How to fix the Veil of Ignorance?

One of the most classic ideas in philosophy (right up there with trolley problems, Omelas and teletransportation) is the veil of ignorance. It’s one of those ideas so simple and elegant, it’s strange to think that nobody had articulated it until the twentieth century. But the idea isn’t perfect. It’s got at least one gap I’d like to address; after eighty years, maybe the veil of ignorance is overdue for a patch version 1.1.

First, though, I’d like to establish my lack of credentials. The minds behind the veil of ignorance were intellectual titans; I’m just a guy with a tendency to care about philosophical minutia and a tenacity for trying to debunk bad arguments (like the SIA) and refine good ones. So before I try to step on the shoulders of giants, I’d like to give them credit.

Proper credit.

Economist, physicist, and legal scholar (whose last name isn’t an economist-iscal coincidence; he’s the son of Milton Friedman) posted last week a suggested defense of utilitarianism with a characteristically thoughtful idea at its heart, but an introductory line that has given me no choice but to cry foul:

The Veil of Ignorance argument, the idea of evaluating a society by how attractive it would be to be randomly placed in it, is usually credited to John Rawls but was proposed by John Harsanyi almost twenty years earlier.

I will not stand for this sort of slander to my man William Vickrey, who actually came up with the veil of ignorance eight years prior to Harsanyi’s independently developed formulation, in his 1945 Measuring Marginal Utility by Reactions to Risk.

Vickrey was an interesting guy. He was a Quaker pacifist who arguably invented congestion pricing. He would roller-skate to work at Columbia University, and would feign falling asleep during seminars only to burst out with questions (“perceptive and sometimes devastating”) when the lecturer wasn’t expecting it. When he earned the 1996 Economic Nobel Prize, he wryly stated:

I’ll try to make the most of the opportunity to keep spreading some of my heretical ideas.

…before dying to a heart attack three days after the Nobel Prize’s announcement and prior to actually receiving it.

Though that’s not to say John Harsanyi wasn’t any less interesting. Harsanyi co-won the 1994 Economic Nobel Prize with John Nash (the A Beautiful Mind’s titular mind) for work on game theory equilibria. In his younger days, he and his wife fled Soviet Hungary for being outspoken anti-Marxists; six years prior to that, Harsanyi had narrowly escaped a Nazis labor camp and survived the war hiding in a Jesuit monastery.

None of these men refined the veil of ignorance (to withstand adversarial hypotheticals like the one I present below) because I believe they were too busy working on more important things: Rawls revolutionizing political philosophy while Harsanyi and Vickrey advanced economics (sometimes to practical result, like Vickrey inventing the famed and oft-used sealed-bid second-price auction, which perfectly incentivizes bidders to bid with their true preferences). But now we’re living in a world where AI might be posed to seize power, and it’s not inconceivable to think that philosophy may be more important than ever before; maybe we’ll train AI to believe in the veil of ignorance, and when that happens, we’ll want proffer the most robust version of the veil as possible.

The unfairness of expected value

Rawls wrote in A Theory of Justice that “the principles of justice are chosen behind a veil of ignorance”, which is to say that in designing a just system, no one should ex-ante know “his place in society, his class position or social status, nor his fortune in the distribution of natural assets and abilities, his intelligence, strength, and the like”. Vickrey portrayed this as an “equal chance” of being any particular member, which Harsanyi explicitly defined as a “1/n” probability from a population of size n.

Say we’d like to determine which possible future world is better: One in which every person on the planet has to work 2 hours per day every day, or one in which 5/6 of the population are masters that never have to work, and 1/6 of the population are slaves that work 12 hours per day.

It’s obvious which world is preferable, but it’s not obvious if we try to rely solely on the veil of ignorance. Some utilitarians will look at the 1/n chance, and use Expected Value (which I’ve argued before is not always an infallible tool) to “shut up and multiply”, thus calculating that both worlds are identical.

In 2007, the state of Maine voted on whether to allow the Passamaquoddy Tribe to build a racing and gaming facility in Calais, Washington County, which borders one of the Passamaquoddy reservations, Sipayik. Polls showed an overwhelming 70% support from Washington County voters, 80% support from the city of Calais, and a tremendous 96% support from Sipayik.

“Imagine the indignity of being told by the people in this building that we don’t have a right to determine our own economic future.” — Senator Kevin Raye“We are not asking for government subsidies. We are asking for a chance to be economically self-sufficient.” — Madonna Soctomah, Passamaquoddy legislative representative“I can’t understand why it’s OK to have a racino in Bangor but not in Washington County and for our tribes.” — Senator Libby Mitchell

For this community to get the racing and gaming facility (or “racino”), they needed statewide approval. They had the support of Maine’s legislature (including a 22 to 15 for/against from Maine’s senate), but when it came to a statewide vote, they lost to a 52.3% no.

It’s likely that this measure would have passed if not for Mary Andrews and James B. Bartlett, citizens of Maine’s York County, a region which is essentially the opposite of Maine’s Washington County: on the opposite side of the state, with the second-most highest population and affluence as compared to Washington’s status as least populous and most rural county, and 18.5x fewer indigenous people per capita. In 2002, these two individuals founded the “Casinos No!” campaign to prevent the creation of a casino nearer to York. Over the following years, Casino No! funneled millions into opposing tribal casinos, including the 2007 Calais proposal. The Casinos No! campaign misleadingly implied that none of the casino money would benefit Calais or Maine, flowing only to the casino’s owners (not true) and also drew a spurious connection between the casino and rising crime.

I think it was right for Andrews and Bartlett to fight the construction of a racino near their home. But why fight the racino in Calais? Its job growth and economic boost would’ve brought prosperity to many locals, and not impacted most Maine residents whatsoever. Yet this local measure required statewide approval—why?

Any randomly selected citizen of Maine might plausibly be impacted by the construction of any given racino, so it’s not wrong to let all Maine citizens vote on such a measure. Even if that connection is unlikely, it’s not the government’s place to say, with high granularity, “You won’t be personally affected by this decision, so you’re not allowed to vote on it”, because along that path lies tyranny. But in a case like this, I think it’s obvious that the voice of people more affected should matter more. A more perfect system might amplify the votes of those who live closest to Calais.

I think this reflects a principle that comes pretty intuitively to people. A young brother and sister bicker over any perceived slight of unfairness, always demanding equal treatment from their parents. But the family’s ping pong table (shoved into one corner of their dusty garage, one side pulled up for solo practice) is mostly used by Sam, 80% of the time, while the family’s only desktop PC (with a CRT monitor and a backspace key that no longer works) is used by Sally 80% of the time. Sam is going to want a greater say over what happens to the ping pong table, while Sally will want the same for the computer.

When making a moral or political decision, the people most impacted should have a stronger say, proportionate to the degree of that impact.

Coming back to the veil of ignorance, and the balanced world versus a world of masters and slaves. What happens if we apportion the likelihood of being someone according to how much they’re impacted?

The final short piece of this post is free-walled. You don’t have to pay anything, just plop in your email if you want to see the conclusion of this post (and how the math works out):

The more plausible the bad argument, the more I want to debunk it. Any question, riddle or paradox where I once believed the wrong answer (like how I was once a Thirder to the Sleeping Beauty problem, or initially would have two-boxed in Newcomb’s) compels me to clear up the confusion, both for my own deeper understanding and to help any others who might fall into the same confusion.

I jest! I have absolutely nothing against David (and am a subscriber).