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I'm not entirely sure that I believe the premise of this game. Essentially, the claim is that 20 of SingInst's regular donors have extra money lying around that they are willing to donate to SingInst iff someone else donates the same amount. What do the regular donors intend to do with the money otherwise? Have they signed a binding agreement to all get together and blow the money on a giant party? Otherwise, why would they not just decide to donate it to SingInst at the end of the matching period anyway?
In response to
The $125,000 Summer Singularity Challenge
This seems relevant:
Five: US tax law prohibits public charities from getting too much support from big donors.
Under US tax law, a 501(c)(3) public charity must maintain a certain percentage of "public support". As with most tax rules, this one is complicated. If, over a four-year period, any one individual donates more than 2% of the organization's total support, anything over 2% does not count as "public support". If a single donor supported a charity, its public support percentage would be only 2%. If two donors supported a charity, its public support percentage would be at most 4%. Public charities must maintain a public support percentage of at least 10% and preferably 33.3%. Small donations - donations of less than 2% of our total support over a four-year period - count entirely as public support. Small donations permit us to accept more donations from our major supporters without sending our percentage of public support into the critical zone. Currently, the Singularity Institute is running short on public support - so please don't think that small donations don't matter!
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Can you explain why "the only measure available is indeed the ordinary amplitude-squared measure"?
Also, I'm confused about this:
According to the Wikipedia entry you linked to, a probability measure is a real-valued function, but X here is apparently just a number? What's the significance of your parenthetical note here?