I wouldn't describe the Taagepera and Shugart treatment as
"prescriptive". Rather, they come up with an explanation for the
observed regularity in terms of bi-directional communication links among
members of the legislature and bi-directional communication links
between legislators and constituents. It turns out, with the help of a
little differential calculus, that the cube root of twice the number of
constituents minimizes the individual representative's total links.
Using the cube root of the total population is only a rough guide, since
the proportion of the population that is eligible to vote (that is,
count as constituents) is never exactly half.
--Bob Richard
On 4/16/2011 6:26 PM, Evan Dower wrote:
Thanks! Unfortunately, it seems to be an expensive and
difficult-to-find book. Most things I've been able to find in the last
45 minutes (obviously not very long) seems to indicate that it is
descriptive rather than prescriptive, though. For example:
http://books.google.com/books?id=hgZYyJ2NiuMC&pg=PA160&lpg=PA160&dq=cube+root+law+assembly+size&source=bl&ots=oElujIcw2s&sig=YBqFX_BCxpcu0CgWTx2sPesY-0U&hl=en&ei=TDuqTdnpEqrSiAL3u6HvDA&sa=X&oi=book_result&ct=result&resnum=3&ved=0CCIQ6AEwAg#v=onepage&q=cube%20root%20law%20assembly%20size&f=false
and
http://www.uselectionatlas.org/FORUM/index.php?topic=101051.0
On his blog, Shugart seems to indicate that there are good reasons for
it, but unfortunately he doesn't even summarize them. See the fourth
comment on http://fruitsandvotes.com/?p=51
On Sat, Apr 16, 2011 at 17:37, Bob Richard<[email protected]> wrote:
A standard source on the cube root rule for the (approximately) "best" size
of a legislative body is Rein Taagepera and Matthew Shugart, "Seats& Votes"
(Yale University Press, 1989), pages 172-183. They provide both empirical
evidence and a conceptual explanation. I'm not familiar with any basis for
using the square root of anything.
--Bob Richard
On 4/16/2011 5:11 PM, Evan Dower wrote:
What are the reasons behind the square roots and cube roots? Can you
point me toward some research papers or something please?
Also, in tiered representation, I would expect the representatives at
one tier to elect the representatives at the next (from among
themselves), but the United States elects people to most "tiers" based
on popular votes for the region represented by that representative. To
be more concrete, for tiered representation, I would expect (in your
example) federal legislators to be elected by state legislators (not
by the general public). Similarly, I would expect (again from your
example) "Flat/Young-Earth Geocentric Creationists" to be the only
ones allowed to vote on which of them should elected to the city
council. This certainly doesn't match what you mean by tiered
representation. Perhaps you could reference the definition you're
using?
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Bob Richard
Executive Vice President
Californians for Electoral Reform
PO Box 235
Kentfield, CA 94914-0235
415-256-9393
http://www.cfer.org
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