Sounds like you agree with both me and Ninety-Three about the descriptive claim that the Shapley Value has, in fact, been changed, and have not yet expressed any position regarding the normative claim that this is a problem?

I'm not sure what you're trying to say.

My concern is that if Bob knows that Alice will consent to a Shapley distribution, then Bob can seize more value for himself without creating new value.  I feel that a person or group shouldn't be able to get a larger share by intentionally hobbling themselves.

If B1 and B2 structure their cartel such that each of them gets a veto over the other, then the synergies change so that A+B1 and A+B2 both generate nothing, and you need A+B1+B2 to make the $100, which means B1 and B2 each now have a Shapley value of $33.3 (up from $25).

Also, I wouldn't describe the original Shapley Values as "no coordination".  With no coordination, there's no reason the end result should involve paying any non-zero amount to both B1 and B2, since you only need one of them to assent.  I think Shapley Values represent a situation that's more like "everyone (including Alice) coordinates".

A problem I have with Shapley Values is that they can be exploited by "being more people".

Suppose Alice and Bob can make a joint venture with a payout of $300.  Synergies:

• A: $0
• B: $0
• A+B: $300

Shapley says they each get $150.  So far, so good.

Now suppose Bob partners with Carol and they make a deal that any joint ventures require both of them to approve; they each get a veto.  Now the synergies are:

• A+B: $0 (Carol vetoes)
• A+C: $0 (Bob vetoes)
• B+C: $0 (venture requires Alice)
• A+B+C: $300

Shapley now says Alice, Bob, and Carol each get $100, which means Bob+Carol are getting more total money ($200) than Bob alone was ($150), even though they are (together) making exactly the same contribution that Bob was paid $150 for making in the first example.

(Bob personally made less, but if he charges Carol a $75 finder's fee then Bob and Carol both end up with more money than in the first example, while Alice ends up with less.)

By adding more partners to their coalition (each with veto power over the whole collective), the coalition can extract an arbitrarily large share of the value.

Seems like that guy has failed to grasp the fact that some things are naturally more predictable than others.  Estimating how much concrete you need to build a house is just way easier than estimating how much time you need to design and code a large novel piece of software (even if the requirements don't change mid-project).

Is that error common?  I can only recall encountering one instance of it with surety, and I only know about that particular example because it was signal-boosted by people who were mocking it.

I'm confused about how continuity poses a problem for "This sentence has truth value in [0,1)" without also posing an equal problem for "this sentence is false", which was used as the original motivating example. 

I'd intuitively expect "this sentence is false" == "this sentence has truth value 0" == "this sentence does not have a truth value in (0,1]"

On my model, the phrase "I will do X" can be either a plan, a prediction, or a promise.

A plan is what you intend to do.

A prediction is what you expect will happen.  ("I intend to do my homework after dinner, but I expect I will actually be lazy and play games instead.")

A promise is an assurance.  ("You may rely upon me doing X.")

How about this: I train on all available data, but only report performance for the lots predicted to be <$1000?

This still feels squishy to me (even after your footnote about separately tracking how many lots were predicted <$1000). You're giving the model partial control over how the model is tested.

The only concrete abuse I can immediately come up with is that maybe it cheats like you predicted by submitting artificially high estimates for hard-to-estimate cases, but you miss it because it also cheats in the other direction by rounding down its estimates for easier-to-predict lots that are predicted to be just slightly over $1000.

But just like you say that it's easier to notice leakage than to say exactly how (or how much) it'll matter, I feel like we should be able to say "you're giving the model partial control over which problems the model is evaluated on, this seems bad" without necessarily predicting how it will matter.

My instinct would be to try to move the grading closer to the model's ultimate impact on the client's interests.  For example, if you can determine what each lot in your data set was "actually worth (to you)", then perhaps you could calculate how much money would be made or lost if you'd submitted a given bid (taking into account whether that bid would've won), and then train the model to find a bidding strategy with the highest expected payout.

But I can imagine a lot of reasons you might not actually be able to do that: maybe you don't know the "actual worth" in your training set, maybe unsuccessful bids have a hard-to-measure opportunity cost, maybe you want the model to do something simpler so that it's more likely to remain useful if your circumstances change.

Also you sound like you do this for a living so I have about 30% probability you're going to tell me that my concerns are wrong-headed for some well-studied reason I've never heard of.

I think you're still thinking in terms of something like formalized political power, whereas other people are thinking in terms of "any ability to affect the world".

Suppose a fantastically powerful alien called Superman comes to earth, and starts running around the city of Metropolis, rescuing people and arresting criminals. He has absurd amounts of speed, strength, and durability. You might think of Superman as just being a helpful guy who doesn't rule anything, but as a matter of capability he could demand almost anything from the rest of the world and the rest of the world couldn't stop him. Superman is de facto ruler of Earth; he just has a light touch.

If you consider that acceptable, then you aren't objecting to "god-like status and control", you just have opinions about how that control should be exercised.

If you consider that UNacceptable, then you aren't asking for Superman to behave in certain ways, you are asking for Superman to not exist (or for some other force to exist that can check him).

Most humans (probably including you) are currently a "prisoner" of a coalition of humans who will use armed force to subdue and punish you if you take any actions that the coalition (in its sole discretion) deems worthy of such punishment. Many of these coalitions (though not all of them) are called "governments". Most humans seem to consider the existence of such coalitions to be a good thing on balance (though many would like to get rid of certain particular coalitions).

I will grant that most commenters on LessWrong probably want Superman to take a substantially more interventionist approach than he does in DC Comics (because frankly his talents are wasted stopping petty crime in one city).

Most commenters here still seem to want Superman to avoid actions that most humans would disapprove of, though.