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Even when their matching donation is anonymous and the direct influence is zero, the orphan crushing facility wants the orphanage to be successful.

The orphanage's rising success serves to limit the supply of orphans. This means that there aren't as many free-roaming orphans available for crushing as more of them get taken off of the market.

This improves the supply-and-demand ratio for orphan-derived products. A successful orphanage means that the the orphan crushing facility can make more money while doing less of that tedious work of -- you know -- crushing orphans.

(I don't know what kind of secondary or tertiary games could be played with anonymous matching donations to archive.org; my creativity has limits. But I do know that my support for enabling people to make informed personal decisions is approximately boundless, as anything less would be stifling.)

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I think in this hypothetical, the existence of an orphan-crushing industry should make you reluctant to donate to orphanages regardless of who's doing the donation matching.
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