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I may be entirely wrong, but I was under the impression that this simply leverages amazon's affiliate program, in which amazon rewards 3rd parties for linking to them. That wouldn't be any sort of public relations play by Amazon, since the policy is transparent to the actual customers.

That doesn't address your point about the tradeoffs involved - if you object enough to Amazon's policies to forgo the benefits, that is entirely your prerogative. Just pointing out that this isn't a case of Amazon baiting people by appearing charitable - rather, some is providing a way to leverage Amazon's existing policies to have Amazon pay commissions on your sale for charity.

Do you get the bonus if you add things to your cart in a different session but "check out" in this session? My most common use case is navigating to Amazon from an external link, so I'd like to know if I can get the same benefit by filling my cart that way and then just using this link to "check out".

Did you mean to have the result of fighting on stormy seas to be -10 points for the attacker? As it stands, I don't believe the math works out exactly.

I'm convinced. Having though about this a little more, I think I see the model you are working under, and it does make a good deal of intuitive sense.

I think in this case, we are assuming total and honest reporting of results (including publication); otherwise, we would be back to the story of filtered evidence. Therefore, the publication is not a result of the plans - it was going to happen in either case.

That's not quite what I meant. It is not the experimenter's thoughts that I am uncomfortable with- it is the collection of possible experimental outcomes.

I will try to illustrate with an example. Let us say that I toss a coin either (i) two times, or (ii) until it comes up heads. In the first case, the possible outcomes are HH, HT, TH, or TT; in the second case, they are H, TH, TTH, TTTH, TTTTH, etc. It isn't obvious to me that a TH outcome has the same meaning in both cases. If, for instance, we were not talking about likelihood and instead decided to measure something else, e.g. the portion of tosses landing on heads, this wouldn't be the case; in scenario (i), the expected portion of tosses landing on heads is 1/4 + .5/4 + .5/4 + 0/4 = .5, but in scenario (ii), it would be 1/2 + .5/4 + (1/3)/8 + .25/16 + ... = log(2); i.e. a little under .7.

Just a note here: the fact that a dataset has the same likelihood function regardless of the procedure that produced it is actually NOT a trivial statement - the way I see it, it a somewhat deep result which follows from the optional stopping theorem and the fact that the likelihood function is bounded. Not trying to nitpick, just pointing out that there is something to think about here. According to my initial intuitions, this was actually rather surprising - I didn't expect experimental results constructed using biased data (in the sense of non-fixed stopping time) to end up yielding unbiased results, even with full disclosure of all data.