[EM] a question about apportionment

Bob Richard lists001 at robertjrichard.com
Sat Apr 16 18:43:57 PDT 2011

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<lists001 at robertjrichard.com>  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?
>> ----
>> Election-Methods mailing list - see http://electorama.com/em for list info

Bob Richard
Executive Vice President
Californians for Electoral Reform
PO Box 235
Kentfield, CA 94914-0235

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