Is John Kerry a dangerous pick?

In my previous post, I introduced the concept of idea futures exchanges. Now I want to talk about a particularly interesting application of those exchanges: measuring correlation between two events.

Let me explain what I mean. Say Event A has a probability of 50%, and Event B has a probability of 10%. If the two events are totally uncorellated, you'd expect the odds that both Event A and Event B will happen to be 50% x 10% = 5%. Suppose you want to measure whether the two events are in fact correlated. You create a contract, C, which pays out on the condition that both A and B pay out.

However, say C actually ended up trading at $0.09, rather than the expected $0.05. You can draw a probability table thusly:

	A	Not A
B	9%	1%
Not B	41%	49%

Notice the A column adds up to 50%, the B row adds up to 10%, and the topleft cell, which corresponds to events A and B coming true, has a value of 9%, or the price of C.

What does this table tell us? Well, it tells us that of the circumstances where A comes true, B comes true 9/50 = 18% of the time. Of the circumstanes where A does not come true, B only happens 1/50 = 2% of the time. Thus, the result of A is an extremely strong predictor of whether B will also happen.

This has an implication for public policy decisions. If you have two contracts, one which corresponds to an important decision, like, say, if the U.S. reelects Bush in 2004 (Bush04), and another which corresponds to a very undesirable event, such as a nuclear attack on U.S. soil by the year 2010 (NukeUS), you might be interested in whether there is any correlation between the two events.

Someone has created a contract to determine just that: GBNuke, which pays out if George Bush is reelected and the U.S. is not nuked by 2010.¹ The current market prices are as follows:

Bush04: 53
NukeUS: 21
GBNuke (Bush04 and not NukeUS): 48

That gives us the following probability table:

	Bush04	Not Bush04
NukeUS	5%	16%
Not NukeUS	48%	31%

In other words, the odds of a nuclear attack on U.S. soil are 5 / 53 = 9.4% if Bush is elected, and 16 / 47 = 34.0% if Bush is not elected, meaning that the U.S. is over three times as likely to be nuked by 2010 if Kerry is elected than if Bush is reelected.

A poster on the Foresight Exchange's discussion list recently observed this anomaly, and a very interesting discussion ensued, where various theories were floated to explain it.²

There are several facts to keep in mind when looking at this data. The first is that the usual distortions may apply, in particular the fact that NukeUS and GBNuke are both contracts which may not expire for up to five and a half years, so their prices may be somewhat detached from their actual probabilities as a result.³ Also, the unpredictable nature of nuclear terrorism makes it very difficult to discern accurate probability estimates, never mind determining accurate estimates of correlation between nuclear terrorism and the odds of particular election results.

Nevertheless, if we assume the prices reflect actual probabilities, there is still the very important question of causality. In other words, just because election of John Kerry is correlated with a higher chance of nuclear terrorism, that doesn't mean that it would cause that higher chance. Logically, it is possible that there is some underlying circumstance or set of circumstances which has a causal affect on both Bush04 and NukeUS.

One such circumstance could be the mindset of the American people. In other words, it could be that an election of John Kerry could signify a more complacent attitude toward terrorism. Then, the election of Kerry per se might not directly increase the odds of a nuclear attack, but it might be symptomatic of an overall attitude by America which would make nuclear terrorism more likely.

A contrary explanation could be that Kerry is perceived by the American people as better at fighting terrorism, and if nuclear terrorism is a real possibility, the American people are going to elect Kerry. On the other hand, if nuclear terrorism is not a real possibility, voters will concentrate on what they perceive as more important issues such as the economy, and vote for Bush. But this contradicts opinion polls which give Bush more confidence in waging the War on Terrorism, and put him behind on issues such as the economy.

There are many other possible ways to interpret these numbers, many of which are talked about in the discusson thread I mentioned earlier. It is quite interesting to note how very few of the posters can actually bring themselves to interpret these numbers favorably for Bush! Some have even gone so far as to suggest that Bush is in bed with Saudi royals, discouraging Arab terrorists from waging war on the U.S.! Uh huh...

My personal theory is that electing Kerry would cause quite an increase in America's vulnerability, because I support Bush's view of the War on Terrorism and I don't think Kerry would provide the leadership necessary to wage the war correctly, broadly targeting all terrorist organizations and their state sponsors. I also think there is something to the theory of complacency: i.e., a vote for Kerry signals that the American people are tired of worrying about terrorism, and that this will have effects in anti-terrorism policy beyond simply the election of Kerry.

Since nobody else is commenting, I just wanted to say that I thought these last two posts are great, and fascinating.

Also, that's important to remember that these numbers don't necessarily represent The Truth, but they represent the aggregate of the opinions of people willing to back their opinions up with money. They're often not the same thing, depending on how much of The Truth is known or knowable.

But, it is interesting, anyway.

I'm glad you liked the posts.

I'm thinking of writing a followup to explain how more accurate implied probabilities can be extracted from these prices, given knowledge of the Foresight Exchange market. My analysis shows that taking into account these effects gives an even worse estimate for Kerry.

A related thing is sports betting.

A lot of people think that when a football team is favored by 7 points, it means that experts have declared that that's the real advantage one team has over the other.

The truth is that the bookmakers don't want to gamble. They want as much money bet on one side of the "line" as the other (because they collect a commission from the winners). They set an initial line that they think will accomplish this, but then the line changes as people place their bets.

At the end, the line represents the collective opinion of betters.

Actually, Intrade is just a brand name for TradeSports. They're run out of Ireland, and they originally started just as a sports betting site, but have since expanded to other purposes, and have deployed the Intrade web site for convenience for traders such as myself who want to concentrate on political/financial/current events.

There are traders who act as "market makers" on TradeSports/Intrade, just as in any exchange, placing orders in both directions, so that they can make money on the "spread" (the difference between the bid and ask price). The difference between them and a bookie is that they have to compete with every other trader in real-time, so they have to offer more competitive spreads, as well as make sure to price their orders around the true market price.

the link to

http://forum.javien.com/conv.php?new=true&convdata=id::4vfHES49-n3ds-SNGm-zMhY-0pJA8ITMzPFq

gives no content. Is it no longer possible to access the
Javien archive for fx-discuss ?

Here is a copy of a mail which I sent to randall_burns :




I just found this thread in the archive. For some reason I can't subscribe to fx-discuss.
I've been probably one of the most active traders in GBNuke since it started.

One point which you haven't mentioned (maybe it was mentioned in some later posts,
I can't check the loong thread) is, that claims with zero probability don't trade at zero
when there are several years until they are judged. See true07 with high volume.

So you must subtract about 8 points from the value to get the probability !

That makes it a bit less probable of US being nuked if Kerry is elected. :-)

I'm speculating that GBNuke will trade at about 80, when Bush wins.

Note, that NukeUS -Yes is paid immediately, when US is nuked, while
No is paid only in 2010. This makes yes-shares more attractive
and results in another probability reduction for US being nuked
(or better: FX-market estimate of this)

Also, you better take the average of the 3 prices over some period
rather than instant values.


regards, fx2km(4823)