# Fat Tails Discourage Compromise

Say that we have a set of options, such as (for example) [wild animal
welfare](https://en.wikipedia.org/wiki/Wild_animal_welfare) interventions.

Say also that you have two axes along which you can score those
interventions: *popularity* (how much people will like your intervention)
and *effectiveness* (how much the intervention actually helps wild
animals).

Assume that we (for some reason) can't convert between and compare those
two properties.

Should you then pick an intervention that is a compromise on the two
axes—that is, it scores decently well on both—or should you max out
on a particular axis?

One thing you might consider is the distribution of options
along those two axes: the distribution of interventions can
be [normal](https://en.wikipedia.org/wiki/Normal-distribution) on for both
popularity and effectiveness, or the underlying distribution could be
[lognormal](https://en.wikipedia.org/wiki/Lognormal_Distribution)
for both axes, or they could be mixed (e.g. normal for popularity,
and lognormal for effectiveness).

Intuitively, the distributions seem like they affect the kinds of
tradeoffs we can make, how could we possibly figure out how?

…

…

…

![](http://niplav.site/img/fat_tails/monte_carlo.jpg "Text: “you can't use Monte Carlo simulations for everything”. Image of sketch man with sunglasses making finger guns, with the text “that's where you're wrong kiddo” next to him")

It turns out that if both properties are normally
distributed, one gets a fairly large Pareto frontier, with a
[convex](https://en.wikipedia.org/wiki/Convexity) set of options,
while if the two properties are lognormally distributed, one gets a
[concave](https://en.wikipedia.org/wiki/Concavity) set of options.

![](http://niplav.site/img/fat_tails/tails.png)

(Code [here](http://niplav.site/code/fat_tails/fat_tails.jl).)

So if we believe that the interventions are normally distributed
around popularity and effectiveness, we would be justified
in opting for an intervention that gets us the best of both
worlds, such as sterilising stray dogs or finding less painful
[rodenticides](https://en.wikipedia.org/wiki/Rodenticides).

If we, however, believe that popularity and effectiveness are lognormally
distributed, we instead want to go in hard on only one of those,
such as [buying brazilian beef that leads to Amazonian rainforest being
destroyed](https://reducing-suffering.org/how-rainforest-beef-production-affects-wild-animal-suffering/),
or writing a book of poetic short stories that detail the harsh life of
wild animals.

What if popularity of interventions is normally distributed, but
effectiveness is lognormally distributed?

![](http://niplav.site/img/fat_tails/different.png)

In that case you get a pretty large Pareto frontier which almost looks
linear to me, and it's not clear anymore that one can't get a good
trade-off between the two options.

So if you believe that [heavy tails dominate with the things you care
about](https://80000hours.org/2023/02/how-much-do-solutions-differ-in-effectiveness/),
on multiple dimensions, you might consider taking a [barbell
strategy](https://en.wikipedia.org/wiki/Barbell_strategy) and taking
one or multiple options that each max out on a particular axis.

If you have thin tails, however, taking a [concave
disposition](https://vitalik.eth.limo/general/2020/11/08/concave.html)
towards your available options can give you most of the value you want.

### See Also

* [Being the (Pareto) Best in the World (johnswentworth, 2019)](https://www.lesswrong.com/posts/XvN2QQpKTuEzgkZHY/being-the-pareto-best-in-the-world)