Here is a link to my appearance on the Bob Murphy show.
Monthly Archive for November, 2018
A commenter in another thread wanted to talk about trolls, so I’m opening up a new post where they’ll be on topic.
The specific trolls I have in mind operate toll-booths (or troll-booths?), both of which you must pass through to get from Hereville to Thereville. The question is whether you, as a traveler, prefer to have both booths controlled by a single troll, or by separate trolls. (This is Problem 12 in Chapter 3 of Can You Outsmart an Economist?.)
(SPOILER WARNING!)
(Note from the proprietor—I am delighted to present this guest post from my correspondent William Carrington, who might or might not have been inspired by the puzzles in Chapter Nine of Can You Outsmart an Economist?. — SL)
Like zombies and Russian spies, there are more economists among us than you might think. This can be dangerous because studies show that economists are more likely than normal people to graze their goats too long on the town commons, to rat out their co-conspirators in jailhouse interrogations, and to show up drunk on their last day at a job. This appears to be both because unethical people are drawn to economics and because economics itself teaches people to be both untrusting and untrustworthy. This feedback loop has led to the creation of famously difficult economists like John Stuart Mill and….well, it’s a long list. Like halitosis and comb-overs, the problem is worse in Washington.
Can you protect yourself against this unseen risk? Sadly, no, as economists often look all too normal and are hard to pick out from the maladjusted crowds that attend us. This is known as the identification problem in economics, and Norway’s Trygve Haavelmo was awarded a Nobel Prize for his work on this issue. Related work by Ken Arrow, also a Nobelist, proved that an infinitesimal group of economists will bollix up the welfare of an arbitrarily large population of otherwise normal people. It’s most disheartening, but I’m here to offer you a failsafe method for identifying economists. You’ll need an old refrigerator.
In honor of the forthcoming visit of Glen Weyl to the University of Rochester, I thought I’d offer a post explaining the idea behind one of Glen’s signature policy reforms: quadratic voting.
Suppose we’re going to hold a referendum on, say, whether to build a street light in our neighborhood.
The problem with giving everybody one vote is that (on both sides of the issue) some people care a lot more about that street light than others do. We’d like those who care more to get more votes.
In fact, we’d like to allocate votes proportional to each voter’s willingness to pay to influence the outcome. There are excellent reasons to think that willingness-to-pay is the right measure of “caring”. Those reasons will be evident to readers with some knowledge of welfare economics and opaque to others, but it would take us to far afield for me to get into them here. (For the record, if you’re encountering this measure for the first time, you’re almost surely raising “obvious” objections to which there are non-obvious but excellent rejoinders.) For this discussion, I’m going to take it as given that this is the right way to allocate votes.
Here’s the problem: If I allocate votes based on willingness to pay, people will simply lie. If you’re willing to pay up to $1 to prevent the street light, but know that you can get more votes by exaggerating your passion, that’s what you’ll probably do.
Okay, then. If we want to allocate votes based on willingness to pay, then we have to make people actually put some money on the table and buy their votes, thereby proving that they care. We could, for example, sell votes for $1 each. That way, people who care more will buy more votes and have more influence, as they should.
Unfortunately, that’s not good enough. If you care more about the issue than I do, you might buy more votes than I do — but there’s no reason to think you’ll buy more votes in direct proportion to your willingness to pay. Let’s suppose, for example, that the ability to cast a vote is worth $2 to you and $4 to me. Then I should get twice as many votes as you. But if votes sell for $3, I might buy quite a few, whereas you’ll buy none at all. That’s a lot more than twice as many.
So let’s try again: Instead of selling votes for a fixed dollar amount, we sell them on an increasing scale. You can buy one vote for a dollar, or two votes for four dollars, or three votes for nine dollars — and we’ll even let you buy in tiny fractions, like 1/10 of a vote for a penny. The price you pay is the square of the number of votes you buy. That’s the definition of quadratic voting.
Why the square, as opposed to the cube or the square root or the exponential? There really is something special about the square. To appreciate it, try an example: If a vote is worth, say, $8 to you, you’ll keep buying additional votes as long as you can get them for less than $8 each, and then stop. With quadratic voting, one vote costs you a dollar. You’ll take it! A second vote costs you an extra $3 (bringing the total to $4). You’ll take that too! A third vote costs you an extra $5, a fourth costs you an extra $7, and a fifth costs you an extra $9. So you’ll buy 4 votes and then stop. You can similarly check that if a vote is worth $24 to your cousin Jeter, Jeter will buy twelve votes and then stop. Jeter cares three times as much as you do, and he buys three times as many votes. And with a little calculus, you can check that if Aunt Murgatroyd’s vote is worth four or five or nine or twenty times more to her than your vote is to you, she’ll buy exactly four or five or nine or twenty times as many votes as you do. That’s exactly what we wanted. In that sense, this voting scheme works — and, except for minor variations, it’s the only scheme that works.
