Fisher/Dembksi versus Bayes/Sober

The following is repeated from something I wrote in 2006 for talk.reason as it has come up in  a recent discussion on UD.


“So far we have established that the use of specifications to reject chance hypothesis has some problems of interpretation and has no justification, while comparing likelihoods seems to account for our intuitions and is justified. Dembski is well aware of the likelihood approach and has tried to refute it by raising a number of objections elsewhere, notably in chapter 33 of his book "The Design Revolution" which is reproduced on his web site (Dembksi 2005b). But there is one objection that he raises which he considers the most damning of all and which he repeats virtually word for word in the more recent paper. He believes that the approach of comparing likelihoods presupposes his own account of specification.

He illustrates his objection with another well worn example in this debate — the case of the New Jersey election commissioner Nicholas Caputo who is accused of rigging ballot lines. It was Caputo’s task to decide which candidate comes first on a ballot paper in an election and he is meant to do this without bias towards one party or another. Dembski does not have the actual data but assumes a hypothetical example where the party of the first candidate on the ballot paper follows this pattern for 41 consecutive elections (where D is democrat and R is republican)

DDDDDDDDDDDDDDDDDDDDDDRDDDDDDDDDDDDDDDDDD

This is clearly conforms to a pattern which is very demanding for the hypothesis that Caputo was equally likely to make a Republican or Democrat first candidate. In fact it conforms to a number of such patterns for 41 elections, for example:

  1. There is only one republican as first candidate.
  2. One party is only represented once.
  3. There are two or less republicans.
  4. There is just one republican and it is between the 15th and 30th election.
  5. Includes 40 or more Democrats.

And so on.

Dembski has decided that the relevant pattern is the last one. (This is interesting in itself as it is a single-tailed test and assumes the hypothesis that Caputo was biased towards Democrats. Another alternative might simply have been that Caputo was biased — direction unknown — in which case the pattern should have been "one party is represented at least 40 times"). His argument is that when comparing the likelihoods of two hypotheses (Caputo was biased towards Democrats or Caputo was unbiased) generating this sequence, we would not compare the probability of the two hypotheses generating this specific event but the probability of the two hypotheses generating an event which conforms to the pattern. And we have to use his concept of a specification to know what the pattern is. But this just isn’t true. We can justify the choice of pattern simply by saying "this is a set of outcomes which are more probable under the alternative hypothesis (Caputo is biased towards Democrats) than under the hypothesis that Caputo is unbiased". There is no reference to specification or even patterns in this statement.

This is clearer if we consider a different alternative hypothesis. Suppose that instead of suspecting Caputo of favouring one party or another we suspect him of being lazy and simply not changing the order from one election to another — with the occasional exception. The "random" hypothesis remains the same – he selects the party at random each time. The same outcome:

DDDDDDDDDDDDDDDDDDDDDDRDDDDDDDDDDDDDDDDDD

counts against the random hypothesis but for a different reason — it has only two changes of party. The string:

DDDDDDDDDDDDDDDDDDDDDDRRRRRRRRRRRRRRRRRRRR

would now count even more heavily against the random hypothesis – whereas it would have been no evidence for Caputo being biased.

So now we have two potential patterns that the outcome matches and could be used against the random hypothesis. How do we decide which one to use? On the basis of the alternative hypothesis that might better explain the outcomes that conform to the pattern.

The comparison of likelihoods approach is so compelling that Dembski himself inadvertently uses it elsewhere in the same chapter of The Design Revolution. When trying to justify the use of specification he writes "If we can spot an independently given pattern…. in some observed outcome and if possible outcomes matching that pattern are, taken jointly, highly improbable …., then it’s more plausible that some end-directed agent or process produced the outcome by purposefully conforming it to the pattern than that it simply by chance ended up conforming to the pattern."

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1 Response to “Fisher/Dembksi versus Bayes/Sober”


  1. 1 uncommondescentdissent November 10, 2010 at 2:30 am

    Hi Mark,
    My link to you is enabled.


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