An important principle of EA is trying to maximize how much good you do, when you’re trying to do good. So EAs probably won’t advise you to base most of your charitable giving on emotional connection (which is unlikely to be highly correlated with cost-effectiveness) -- instead, according to EA, you should base this on some kind of cost-effectiveness calculation.
However, many EAs do give some amount to causes they personally identify with, even if they set aside most of their donations for more cost-effective causes. (People often talk about “warm fuzzies” in this context, i.e. donations that give you a warm fuzzy feeling.) In that sense, some amount of emotion-based giving is completely compatible with EA.
There have been a few posts discussing the value of small donations over the past year, notably:
Benjamin Todd on “Despite billions of extra funding, small donors can still have a significant impact”
a counterpoint, AppliedDivinityStudies on “A Red-Team Against the Impact of Small Donations”
a counter-counterpoint, Michael Townsend on “The value of small donations from a longtermist perspective”
There’s a lot of discussion here (especially if you go through the comments of each piece), and so plenty of room to come to different conclusions.
Here’s roughly where I come out of this:
What’s the relevant counterfactual? Many of these comment threads turn into discussions about earning-to-give vs direct work, but if you have $1000 in your hand, ready to donate, that’s not the relevant question. Rather, you should ask, “if I don’t donate this, what would I do with it instead, and how much impact would that have?”
You say “I know that professional grant makers think that last-dollar funding is not cost effective because they aren’t funding more projects, but aren’t out of dollars.” I think this frames the issue incorrectly. It’s not that big funders know that other projects aren’t cost-effective, it’s that they don’t currently have enough projects that clear a certain cost-effectiveness bar. But crucially, that bar is still far above zero!
This means
there are probably many opportunities that are just as cost-effective that they haven’t found (potentially you have information they don’t that you could exploit; see this section of the above ADS post)
marginal donations should have a cost-effectiveness at worst just below that bar, which means you’re only doing a little worse than the big funders. (This point taken from Benjamin Todd here.)