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Jimbo
10-09-2002, 11:24 AM
I discovered last night that the Taft-Hartley act about to be invoked by President Bush has been used 11 times in the past. It is generally accepted that in only three of these eleven instances was it successful in settling the labor dispute. The last time it was used is 25 years ago by then President Carter to settle a coal miners strike where it led to a successful labor agreement.

My question is what is the probability that it will be successful in this instance. Is it simply the ratio of 3 to 11 or is there more to it than that? For general information the act was established in 1947 and utilized 11 times in the first 30 years. I do not know which of the 11 invocations were successful other than the last one as mentioned above. Would this be pertinent information to the calculation?

Many Thanks in advance to all who respond.

Jimbo

Mike Haven
10-09-2002, 12:24 PM
if you could find the exact order of successful (S) and unsuccessful (U) invocations this could be perfect for a markov chain prediction

can you find out and write UUUSUUS ... etc?

(see http://www.twoplustwo.com/forums/showflat.php?Cat=&amp;Board=probability&amp;Number=148455&amp; Forum=All_Forums&amp;Words=Mike%20Haven&amp;Match=Username &amp;Searchpage=3&amp;Limit=25&amp;Old=allposts&amp;Main=148455&amp;Se arch=true#Post148455 for an example of a markov chain)

10-09-2002, 03:56 PM
&gt; i don't think anyone has bothered their ass to count all the vowels ...

I think you might be surprised about what "anyone" might bother to do. For instance, in the article which I started to quote above, there where 705 consonants and 448 vowels. A consonant was followed by a vowel 53.9% of the time and a vowel was followed by a consonant 85.0% of the time.

Mike Haven
10-09-2002, 04:57 PM
you are right of course - someone somewhere has done anything that you can think of, no doubt, even if you and i might think it was a ridiculous thing to do

your count fits the markov chain theorem to a T

thanks for that

lorinda
10-09-2002, 05:56 PM
Maybe we could make some formula based on the order in which they failed/succeeded
lets say one of the first 5 worked, then whoever invoked the 6th one would know he's up against a pretty tall order and would require a pretty large confidence level for it to work. Depending on how this turned out, then the next president would have more data with which to base his decision and so on :O
so if it has only worked 20% of the time before at that stage and fails again, not only is it now only working 17% of the time, but the 6th use was done on logic expecting it to work half the time, even knowing that they had a 20% chance.
Could someone who understands what I mean please translate this, because I think it's interesting.

Bozeman
10-09-2002, 06:09 PM
I think I know what you are saying. However, after five (hypothetically independent) trials failed, you can only reject the null hypothesis with 97% confidence. And you can only reject the 60%/40% hypothesis with 92% confidence. Thus, it is not clear that the 6th trial should use the past precedence as the Bayesian baseline for success here. In particular, a past success rate of 1/5 only rejects the null hypothesis with 81% confidence (or 62.5% confidence two-way).

Even assuming each trial is aiming to have 50+% success based on prior knowledge, it is not clear how much revision of prior probability should be done.

Thoughts?
Craig