Saturday, January 04, 2014

If big donors have much better opportunities than small donors, then small donors can go to Las Vegas, or Wall Street

Summary: For various reasons, donors giving large amounts may be able to achieve more per dollar with their donations, enjoying economies of scale. When this is true, small donors may be able to do more good by exchanging a donation for a lottery with a 1/n chance of delivering a donation n times as large. In practice, transaction costs and taxation mean the donation will be smaller, a cost which must be compared against scale economies. However, the use of randomization, casino gambling, derivatives, and other institutions can limit lottery costs to a modest factor, lowest when investments are used. So small donors who believe strong scale economies exist can take advantage of them.

Scale economies of donation
In a recent blog post Will MacAskill described a donation opportunity that he thought was attractive, but less so for him personally because his donation was smaller than a critical threshold:
This expenditure is also pretty lumpy, and I don’t expect them to get all their donations from small individual donations, so it seems to me that donating 1/50th of the cost of a program manager isn’t as good as 1/50th of the value of a program manager.
When this is true, it can be better to exchange a donation for a 1/50 chance of a donation 50 times as large. One might also think that when donating $1,000,000 rather than $1 one can afford to spend more time and effort in evaluating opportunities, get more access to charities, and otherwise enjoy some of the advantages possessed by large foundations.

Insofar as one believes that there are such advantages, it doesn't make sense to be defeatist about obtaining them. In some ways resources like GiveWell and Giving What We Can are designed to let the effective altruist community mimic a large effectiveness-oriented foundation. One can give to the Gates Foundation, or substitute for Good Ventures to keep its cash reserves high.

However, it is also possible to take advantage of economies of scale by purchasing a lottery (in one form or another), a small chance of a large donation payoff. In the event the large donation case arises, then great efforts can be made to use it wisely and to exploit the economies of scale. The question, then, is how much of the expected (financial) value of a donation must be lost in converting it into a lottery of the right type.

Casino Gambling
In European roulette (which is offered in Las Vegas), a bet on a single number yields a 1/37 chance of multiplying the bet 36x, otherwise losing the bet. For American Roulette, the chance of a win is only 1/38. These correspond to losses of 2.7% and 5.26% of the bet.

If one undertakes one European bet, and bets one more time in the event of a win, then one has a 1/1,369 chance of winnings 1,296 times as great as the initial stake, retaining almost 95% of the expected value of the original amount available for donation.

If trying to reach large scale, maximum table bets could be a problem: typical maximum bets of $5,000-$10,000 would limit final payouts to $180,000-$360,000. But this could be dealt with by entering high-stakes private tables, or switching to sports betting. In any case, up to at least the level of millions of dollars, casino gambling can provide a chance at the necessary scale with limited direct transaction costs.

More important would be income taxation of gambling winnings, which in the United States at least are treated as ordinary income. Gambling winnings of millions of dollars would be taxed largely at the maximum rate of 39.6% plus applicable state taxes. Charitable donations are tax-deductible up to 50% of income so for very large donations this would cut the net tax rate to the range of 20-25%. For smaller donations (especially less than twice one's non-gambling income) the effective tax take would be even smaller.

So, all told, it seems that casino-based methods should permit small donors to convert a given donation amount into a chance of multimillion dollar donations for a cost of less than 30%, with income tax as the primary cost.

High-risk investments
Various financial instruments involve a small chance of extremely large upside payoffs, including out-of-the-money options, distressed debt, certain growth equities, and so forth. To the extent market efficiency holds, the loss in expected value from purchasing such instruments should be small.

Financial assets held for more than one year can benefit from lower income tax rates on long-term capital gains. In the United States, the top long-term capital gains rate is 20%, as opposed to 39.6% for ordinary income.

Even better, when donating appreciated securities capital gains tax on the securities is waived, while one can still take a charitable deduction to apply to other income. So if one can make one's donation to one's charity of choice in the form of the high-risk securities transaction costs may be under 10%.

Alternatively, one might donate the high-risk securities to a foundation (perhaps one's own small foundation, perhaps something like the Giving What We Can Trust) with a request that if they bear fruit the proceeds will be applied to the opportunity with economies of scale that one is interested in.

Donor cooperation mechanisms
A donor using Las Vegas or Wall Street to increase variance in her donation size winds up paying fees to casinos or brokerages. These could be avoided through deals between donors, although the difficulty in coordinating them makes them less plausible.

For example, say that A is donating $500,000 to a fairly scalable intervention like Against Malaria Foundation or GiveDirectly, while B is donating $1,000 but thinks her best option requires at least $100,000 to take advantage of economies of scale. Then they can use a random number generator and have B donate to A's charity, in exchange for A donating $100,000 to B's with probability 1/100.

A group of small donors might also contribute to a common donation pool, with each dollar contributed to the pool buying one "ticket" in a lottery to select the donor who gets to choose the allocation of the entire pool. The accumulation of funds could be managed with a crowdfunding coordination mechanism along the lines of Indiegogo.

For those who see strong increasing returns, I would first recommend debate with those who disagree: you may be able to convince others and you may be wrong! However, the option of purchasing investments with a small chance of very high payoffs (but with bounded losses) is also a tractable option: donors should not be bemoaning missed economies of scale that supposedly could have doubled their donations without taking advantage of randomization methods.


Brian Tomasik said...

Interesting ideas. :)

There may indeed be cases of increasing marginal returns, but I'm not sure this is the norm. Most of the altruistic uses of money that I see have diminishing marginal value for additional dollars: e.g., helping a new charity get started, giving to a particularly talented person, paying yourself to retire, saving for a startup, etc. If finding and overseeing the project that you're donating to is a bottleneck, then it's better for lots of people to donate small amounts. When you're a big donor, you don't have the resources to make sure the money is being used as you intended.

Carl said...

Brian, I agree that the overall curve for charitable efficacy with increasing budgets shows diminishing returns, with exceptions.

This post is directed at those who disagree, or face unusual situations.

Toby Ord said...

This is a nice explanation of how to deal with increasing marginal returns on money. I think that there are situations of increasing marginal returns that we face, though often this is just one part of a process where the other parts have sufficiently diminishing returns to make the whole process have diminishing returns overall. Note that even if there is only one stage with increasing returns in money input, then we can use this gambling technique to overcome that.

However most of the stages that plausibly strike me as increasing returns are where the input is in something like hours worked, rather than money and it doesn't look like you could use this.