all possibilities that could occur — JeffJo

And her being woken a second time if the coin lands heads can't occur, which is why its prior probability is 0, not $1\over4$.

And that is important here, because you are insisting that a two-day collection of events (I'll call your two passes Monday and Tuesday since only the order matters to anything). You are calling Monday+Tails and Tuesday+Tails the same event. But to SB, who can only observe one at a time, they are distinct events that each have half the prior probability that you assign to the combination. — JeffJo

There aren't two days in my example.

When I will read again the note that I am currently writing, on Wednesday, I will be able to rationally infer that it is twice as likely that this note was written by me on the occasion of a T-awakening. — Pierre-Normand

That depends on the probability that you will be given the opportunity to write a note. If that probability is 1/2 then it won't be rational on Wednesday to infer that it is twice as likely that this note was written by me on the occasion of a T-awakening.

That was only in the specific case where n = 2. As n grows larger, P(H) tends towards 1/3. — Pierre-Normand

And as it grows smaller, P(H) tends to 1. I don't understand the relevance of any of these three answers.

Why is the correct answer given by any of these situations, let alone by the situation where n is arbitrarily large?

Yes, I got the maths wrong there (and deleted my post before you replied; apologies).

Though I don't see why I should accept your claim that if "she receives a single note on Wednesday, Sleeping Beauty comes to be causally and epistemically related to the coin result in the exact same manner as she was when she originally wrote the note."

As you said yourself, if the probability of her writing a note is 1/2 then if she finds exactly one note on Wednesday then her credence in Heads is 1/2.

As the occasions to write a note become rarer (e.g. 1/n with n >> 1), the frequency of those overlapping notes become negligible (n times as many single notes are received as double notes) and Sleeping Beauty's epistemic state (i.e. the value of her credence) approaches asymptotically her epistemic state as she was writing the note. And, as I had suggested in my previous post, this is because when she receives a single note on Wednesday, Sleeping Beauty comes to be causally and epistemically related to the coin result in the exact same manner as she was when she originally wrote the note. — Pierre-Normand

If heads and n = 100 then the probability of writing a note is 1/100

If tails and n = 100 then the probability of writing exactly one note is 1/100.

So if she finds exactly one note on Wednesday then her credence in heads is 1/2.

@Pierre-Normand

These cannot all be true:

1. Credence "is a statistical term that expresses how much a person believes that a proposition is true"
2. My current interview is a heads interview iff I have been assigned one heads interview
3. The fraction of interviews which are heads interviews is $1\over3$
4. The fraction of experiments which have one heads interview is $1\over2$
5. My credence that my current interview is a heads interview is equal to the fraction of interviews which are heads interviews
6. My credence that I have been assigned one heads interview is equal to the fraction of experiments which have one heads interview

Propositions like 5 and 6 might usually be true, but they are not true by definition.

Given 1 and 2, my credence that my current interview is a heads interview is equal to my credence that I have been assigned one heads interview.

Therefore given 1, 2, 3, and 4, one or both of 5 and 6 is false.

So how will your reasoning let you choose between 5 and 6 without begging the question?

I accept 6 and reject 5. My credence that my current interview is a heads interview isn't equal to the fraction of interviews which are heads interviews.

My argument is:

P1. If I am certain that A is true if and only if B is true then the degree to which I believe that A is true is equal to the degree to which I believe that B is true
P2. I am certain that my current interview is my only interview if and only if I have been assigned only one interview
C1. Therefore the degree to which I believe that my current interview is my only interview is equal to the degree to which I believe that I have been assigned only one interview (from P1 and P2)
P3. I am certain that if I have been assigned at random by a fair coin toss either one or two interviews then the probability that I have been assigned only one interview is $1\over2$
P4. I am certain that I have been assigned at random by a fair coin toss either one or two interviews
C2. Therefore I am certain that the probability that I have been assigned only one interview is $1\over2$ (from P3 and P4)
P5. The degree to which I believe that I have been assigned only one interview is equal to what I am certain is the probability that I have been assigned only one interview
C3. Therefore the degree to which I believe that I have been assigned only one interview is $1\over2$ (from C2 and P5)
C4. Therefore the degree to which I believe that my current interview is my only interview is $1\over2$ (from C1 and C3)
P6. I am certain that my current interview is my only interview if and only if the coin landed heads
C5. Therefore the degree to which I believe that the coin landed heads is $1\over2$ (from P1, C4, and P6)

Suppose we update the protocol so that on rare occasions, which present themselves with equal probability on each awakening episode, Sleeping Beauty is able to write down a note saying "I have now been awakened and interviewed." She can retain this note and read it again on Wednesday. Upon rereading the note on Wednesday, she can reason that it is twice as likely that such a note was produced if the coin landed tails since she would have been twice as likely to write it during such an experimental run. — Pierre-Normand

Not necessarily.

Assume a probability of 1/2 each time. The probability of writing it if the coin landed heads is 1/2. The probability of writing it (at least once) if the coin landed tails is 3/4. It is 3/2 times as likely to have been tails.

Assume a probability of 2/3 each time. The probability of writing it if the coin landed heads is 2/3. The probability of writing it (at least once) if the coin landed tails is 8/9. It is 4/3 times as likely to have been tails.

But notice that as the probability of writing a note each time approaches 1 the "greater likelihood" of it having been tails gets smaller, approaching 1.

Also, apply the principle of this reasoning to this.

A fair coin toss is equally likely to be heads as tails, she is less likely (not guaranteed) to wake if tails, therefore if she does wake then she reasons that it's less likely to be tails. In waking she rules out TTT.

If the answer to this problem is 4/7 then the answer to the normal problem is 1/2. If the answer to the normal problem is 1/3 then the answer to this problem is 1/2.