Prediction Markets This Morning

I was feeling optimistic for the first time in a while about Senator Obama's chances for the Democratic party nomination, so I headed over to Intrade to see what the prediction markets were saying. I was a little surprised when I saw the following prices:

1. Hillary Clinton as Democratic nominee: 29.9
2. Hillary Clinton as General Election Winner: 21.5

This means that the Intrade market thinks that Clinton has a 29.9% chance to secure the Democratic Party nomination and a 21.5% chance to win the election. To see why these numbers are surprising, consider the following equation:

P(2) = P(2 | 1) P(1) + P(2|~1) P(~1)

That is, the probability of Clinton being elected is equal to the conditional probability of her winning in the event that she gets the nomination plus the conditional probability of her winning in the event that she doesn't. Since we know that she almost certainly can't win the election without getting the nomination, we know everything in the equation except for P(2|1). If we plug in the numbers we have from Intrade and solve, we find that the market's estimation of Clinton's chances of winning the election if she gets the nomination is 0.215 ÷ 0.299, or about 72%.

This seems amazingly high to me, in light of the fact that Clinton has not had a commanding lead in head-to-head polls. Moreover, McCain is trading at about 32% to win the general election, which suggests that one or both of them are overvalued (since 32% + 72% = 104%).

In practical terms this suggests that there is an opportunity for arbitrage in these markets. If a market were showing 32% and 72% for two mutually exclusive outcomes, for instance, you could bet against both of them for $96 and be guaranteed of winning $100, for a risk-free gain of $4. In practice this never happens because traders quickly recognize such absurdities and arbitrage them away. Unfortunately, I can't find a similarly sure-fire strategy for hedging irrational conditional probabilities. There are some strategies with positive expectation values, to be sure, but all of them have some scenarios in which they generate a loss (unlike the case above). This could mean one of (at least) two things:

1. I haven't looked hard enough (entirely possible, since I have a lot of other stuff to do).
2. I've botched the analysis (wouldn't be the first time).
   
3. Prediction markets can support irrational values for conditional probabilities implied by related (but independently traded) claims.

Thoughts?

Siegel on the Stars and Bars

My good friend Mike Siegel takes on the Confederate Flag in South Carolina

Mike makes two observations:

(1) Even if the Civil War wasn’t “about” slavery, the issue was so entrenched with the war, the distinction is academic. Without slavery, there would have been no war.

(2) It doesn’t matter if blacks’ offense at the Confederate flag is rational or not. The flag is supposed to represent all the people of the state. If some fraction finds the flag offensive — whether their offense is reasonable or not — it should be changed.

It's pretty hard to argue that the Civil War wasn't about slavery, especially in South Carolina. Consider the following snippet from South Carolina's Articles of Secession:

[p17]
The Constitution of the United States, in its fourth Article, provides as follows:

[p18]
"No person held to service or labor in one State, under the laws thereof, escaping into another, shall, in consequence of any law or regulation therein, be discharged from such service or labor, but shall be delivered up, on claim of the party to whom such service or labor may be due."

[p19]
This stipulation was so material to the compact, that without it that compact would not have been made. The greater number of the contracting parties held slaves, and they had previously evinced their estimate of the value of such a stipulation by making it a condition in the Ordinance for the government of the territory ceded by Virginia, which now composes the States north of the Ohio River.

This is the first substantive issue raised in the document, and it recurs throughout. To me, that says that it was the most important issue on their minds.

On the other hand, I don't think that the display of the confederate flag today is about slavery or even racism. I think it stems more from the fact that all people, regardless of their station in life, want to believe that they are descended from distinguished and honorable forebears. I expect there is no history so infamous that the descendants of the perpetrators will not try to whitewash it, or failing that suppress it.

I'm generally sympathetic to this impulse. It seems unjust to hold people responsible for events in which they had no say. However, distorting the historical record is the wrong way to deal with the problem. The right way involves a frank admission of what happened in the past, a recognition that we are not our ancestors, and a resolve that we will be better than they were. That, however, is a lot of verbiage, so maybe we need a name for the concept that is a little punchier, something like "Truth and Reconciliation". It has kind of a ring to it.

That said, I do have to object to the "whether they are reasonable are not" comment. Surely what we mean by an "unreasonable" objection is that it should not be heeded. If not, then I wonder, what exactly is the difference between a reasonable and an unreasonable objection? Furthermore, rejecting any standard of reasonableness when "some fraction of the population" objects to something seems like bad policy. Surely there exists a fraction that is too small or an objection that is too wacky to merit serious consideration. The point is that that's not the case here. Trying to weasel on whether or not the objections are reasonable only weakens the argument.

The Daily Show - Wait and Switch

The Daily Show takes on lobbyists. Apparently there is a law afoot (for now, still just a bill) that would prohibit lobbyists from hiring people to wait in line for front-row seats at meetings of committee meetings and the like. My question: who wins and who loses if this bill passes?

First, let's set aside the notion, compelling though it may be, that lobbyists are anthropomorphic pond scum bent on buying out our government. There are good causes, and there are bad causes, all of which have lobbyists. For example, I once met a lobbyist for the National Science Foundation. I presume we can all agree that we're in no danger of the government selling out to… the government.

In fact, consider this: there are 300 million people living in this country. With only 535 members of the two houses of Congress, that's roughly 600,000 apiece. If a legislator spends all day, every day, 365 days a year talking to citizens, never stopping to sleep, that would give us each about 50 seconds a year to make our concerns known--to just one member out of 535. Clearly, we can't all go up to Capitol Hill and make our concerns known. What we can do, however, is to get together with a bunch of like-minded people and hire a spokesman to go up to Capitol Hill for us and tell our concerns to as many Congresspeople as will listen. That is, we could hire a lobbyist. In this sense lobbyists perform a valuable service. Without them, only a select few would get to express their views to the Congress, and I have a hunch that it wouldn't be you and me.

It's not a perfect system, I concede. People with more money can hire more and better lobbyists. Some lobbyists engage in questionable practices, if not out-and-out bribery; however, sadly, it's the best we've got.

But, we were talking about the effects of the new (proposed) law. It turns out that you have to wait quite a long time to get into these meetings where you can get on with educating legislators, expressing concerns, and whatnot. And it turns out that good lobbyists are in demand, so they command shockingly high salaries (as anyone who has competed in the housing market in the DC area will ruefully tell you). Consequently, having them wait around in a queue for the legislators to show up is a tremendous waste of money. Better to hire a bike messenger (or even an "unemployed puppeteer") at much less cost to wait while the expensive guy does something productive (inasmuch as the deadweight losses associated with influencing government can be considered "productive" -- work with me here).

So, what happens if you can't hire cheap placeholders for the line? Well, then you have to have the actual lobbyists do it, which means that each one accomplishes a lot less in a day. Equivalently, lobbying gets a lot more expensive. Who loses from this (apart from the placeholders themselves, of course--apparently the pay is pretty good)? At the margins, every cause will consume less political lobbying, but for interest groups who can already can afford to do only a little bit, that marginal decrease translates to a huge reduction in their effectiveness at influencing policy. Conversely, well-funded interests may at the margin get fewer hours of face time with legislators, but will overall be more effective due to reduced competition from other interests.

Conclusion: Congressmen Cohen's bill, however well-intentioned it may be, will probably have the effect of concentrating influence in the best-funded special interest groups while driving niche interests out of the political process.

Free Trade and Fair Trade on EconTalk

This week's EconTalk sees the return of my favorite guests, Mike Munger, to talk about Free Trade and Fair Trade. Munger has the best quote of the podcast (arguably any podcast) when he says, "I'm a big coffee drinker. Sometimes I apply it topically."

Apart from Munger's offbeat sense of humor, the interview is one of the best discussions I've seen in a while of the mechanics of how trade creates wealth for the parties involved and why attempts to channel extra wealth to one of the parties through Fair Trade premiums don't always work out as expected. They also address the common misconception that trade is a zero-sum process in which nations compete to capture as much as they can from a fixed-size pool of jobs. It's well worth a listen, if you have 58 minutes to spare.

Virtually Everyone is Sincere, but They Still Can't Agree

Over at EconLog, Bryan Caplan makes a discovery:

Since the publication of my book, I've been meeting a much wider range of people.
...
What have I learned? Primarily, I'm more convinced than ever that virtually everyone is sincere.

This is not terribly surprising to me. Robert Heinlein said it a long time ago: "Your enemy is never a villain in his own eyes Keep this in mind; it may offer a way to make him your friend," and he doubtless ripped that off from somewhere else much older. So, if we're all sincere, why do we disagree so vehemently, particularly about issues of politics? Caplan continues:

Even when you've got undeniable facts on your side, your opponents probably think that those facts don't matter...

I think Caplan is on to something here, but I think he doesn't go far enough. Often you won't even be able to get your opponents to agree on the facts in question. What fraction of taxes are paid by "the rich"? Does the Canadian health care system make people wait a long time for treatment or doesn't it? These are strictly positive questions that should have answers that everyone can agree on. Yet, when you listen to people argue about the issues surrounding these questions, often their versions of the facts are so different that if you didn't know better you'd conclude that they must live in two very different countries.

Even if we could agree on the facts, there would still be plenty of room for disagreement over the normative aspects of the problem, but if you can't agree with your opponent over the basic facts surrounding the problem, then the argument probably isn't worth having in the first place.

What price, voting?

At the Freakonomics blog, Ryan Hagen asks, Is it Smarter to Sell Your Vote or Cast It? A recent poll asked students at NYU whether they would sell their right to vote either in the next election or in perpetuity for a variety of proposed compensations. It turns out that over 60% of them would sell their 2008 vote for a year's tuition, and around 50% would sell their vote in perpetuity for $1 million.

What is a vote really worth? The poll questions seem to concentrate solely on the supply side (i.e., what would students sell their votes for, irrespective of whether there is anyone actually willing to pay that), which would suggest that we're trying to get at voters' personal valuation of their voting rights, all else being equal. So, let's assume that this opportunity is being offered to me only. The effect of my individual vote on the election's outcome is for all practical purposes nil, so from the standpoint of influencing the results of the election it is worth nothing. However, I do derive some personal satisfaction from voting that, on reflection, I'd value at a few tens of dollars; $50 would be a reasonable estimate. So, I should be willing to sell my vote for anything more than $50 (although I'd try to get the best price I could, of course). To sell my vote in perpetuity I'd want the discounted value of all of those future $50 votes. At first blush I might want some sort of risk premium, in case there might be some election in the future that I really want to influence, but since my probability of successfully influencing such an election is so small, that component is basically negligible. Depending on what discount rate you assume, that works out to about $2000 (assuming only one vote per year; if you include primaries and such it could come to several times that). Considering how many people voluntarily abstain from voting for no compensation at all, that seems like a reasonable number.

If we consider the possibility of the same deal being offered to everybody, then it gets a little harder to calculate a reasonable price. It's not too difficult to come up with our buying price for such a scenario. One or another candidate is bound to favor policies that will either cost us money directly or eliminate some benefit that we previously enjoyed. With a little work we could attach a value to those policy differences. To use myself as an example, my interaction with the government is primarily through taxes, but some policies might affect the costs of things I use. Let's say, for the sake of argument, that the present value of the benefit comes to $20k (although the fact that I would have a hard time telling you which side provides the benefit suggests that the number is actually much smaller than that). Suppose it takes about 5M votes to change the results of a large election. Then we're looking at about half a cent per vote. Clearly vote buying isn't a good strategy for little old me. For someone more entangled with government the total would be higher; someone standing to gain a billion dollars from having his candidate elected should be willing to pay $200 per vote in our example.

Clearly a rational selling price should be higher than the buying price, but how much? The total benefit from the preferred candidate winning provides an upper bound, since that price fully compensates the seller for having the unfavorable candidate win, but should he be willing to accept less? That depends on the probability that the seller and others like him will actually change the results of the election through the sale of their votes. For example, if you think there are 10:1 odds against your vote sale affecting the election, then you might be willing to accept $2000 for your vote. The exact odds calculation depends on who's buying and what their motivation is, but something in the $1k - $10k range seems plausible. One of the commenters at the Freakonomics site opines that the bid-ask spread in vote-buying is likely to be large. Evidently, this is borne out by our analysis.

For selling your vote in perpetuity in this scenario, risk comes to the fore. You may be fairly confident that the value of this election to you is small, but what about all future elections. What if Dr. Evil decides to run in 2024? In this case the risk premium you would have to assign is large enough that the practical answer is "not at any price".

My takeaway from all of this is the result that although the right to vote is precious to residents of a democracy, the act of voting itself is of little value to us. This result seems curious, but it makes a kind of sense. The right to vote ensures that in a broad sense candidates are aligned with the will of the voters in a way that they generally aren't in nondemocratic governments, so voting rights serve a useful purpose. Once that is established, however, the purpose of democracy has been served, and actually going to the polls to vote serves no further purpose.