Sunday, 9 December 2018

Slime molds and the independence of irrelevant alternatives

Many people believe that rational decision making is the sole preserve of human beings. Still others recognise that isn't the case, as many studies in animals as varied as dolphins (e.g. see here), monkeys (e.g. see here) or crows show. How far does that extend though?

I've been reading How Not to Be Wrong - The Power of Mathematical Thinking by Jordan Ellenberg (book review to come in a few days). Ellenberg pointed me to this 2011 article (open access) by Tanya Latty and Madeleine Beekman (both University of Sydney), published in the Proceedings of the Royal Society B; Biological Sciences. You're probably thinking that's a weird source for me to be referring to on an economics blog, but Ellenberg explains:
You wouldn't think there'd be much to say about the psychology of the plasmodial slime mold, which has no brain or anything that could be called a nervous system, let along feelings or thoughts. But a slime mold, like every living creature, makes decisions. And the interesting thing about the slime mold is that it makes pretty good decisions. In the slime mold world, these decisions more or less come down to "move toward things I like" (oats) and "move away from things I don't like (bright light)...
A tough choice for a slime mold looks something like this: On one side of the petri dish is three grams of oats. On the other side is five grams of oats, but with an ultraviolet light trained on it. You put a slime mold in the center of the dish. What does it do?
Under those conditions, they found, the slime mold chooses each option about half the time; the extra food just about balances out the unpleasantness of the UV light.
All good so far. But this isn't a post about the rationality of slime mold decision-making. It's actually about the theory of public choice. And specifically, about the independence of irrelevant alternatives. Say that you give a person the choice between chocolate and vanilla ice cream, and they choose chocolate. Before you hand over the ice cream though, you realise you also have some strawberry as well, so you offer them that instead. The person thinks for a moment, and says they would like vanilla instead. They have violated the independence of irrelevant alternatives. Whether strawberry is available or not should not affect the person's preference between chocolate or vanilla - strawberry is irrelevant to that choice. And yet, in the example above, it made a difference.

Ok, back to slime molds. Ellenberg writes:
But then something strange happened. The experimenters tried putting the slime mold in a petri dish with three options: the three grams of oats in the dark (3-dark), the five grams of oats in the light (5-light), and a single gram of oats in the dark (1-dark). You might predict that the slime mold would almost never go for 1-dark; the 3-dark pile has more oats in it and is just a dark, so it's clearly superior. And indeed, the slime mold just about never picks 1-dark.
You might also guess that, since the slime mold found 3-dark and 5-light equally attractive before, it would continue to do so in the new context. In the economist's terms, the presence of the new option shouldn't change the face that 3-dark and 5-light have equal utility. But no: when 1-dark is available, the slime mold actually changes its preferences, choosing 3-dark more than three times as often as it does 5-light!
What's going on here? The slime mold is essentially making collective decisions (which is why I said this was a post about the theory of public choice). And with collective decisions, the independence of irrelevant alternatives can come into play. As Ellenberg notes, in the 2000 U.S. presidential election, the availability of Ralph Nader as a candidate has been credited with George W. Bush's victory over Al Gore. Nader took just enough votes from Gore supporters (who would have probably voted Gore if Nader was not available) to ensure that Bush won the critical state of Florida, and ultimately, the election. Something similar is going on with the slime molds, as Ellenberg explains:
...the slime mold likes the small, unlit pile of oats about as much as it likes the big, brightly lit one. But if you introduce a really small unlit pile of oats, the small dark pile looks better by comparison; so much so that the slime mold decides to choose it over the big bright pile almost all the time.
This phenomenon is called the "asymmetric domination effect," and slime molds are not the only creatures subject to it. Biologists have found jays, honeybees, and hummingbirds acting in the same seemingly irrational way.
Except, it's not irrational. In the case of the slime molds at least, it's a straightforward consequence of collective decision-making.

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