Compute Winning Coalitions?
Angela Merkel
Being fairly new to SPSS I have the following question. Currently Im
doing research on European Union decision making decision making
efficiency (just started).
The EU has 27 states. In order to approve legislative proposals 55
percent of the states, constituting 65 percent of the EU-population,
need to vote in favor of the proposals.
The questions are: How can you calculate 1.) the total number of
"coalitions" (= possible voting combinations); 2.) and the number of
"winning coalitions" (= combinations adhering the the 55 and 65%
percent rules)?
I realllly cant find it in SPSS.....
Thank you!
GW
Rich Ulrich
SPSS is not a tool for combinatorial manipulations.
How many ways are there to select 15 out of 27?
The "combinatorial" is a very large number, 27!/ (15!12!) .
I suppose you might generate all of them and count
how many meet the criterion. There are computational
shortcuts, if you generate the combinations in a particular order
(using largest, down to smallest, in the ordering)....
I think that I read about such things in reading about the
computations that are needed by programs like
ExactStats, for computing p-levels. But I don't remember
hearing of a program or procedure, anywhere, that you
can plug into for your question.
--
Rich Ulrich
Ryan
>
> - Show quoted text -
Hi Rich,
I'm not sure if this relates, but I recently had an exchange with Dale
on the SAS-L, where he reminded us that
X! = GAMMA(X+1)
You can see the full exchange here:
Further down the thread you'll see that I used "lngamma" (in SPSS) to
solve for the one-tailed p-value in a Fisher exact problem we were
discussing.
Ryan
Ray Koopman
Using the population percentages from column 3 in the table at
http://en.wikipedia.org/wiki/Demographics_of_the_European_Union
(which sum to 99.95%, not 100%), a check of all 17383860 possible
groups of 15 states (generated by 15 nested Do loops) shows that
3898067 of them have combined populations that comprise at least
65% of the total EU population.