Paying off small debts first isn't just a "natural tendency." Consumer advice sites actually encourage this as a motivational strategy. Every single one of them. Having read this, now I question the objectivity of those types of advice pieces. For example, here's a story on US News that covers three strategies for paying off credit card debt. The first tip is to pay off higher interest cards. But the second is to pay…
The optimal (highest rate first) approach is a slow slog that can be discouraging and result in relapses. The sub-optimal (smallest debt first) approach shows progress much faster, and if paired with the snowball approach (as debts are paid off, freed cash goes to the next debt), it creates the illusion (until high value debts are all that remain) of fast progress. It's psychologically easier to stick with.
> But the second is to pay off the smallest debts first and pay the minimum on the other cards. What?!?
Again, this article in particular, but the actual recommendation is to pay at least the minimum, which is not the same.