The Meaning of Odds

According to @CJFDillow (via @diane1859) "Paddy Power say there is twice as much chance of alien life being discovered this year as of Arsenal winning the quadruple: 40/1 vs 80/1"

Chris's interpretation of the odds offered by bookmakers such as Paddy Power is that they reflect the subjective probability of certain events - either as determined by the bookmakers themselves or as determined by "the wisdom of crowds".

But I prefer to think that these odds merely reflect a lower elasticity of demand on silly wagers, indicating the irrationality of those who bet on such events. Perhaps Paddy Power reckons that the number of people betting on aliens is likely to be largely unaffected by the odds (economists call this an inelasticity of demand), in which case there is no incentive for the bookmakers to offer more favourable odds, or even to devote much effort to calculating more accurate odds.

Missouri loses bellwether status

As was widely predicted, Missouri has lost its bellwether status [BBC News, 21 November 2008]. For only the second time since 1904, Missouri voted for the losing candidate in the presidential election. Aw, shucks! Immediately after the election, David McCoy pointed out that the concept of bellwetherhood was Bad Statistics. It is also bad inductive reasoning to suggest that something is unlikely because it hasn't happened before, or that something is remarkable because it is unlikely. J.R. Lucas (author of several books of philosophy including The Concept of Probability) used to call this the Dover Fallacy.

There was a young curate of Dover Who bowled twenty-five wides in an over, Which had never been done By a clergyman’s son On a Tuesday in August in Dover.

The BBC reports Larry Sabato, Professor of Political Science at the University of Virginia, as saying that trying to identify bellwethers may not be a worthwhile enterprise. But if you search for "Larry Sabato bellwether" you can find what appear to be many attempts by Professor Sabato to do just that for various state and national elections including the most recent.

• Virginia's Bellwethers May Point the Way to Victory and Defeat (2001)
• WA-SEN: Sabato Pegs Cantwell Race as Bellwether (2006)
• N.C. a presidential bellwether? (July 2008)
• Battle for Votes in Bellwether Ohio (October 2008)

Glad to see a professor willing to change his mind about something. Meanwhile, there is apparently some status involved in being a bellwether state. Now I don't know a lot about herding sheep, but I think the way it works is that if you are herding sheep you only need one bell, but if you are herding goats you need one bell for each goat. Perhaps having a bell around its neck made Missouri feel more important than the other sheep. Now people are already discussing how to get Missouri its bell back.

• What killed Missouri's bellwether status? (Saint Louis Beacon)
• Missouri: Promoting Diversity Key to Reclaiming Bellwether Crown (Moderate Voice)
• So Long Bellwether Status (Midwest Voices)

Listen Missouri, you don't need this. Did you know that the bellwether was originally a castrated ram? Or you could always try astrology instead: Reclaiming our Revolutionary Roots.

 

See also You Don't Need to be Smart Here (October 2008)