Re: Model of induction

Posted by Roger Critchlow-2 on Dec 12, 2016; 7:23pm
URL: http://friam.383.s1.nabble.com/Model-of-induction-tp7588431p7588437.html

Seems like the abduction step would be assuming that there are loaded wheels before you have any empirical evidence.

A wheel could be fat-tailed, tending to longer runs, without being biased toward any particular numbers.  There would be an incentive to bet on a run continuing, but no particular number would be more likely to have long runs.  That wouldn't be a loaded wheel in the usual understanding of crooked gambling devices.  But it would be the sort of device to encourage gamblers to believe they have a hot hand.

-- rec --

On Mon, Dec 12, 2016 at 2:06 PM, Frank Wimberly <[hidden email]> wrote:

Mathematical induction is a method for proving theorems.  "Scientific induction" is a method for accumulating evidence to support one hypothesis or another; no proof involved, or possible.

Frank

On Dec 12, 2016 11:44 AM, "Owen Densmore" <[hidden email]> wrote:

What's the difference between mathematical induction and scientific?

  https://en.wikipedia.org/wiki/Mathematical_induction

   -- Owen

On Mon, Dec 12, 2016 at 10:44 AM, Robert J. Cordingley <[hidden email]> wrote:

Based on https://plato.stanford.edu/entries/peirce/#dia - it looks like abduction (AAA-2) to me - ie developing an educated guess as to which might be the winning wheel. Enough funds should find it with some degree of certainty but that may be a different question and should use different statistics because the 'longest run' is a poor metric compared to say net winnings or average rate of winning. A long run is itself a data point and the premise in red (below) is false.

Waiting for wisdom to kick in. R

PS FWIW the article does not contain the phrase 'scientific induction' R

On 12/12/16 12:31 AM, Nick Thompson wrote:

Dear Wise Persons,

 

Would the following work? 

 

Imagine you enter a casino that has a thousand roulette tables.  The rumor circulates around the casino that one of the wheels is loaded.  So, you call up a thousand of your friends and you all work together to find the loaded wheel.  Why, because if you use your knowledge to play that wheel you will make a LOT of money.  Now the problem you all face, of course, is that a run of successes is not an infallible sign of a loaded wheel.  In fact, given randomness, it is assured that with a thousand players playing a thousand wheels as fast as they can, there will be random long runs of successes.  But the longer a run of success continues, the greater is the probability that the wheel that produces those successes is biased.  So, your team of players would be paid, on this account, for beginning to focus its play on those wheels with the longest runs.

 

FWIW, this, I think, is Peirce’s model of scientific induction. 

 

Nick

 

Nicholas S. Thompson

Emeritus Professor of Psychology and Biology

Clark University

http://home.earthlink.net/~nickthompson/naturaldesigns/

 

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