[EM] Joe: Bias

[Dan Bishop]

Joseph Malkevitch wrote:
 >
> How do YOU measure bias [of an apportionment method]?
> 
> Can you provide the data for bias based on your definition of small 
> state and bias?

Although I'm not the one who was asked, I'll propose a method of 
measuring the bias of an apportionment method: Compute the correlation 
between states' populations and their seats/population ratio.

For apportionments based on the 2000 Census 
(http://www.census.gov/population/cen2000/tab01.txt), the biases of each 
method are:

*** Divisor Method with geometric rounding (Huntington-Hill) ***
-0.0163 (Pearson)
-0.0894 (Spearman)

*** Divisor Method with arithmetic rounding (Webster) ***
For the 2000 Census, produces the same apportionment as H-H.
-0.0163 (Pearson)
-0.0894 (Spearman)

*** Divisor Method with harmonic rounding (Dean) ***
MT +1, UT +1
CA -1, NC -1
-0.1844 (Pearson)
-0.2564 (Spearman)

*** Divisor Method with truncation (Jefferson) ***
CA +2, FL +1, IL +1, MI +1, NY +1, TX +1
HI -1, IA -1, MN -1, NB -1, NM -1, RI -1, WV -1
+0.3243 (Pearson)
+0.4064 (Spearman)

*** Divisor Method with ceiling (Adams) ***
CT +1, DE +1, MS +1, MT +1, OK +1, OR +1, SD +1, UT +1
CA -3, FL -1, NY -1, NC -1, OH -1, TX -1
-0.3829 (Pearson)
-0.6430 (Spearman)

*** Largest Remainder with Hare Quota (Hamilton) ***
UT +1
CA -1
-0.0721 (Pearson)
-0.1482 (Spearman)

*** Largest Remainder with Droop Quota ***
For the 2000, produces the same apportionment as H-H or Webster.
-0.0163 (Pearson)
-0.0894 (Spearman)