A foundation finds an organization doing good work with a funding gap of about $5M. They could just give the organization $5M, but instead they decide to try and help the organization find some small donors to spread its reach. The foundation offers to match donations up to $2.5M. This is a real match: they will give $1 for every $1 anyone else gives, up to their limit. When the match is over, however, if the funding gap still hasn't been met they plan to make up the difference.
Let's consider some possiblities:
|Amount Raised||Match Given||Makeup Contribution||Total Received|
Most donation matching isn't this extreme, but this example shows the main consideration in donation matching: how is the world different if you do donate versus if you don't? This is counterfactual reasoning, and in the case of donation matching it's specifically a question of counterfactual trust. You trust them to match your donation if you give one, but do you trust that your donation is necessary to prompt them to give?
Good Ventures today announced $5M in matching funds for donations made to GiveDirectly from 2013-12-03 through 2014-01-31. All donations to GiveDirectly during the period, up to $100,000 per donor, will be counted toward the match.
Suppose that, over the time period the match was active, GiveDirectly raised $4.5M. If you had donated $10 to GiveDirectly at that time, how much more money would they have received than if you had not donated anything?
This is asking us how much we trust GiveDirectly's match to be counterfactually valid. If we think they would have just gone ahead and donated the $5M regardless then we'd answer $10, while if we think they'll would only donate in response to our donation we'd answer $20. If we weren't sure how much to trust the match we might say something between $10 and $20.
Ben writes that $20 seems to have been accurate here:
Interestingly, for both the Good Ventures and HCEA matches, we can check people's beliefs against reality. For Good Ventures, we can look at GiveWell's blog post on the match:If the full amount of the match is reached, we believe Good Ventures will be giving more in total to our top charities this year than they would have been had a match not been a possibility.The wording "If the full amount... is reached" suggests that Good Ventures was in fact planning to donate only the amount matched, so at least on the margin the match was fully counterfactual.
Unfortunately "fully counterfactual" is too strong. Good Ventures has a bunch of money that they intend to give to the most effective charities they can, and this is great! But their plan to use the money as close to optimally as possible means this money can't actually be swayed very much. Say I give $10 to Give Directly and Good Ventures matches my donation with $10 they wouldn't otherwise donate this year. If I hadn't donated, however, they would have kept that $10 to spend in a later year on an opportunity they consider approximately as valuable.
Why do I say "approximately as valuable"? Good Ventures is run by clear thinking people who want to have as big a positive impact on the world as they can. If they thought that Give Directly represented a better opportunity for giving than they were likely to see in the future they would donate more to it until that was no longer the case, and vice versa. The only reason they're willing to offer a match is that they don't have a precise target for Give Directly in mind and they think the benefit of bringing in more donors outweighs the benefit of being slightly more deliberate about which donations happen in one year vs another.
There's one little gap here, however, which we can get a good bit of mileage out of. What I describe only holds if you and the matcher have approximately the same values. If you, say, think current people matter far more than future people, however, then taking Good Ventures up on their match is great, because it gets them to spend money now instead of delaying and spending it on others later. This situation is most apparent with "general" donation matches, like an employer offering to match donations to any 501(c)3 organization. If the size of the employer pool is not fixed or you plan to give to a charity you think is much more effective than the 501(c)3s the money would otherwise go to, the counterfactual effect of your donation really is doubled.
There's a spectrum here, from "funder negates your match" through "funder ignores your match" through "funder acts on your match but would otherwise fund something about as valuable (to you)" up to "funder acts on your match and would otherwise fund something much less valuable (to you)". A good guideline is to respect a match only when the match is untargeted, when the funder is willing to match donations to any charity: this matches up almost exactly with when matches are fully counterfactually valid. 
(Similarly you shouldn't offer a fully general match, because charities vary dramatically in their effectiveness.  If you would like something with the social proof benefits of matching but without the dishonesty of misleading people about the effects of their donation, consider making a donation and then challenging others to do the same.)
I also posted this on my blog.
 Intent matters a lot here in figuring dishonesty. If the funder planned from the beginning to hit a target regardless of other people's actions that's bad, but if instead after failing to hit a target they decide to be generous and gill the gap that sounds good. Yet both are the same from a counterfactual reasoning perspective: they give one dollar fewer for every dollar you give.
 Tomasik claims to disagree, but this is a matter of degree. While he rejects claims 1000x claims of variance he does "suspect many charities differ by at most ~10 to ~100 times, and within a given field, the multipliers are probably less than a factor of ~5" which is strong enough to argue against fully general matches, and probably field-restricted matches as well.