Reuters recently ran a story on political prediction markets, quoting prices from intrade and IEM. (Apparently the story was buzzed up to the Yahoo! homepage and made the Drudge Report.)

The reporter phrased prices in terms of the candidates’ percent chance of winning:

Traders … gave Democratic front-runner Barack Obama an 86 percent chance of being the Democratic presidential nominee, versus a 12.8 percent for Clinton…

…traders were betting the Democratic nominee would ultimately become president. They gave the Democrat a 59.1 percent chance of winning, versus a 48.8 percent chance for the Republican.

The latter numbers imply an embarrassingly incoherent market, giving the Democrats and Republicans together a 107.9% chance of winning. This is almost certainly the result of a typo, since the Republican candidate on intrade has not been much above 40 since mid 2007.

Still, typos aside, we know that the last-trade prices of candidates on intrade and IEM often don’t sum to exactly 100. So how should journalists report prediction market prices?

Byrne Hobart suggests they should stick to something strictly factual like "For $4.00, an investor could purchase a contract which would yield $10.00" if the Republican wins.

I disagree. I believe that phrasing prices as probabilities is desirable. The general public understands “percent chance” without further explanation, and interpreting prices in this way directly aligns with the prediction market industry’s message.

When converting prices to probabilities, is a journalist obligated to normalize them so they sum to 100? Should journalists report last-trade prices or bid-ask spreads or something else?

My inclination is that bid-ask spreads are better. Something like "traders gave the Democrats between a 22 and 30 percent chance of winning the state of Arkansas". These will rarely be inconsistent (otherwise arbitrage is sitting on the table) and the phrasing is still relatively easy to understand.

Avoiding this (admittedly nitpicky) dilemma is another advantage of automated market makers like Hanson’s. The market maker’s prices always sum to exactly 100, and the bid, ask, and last-trade prices are one and the same. Auction-type mechanisms like intrade’s can also be designed better so that prices are automatically kept consistent.

The problem with this kind of arguing is that there are factors other than the odds, and those factors are hard to determine. The confidence people have in their ability to get their money if they win, the speed at which the exchange clears transactions, the legal status of gambling, the tax status of their gains, and the possible returns of other investment opportunities, all play a role in determining prices.

Instead of a footnote to this effect under every mention of the ‘odds’ versus the price, it would be better (in my opinion) to just state the outcomes. When the media talk about stock options, they say they give the right to buy the stock at X price on Y date, giving a particular profit if by that time the stock has risen to Z. They rarely take us through the Black-Scholes. Somehow, this is enough to get the idea across, but doesn’t stop professionals from using more powerful and precise tools.

The strictly factual description is great for educating people about prediction markets, but too long and requires too much parsing in nearly all “reporting” contexts I imagine.

Any market with a large bid/ask spread is probably too illiquid to bother reporting. If the market is liquid, the spread doesn’t add much information, again for typical “reporting” uses, e.g. everyday financial reporting uses last trade.

Better market technology is badly needed in any case.

Byrne, while I agree “percent chance” glosses over many factors, I still think it’s the most succinct and understandable way to state the “prediction” part of a prediction market.

Mike, you may be right. Without the typo, the Reuters numbers would probably have been within 0.2% or so of adding up “correctly”.