Thursday, 13 March 2014

Bragging rights contest – Pick the South Australian election winners

A little contest to test your political wisdom when the votes come in from Adelaide on Sunday night. Mark your assessment of the Liberals winning in every seat and the honour and glory could be yours.
In keeping with The Owl’s desire to be the thinking person’s political blogger the contest is not completely straight forward. We have chosen the methodology of the wonderful Probabilistic Competition that the smart people of Monash University run each year on the AFL. I’ll defer to their explanation of the scoring:
The probabilistic competition involves the tipper entering the probability (between 0 and 1) that they believe a team will win the match. It is sometimes also referred to as the information theoretic or info competition. The father of information theory was Claude Shannon.
In a traditional tipping competition, the tipper is forced to choose one team as the outright winner. However the tipper still believes that the other team does have some chance, just not as much as the team they chose. (In closely matched games, you may even think it will be a draw.) Choosing a probability allows the tipper to express their uncertainty or confidence level in the outcome.
It can be simply proven that the highest expected score can be achieved by tipping the true probability. (Even though the true probability is never known.)
The scoring system works as follows: If the tipper assigns probability p to team A winning, then the score (in “bits”) gained is:
  • If A wins: 1 + log2(p)
  • If A loses: 1 + log2(1 - p)
From the above we can see that the maximum gain of 1.0 is obtained by tipping 1.0 on the winning team. This however is very risky as maximum loss of -Infinity is achieved by tipping 1.0 on the losing team.
The scoring is not symmetrical and can be very non-intuitive for the beginner. The table below gives example tips and the scores (in bits) you would receive if your team won and if your team lost. Note that p values less than 0.5 are equivalent to tipping the other team with 1.0-p. Also, p=0.5 is equivalent to sitting on the fence – you neither gain nor lose any bits. Some examples:
2014-03-13_effectofp


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