Selective Empathy: When would you NOT save the drowning child?

Recently a friend and I were having a conversation about his self-perceived “unempathetic” nature. Ultimately, he allowed that he isn’t so much unempathetic as selectively empathetic.

I immediately loved this categorization, and I’d hypothesize that we all act along a continuum of selective empathy as a means of survival and sanity. Biologically, it would be of little advantage for any creature to be fully empathetic at all times. In fact, humans who experience the emotions of others in their own body (called empaths) often report feeling overwhelmed, anxious, and exhausted.

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If sociopath is at one extreme and empath at the other, I think it’s rare that any of us fall into just one category or in any position along the continuum on a consistent basis. After all, aren’t most situations environmentally and context-dependent, and therefore wouldn't your reaction to them be as well?

Peter Singer recently authored the book The Life You Can Save. In it, he prompts the reader with the following ethical dilemma:

On your way to work you see a child drowning in a shallow puddle. Do you wade into the water to rescue the child knowing that you will ruin your expensive clothes and shoes and then have to return home to change, rendering you late for work? Or do you ignore the child and continue on your way? 
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Singer argues that of course we all feel morally obligated to save the child. All of us probably register at empathic scales in that scenario regardless of how selectively empathic we might be. His main query in the remainder of the book is this: If you are willing to endure a financial sacrifice (your expensive clothing) to the immediate puddle, why aren’t you willing to donate to charities to help prevent the poverty-related deaths of an estimated 27,000 children a day? While I’d love to dive into the reasons, I’ll simply encourage you to read the book. Instead, here I want to consider a different question:

How many days in a row would you rescue that child before you would become a sociopath—how many sacrifices of clothing and shoes before you’d tune out and walk by?

Being selectively empathic in this scenario on day one seems callous and cold and absolutely sociopathic. But wouldn’t biology have programmed a mechanism to help us behave in that sociopathic manner at some point to allow our own survival?

Day 92?

423?

When does the burden of empathy break toward self-preservation?

I’ll look forward to your thoughts!