仏大 社会学部論集６０号（Ｐ）☆／７．山口
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1
2 : : : / N m * * : 67 2Bohrnstedt & Knoke : : , Bohrnstedt & Knoke
3 Mosteller, Youtz, & Zahn1967 Diaconis & Freedman π 1/
4 Balinski & Young, Balinski & Young i i$1"!!!" n i N i p i$100"(n i$n ) m d i m u i p i p d i d 315.3p 3 2 u i u 315.4p 3 2 q i q 315.3p 3 2 r i r q 3 p i!d i#u i!p i q i$d i p i!d i#u i!p i q i$u i m 1$10 m!1 p i m q i
5 m 5 m#1 5 q i!i q i i r i i r i$"q i r i$q i m 1!10 m!1 2 q i !10 m! : : : :
6 : 237 i n i p i q i r i q i r i !max(r i!q i )"min(r i!q i )!max(r i!p i )"min(r i!p i ) max(x!y)x y min(x!y)
7 "max(q i!p i )!min(q i!p i ) "max(q i!p i )"min(q i!p i ) Balinski & Young,
8 100 m 1 m m 1 1"10 m! !i max(r i!p i )!min(r i!p i ) : i n i p i q i d i r i * 7* * :
9 !i q i#100 r i#q i!i q i#100 r i#q i!(1"10 m!1 ) ri#q i!i q i!100 r i#q i"(1"10 m!1 ) ri#q i m 1 m s s a b c N
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12 a b c a b 9 b a 10 b b c c a b c a b c
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14 m m
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17 : : : / : : 169 Balinski & Young, Balinski1996 m Diaconis & Freedman, Excel5
18 100 i 1 (q i#1)#q i q i#(q i!1) q i 1 q i! ! 1.5 (1"2) $1! d u x u#x$x#d x 2$du x$(du) max(1"p#q)!min(1"p#q) d u 2du#(d#u) d$1"u$ abc a 34 a b c 34 2 a b c b c Balinski & Young,
19 Balinski, M. L., 1996, How should data be rounded?, Institute of Mathematical Statistics Lecture NotesMonograph Series, 28 : 33. Balinski, M. L., and Young, H. P., 1982, Fair Representation, Yale University.M. L. H. P Bohrnstedt, G. W., and Knoke D., 1988, Statistics for Social Data Analysis 2nd. Ed., Peacock Diaconis, P., and Freedman, D., 1979, On rounding percentages, Journal of the American Statistical Association, 74 : : Mosteller, F., Youtz, C., and Zahn, D., 1967, The distribution of sums of rounded percentages, Demography, 4 : ABCD
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