Reason is not the only means of overcoming bias

Random thought about scope insensitivity:

One person in need is a potential ally.
A group of people in need are a potential threat.

Sometimes the best way to overcome bias is through an emotional appeal.

Yes. Another good example is in debating (at least, debating to change someone's mind, not just to win in the eyes of observers).

For the fast majority of the population of people who disagree with you, you can't just drop a logic dump on them and expect them to magically change their minds. The only way they will be able to consider your arguments rationally is if you can get around all the biases they currently hold towards you or the topic of your argument. Sweeping the field clean of their biases, or compensating for them, may require various forms of influence, including emotional appeals, Cialdini's 6 weapons of influence, and various forms of signaling and framing.

The goal of using these forms of influence and rhetoric is not to switch the person you are debating from mindlessly disagreeing with you to mindlessly agreeing with you. The goal is just to get them to consider what you are saying in a less-biased way.

One of the best ways to change the minds of people who disagree with you is to cultivate an intellectual friendship with them, where you demonstrate a willingness to consider their ideas and update your positions, if they in return demonstrate the willingness to do the same for you. Such a relationship rests on both reciprocity and liking. Not only do you make it easier for them to back down and agree with you, but you make it easier for yourself to back down and agree with them.

When you have set up a context for the discussion where one person backing down isn't framed as admitting defeat, then it's a lot easier to do. You can back down and state agreement with them as a way to signal open-mindedness and the willingness to compromise, in order to encourage those qualities also in your debate partner. Over time, both people's positions will shift towards each other, though not necessarily symmetrically.

Even though this sort of discourse is full of influence, bias, and signaling, it actually promotes rational discussion between many people better than trying to act like Spock and expecting people you are debating to do the same.

Reason is not the only means of overcoming bias.
Sometimes the best way to overcome bias is through an emotional appeal.

You still use reason to decide that a given intervention (which doesn't necessarily have a form of a rational argument) is the correct thing to try in order to attain your goals. Obviously, rational argument is a very special kind of intervention, and one can make use of any number of environmental parameters in order to tweak one's mind.

I'll just throw these links here for counterpoint:

James Shikwati: For God's Sake, Please Stop the Aid!

Dambisa Moyo: Dead Aid

Kevin Myers: Africa is giving nothing to anyone -- apart from AIDS

And yeah, I agree with Tim that the line about "your daughter" is blatantly manipulative and I immediately tune out anyone who uses such rhetoric for any goal. I spend my resources on helping people who are important to me. (For real - most of my salary every month goes to friends and relatives.) Don't trick me into thinking you're important to me so you can get some of my money.

The video titled The Life You Can Save in 3 Minutes does a great job of overcoming the absence of an identifiable victim effect without providing an identifiable victim and without explicitly mentioning the identifiable victim effect at all. The first 1:15 minutes make a case for the viewer donating money to save lives in the developing world.

It asks: "What if it was my daughter?" Then I would spend to save her.

...but it is not my daughter - and that would make an enormous difference to most humans who are in reasonable working order. Is anybody really taken in by the counter-factual "What if it was my daughter" line? It seems like a straightforward case of attempted manipulation to me.

It is in a charity's interests to fool people to thinking prospective aid recipients are akin to family members. So, they are inclined to encourage the association - thus attempting to manipulate viewers. However, it is basically a simple psychological trick - intended to part the individual from their money.

I see a lot of this sort of thing. Charities - with the best of aims - are using much the same box of tricks that con-artists do.

For about 3 years now I've been giving to a number of charities through a monthly standing order. Initially setting it up was very satisfying and choosing the charities was a little like purchasing a new gadget, assuming a hands on experience is not available, and there are no trusted reviewers, I look at the various options and go with the ones whose advertising most closely reflected my personality and who looked the least like charlatans. With gadget purchases I find these indirect signals much more informative of the experience with the product than any enumeration of features, while individual statistics can convey value (and certainly attract attention) they often obscure the interaction experience or final quality.

So it is with charities, I cannot easily experience for myself whether they convey benefit, nor have I found a trusted source of recommendations. Charities don't tend to focus on the statistics of their work often preferring to focus on the emotions of the problem, perhaps reflecting the reality that naive, emotional people are the most likely to give to charity. Even when statistics are used they are like the feature lists for the gadgets, I feel no confidence that they reflect the whole picture.

While I have received some satisfaction from my donations, I do feel uncomfortable with the lack of confidence I have that my donations are actually causing an improvement, or whether they are directed towards genuine priorities. From my experiences in work I am familiar with the enormous waste within many organisations and how small steps of progress can be eradicated by later poor decision making.

What I really want is a kind of economics of suffering, a measurement of the various problems that I can apply my own weights and hypotheses to. I would like to see a comparison of the expected loss of life, and loss of quality of life, due to temperature rises, famines, AIDs, cancer etc. as well as the expected rate of return on my investment: have any of the charities I can give money to achieved progress or do they just maintain a status quo. How many charities have done the equivalent of eradicating small pox (i.e. solved a problem). Does anyone know of anything like this? I think it would be a much more valuable step than using rationality to empower the emotional arms race between charities.

The video identifies two broad objections to giving: that the aid is not helpful (1:18–1:21) and that the aid's help is insignificant (1:22–1:29). Even emotionally, it doesn't address the first of these; it does address the other.

Interestingly, the rational answer to the second objection is also very short, and runs along much the same lines as the emotional answer. To wit: the correct comparison is not between the effect that your aid has and the size of the problem, but between the good that your aid does and the harm that it does in wasting money. To connect to the emotional argument: if a life saved beats a pair of expensive shoes, then this is true regardless of how many other lives there are to save. So the second objection is now reduced to the first one: am I in fact saving a life?

Overall, I agree with the OP: there are emotional replies to emotional bias, so emotion can overcome bias. In this case, the question ‘What if [it was] your daughter […]?’ can encourage emotions that overcome bias. That doesn't mean that I like the rest of the video, however. I can also see why even that line (which I do like) can turn off people, like the readers of LessWrong, who recognise emotional manipulation.

I went to the website, where they have plenty of room to give long answers to the first objection; I found nothing! The pledge is very vague, and I already meet its requirements (so I signed it). Given that Peter Singer seems to be behind this, I'm rather disappointed, actually; I respect him as a philosopher.

I still haven't seen a shred of evidence that ongoing "aid" of any kind was ever helpful, and huge volume of evidence against it.

Tricking people into giving away their money is not overcoming bias, it is increasing bias.