# Fisherian Runaway as a decision-theoretic problem

*Introducing what I think may be an interesting toy problem for timeless-like considerations.*

The [Fisherian Runaway](https://en.wikipedia.org/wiki/Fisherian_runaway) is a proposed mechanism for the development of apparently-detrimental ornamentation such as peacock tails. It goes something like this: You start out with females being selective about their mates. They develop some form of evaluation system to select for fitness in their mates. Then, a male with some new trait comes along. For whatever reason, the existing fitness-evaluation system rates this trait very highly. The male finds many mates and has many offspring. His sons will also carry the new trait, and will similarly have more offspring than replacement. The trait will spread through the population. Then, a female which weighs the trait stronger in its fitness-evaluation comes along. She mates with carriers of the new trait more than other females, and consequently her sons will disproportionately carry the trait and disproportionately reproduce. Some of their children will be female, and they inherit the new evaluation from their grandmother (just like her direct daughters, but theres only a proportionate amount of those). The new evaluation will spread through the population. If the trait is continuous like tail length, this can lead to yet stronger selection for the trait, which will lead to yet higher requirements for it in mates, etc.

Notice that this doesn't really depend on what the trait is. If it had no effect outside the females evaluation, it could still happen and intensify indefinitely (or at least until it stops having no side effects). If it is otherwise detrimental, the benefit in reproduction can still outweigh that more or less indefinitely, or at least until it gets so bad that females can't find even one male with the detrimental trait anymore.

Now, intuitively it seems that there is something going wrong here. Traits become attractive based on nothing other than that they are attractive. The challenge is to make this intuition precise, and formally define the boundary of the problematic behaviour. This is surprisingly hard. I will outline some approaches and how they fail.

"Real" Fitness
--------------

A first response might be that if the females were better in selecting for fitness this wouldn't happen. But it's not clear they're making any mistakes in this: fitness just is the expected number of offspring after all, and the trait they were selecting for really did lead to more offspring. In part because of their decision, of course, but as defined those decisions affect fitness.

So they would actually need to select for something other than fitness itself - a version of it that was "controlled for" reproduction effects like that. And then if they all selected that fitness would become identical to it. But where do you draw the line? Obviously efforts made to meet potential mates at all need to count as real. But some details of how the offer is made clearly need to count as well: making a nesting place or food for the female for example. But even making fitness more legible might count (so long as its only "real" fitness you're making legible) - at least, it seems like that would be a "real" contribution if it didnt have other costs, so presumably it's still a contribution if the costs are low enough. More generally, theres not a clear separation between "mating successfully" and "the rest of life" from the point of view of evolution - everything you're doing is just to mate successfully. The problems here are similar to building a "neutral" [Predict-O-Matic](https://www.lesswrong.com/posts/SwcyMEgLyd4C3Dern/the-parable-of-predict-o-matic) \- but with a less good fallback. Because it *seems like* the runaway is the effect of evolution being hill-climb-y, and rational offspring-maximizers could avoid it - they don't have anything else to "really" care about.

Coordination
------------

The other obvious approach would be to focus on the species-level detriment of the outcome. The ornaments are a cost incurred to get an advantage in the zero-sum competition for being choosen as a mate, so if we looked at the collective there wouldn't be any advantage to be gained through this. So lets say we allow groups of birds to coordinate; then wouldn't the ones which come up with more "reasonable" mate-allocation internally eventually take over? At first pass it seems so. Still, I don't think this defines the problem very well. For one, it also eliminates all other forms of intra-specific competition, and these seem different. If you stab rivals with your horns they *just are* dead and can't compete with you anymore no matter what anyone thinks, which isn't "based on nothing" in the same way as the ornamental attractiveness.

More than that, this formulation only makes sense for changes whichs effect is relatively independent of group size. Consider for example the aggressive green beard gene, which makes carriers develop a green beard and attack anyone who doesn't have one, and the aggressive blue beard gene which is the same but the beard is blue. None of these can be invaded by a small population of the other, so either could count as "optimal" by the group-selection criterion.

But even more generally, I don't think this group evalution is really solving anything, conceptually. The groups here act a lot like organisms of their own (much like you are a culture of group-selected cells). And these collective organisms initially reproduce asexually (just by growing in membership), so their incentives arent skewed by the runaway, and *ex hypothesi* they pass this on to their members perfectly. But what if these group-organisms were to develop sexual reproduction as well, just like multi-cellular organisms did? Then the problems would return. So the coordination approach is really just hoping that the meta-level version of the problem turns out fine, and leveraging that.