So if your utility function is linear in the number of lives saved, then you should invest in a single charity.

Also, the reason to invest in a mix of high and low risk investment is if the two types have lower cross-correlation than internal correlation. If the correlation between high risk investments and other high risk investments is no larger than the correlation between high risk and low risk investments, there’s no need to have a mixture; if you’re disaster averse, you should just not invest part of your nest egg.

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You’re right that I didn’t speak entirely accurately. I was trying to make the same point that both BJ and Keith did a better job of making farther down: taking advantage of buckets isn’t the only reason to diversify. Ken and BJ’s posts make clear that this benefit of diversification also requires diminishing marginal utility, which I’ll grant. However, I will then argue that we do in fact have diminishing marginal utility on charity contributions (as in almost everything).

This point is easiest to make if we restrict ourselves to present lives (as many EAs choose to do). Given that restriction, we do not value saving 10 billion lives twice as much as saving 5 billion lives, because we don’t have 10 billion lives to save. I’ll grant that this is a somewhat pathological example, but given the extreme uncertainty we look at in many potential interventions, even this small amount of diminution may very well be relevant and make it worth considering diversification.

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Regarding my Point 3, I disagree that it requires decreasing marginal utility or any consideration of marginal utility whatsoever.

Using leverage (borrowing cash) or sizing of the cash component, one can achieve the same risk/uncertainty/variance in a stock portfolio (as a non-diversified portfolio) and a higher expected return.

That’s correct… a higher expected return with no increased risk(!)

The reason for this diversification is therefore fundamentally different to the reason that one might diversify because of nonlinear utility functions (e.g. Point 2).

(Of course, in practice one might struggle to estimate the expected payoffs, variances and correlations between payoff distributions.)

In the academic finance lingo, one exposes one’s self to only priced risk and eliminates unpriced risk by diversifying.

See Markowitz’s work on Modern Portfolio Theory (MPT) for more.

As far as I can see the ideas behind diversification in MPT are of no use in forming a charity portfolio.

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Diversification plays three different roles in three different contexts:

1. For charities one is arguably only interested in expected value. The highest expected value is preferred. The magnitude of uncertainty can be ignored. Diversification is avoided as this would not increase the expected value of the payoff.

2. For egg-carrying, one diversifies. One literally does not carry all one’s eggs in one basket because of a nonlinear utility function. Having two eggs isn’t twice as good as having one, so diversification of egg payoffs increases expected utility.

3. In stocks, one can diversify and increase the size of stock holding versus cash. Instead of x% cash and y% in one stock, one has (x-a)% in cash and (y+a)% in more than one stock. One’s entire portfolio can therefore have a higher expected payoff for the same distribution variance/risk/uncertainty.

Number 3 doesn’t seem to have been mentioned and is a different argument for diversification than number 2. (Harry Markowitz won a Nobel prize in part for his work on point number 3.)

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Yes, people typically get diminishing marginal utility from wealth. That is, they are risk-averse and should diversify investments. Yes, under a certain moral framework, you can say that people do not have decreasing marginal utility of [amount of good done] by definition. In addition, charities do not typically have diminishing [amount of good done per dollar] on the scale of one individual’s donation. That is, there is apparently no risk aversion involved. Hence there is no reason to diversify. This is an interesting point. It’s plausible that things would be better if more people took this into account.

But there are many moral, psychological, and practical complications. The conclusion holds only given certain simplifying assumptions about these complications. I list some of them. It is not entirely clear that these assumptions hold or should hold in practice.

There are also many complications related to economics and decision theory. Again the conclusion holds only given certain simplifying assumptions about these complications. I also list some of these. It is not entirely clear that these assumptions hold or should hold in practice.

Scott has dismissed one of these complications as unnecessary complicated game theory. I believe that this conclusion is premature. First we need to fully understand the circumstances in and mechanism by which diversification makes a difference. Thus I attempt to illustrate a case where diversification does matter. To do this I make explicit assumptions about diminishing marginal returns and uncertainty about total fundraising. I find that it makes sense to diversify.

I then treat the output of my own decision process as evidence about total fundraising. This is a valid move without invoking CDT vs. EDT vs. TDT vs. superrationality vs. “universalization.” I find that diversifying matters even more.

I believe that the assumptions I made are realistic enough to suggest that there may be good reasons to diversify in real life, even given all but a few of the anti-diversifying simplifications. (I’ll add now that uncertainty or confusion about this line of thinking alone is a good reason to diversify.)

It is helpful to take these complications seriously, especially if you want to be taken seriously by smart people encountering these ideas for the first time.

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