Transcript
Granting Certiorari: A Mathematical Model for Supreme Court Acceptance of Appealed Cases Texas Oklahoma Research Undergraduate Symposium February 26, 2011 Checed Rodgers, in collaboration with Anita Walker, Ph. D., Of East Central University
I. Context
http://www.ncsconline.org/D_Research/Ct_Struct/state_inc.asp?STATE=OK
I. Context Example Scenario: Store Owner and Wet Floors
SC: Store owner is not liable for slips if warning sign is present.
Customer slips; no sign is present. If owner loses negligence lawsuit, he can be fairly certain he will lose appeal.
SC: Store owner is not liable for slips if customer has “sufficient notice of danger.”
Customer slips; no sign is present. If owner loses, he may be able to win on appeal.
II. Model Goal: a mathematical model that will allow us to estimate the likelihood that the SC will grant certiorari. Hypothesis: Doctrinal shifts lead to increased uncertainty. The SC will attempt to mitigate this uncertainty through the resolution of subsequent appellate cases.
II. Model Variables: • Vt = uncertainty caused by doctrinal shift (range (0, 1)) • Rt = reduction in uncertainty due to new case law (range (0, 1))
II. Model • How do we expect our variables to behave? • Uncertainty caused by doctrinal shift (Vt) should remain relatively stable until the shift. It should then increase rapidly and approach a maximum. • Uncertainty reduction due to new cases (Rt) should not exist until the shift. It should then increase slowly and approach a maximum that is lower than the limit of (Vt). • Total uncertainty (At) will be the difference between uncertainty caused by the shift and uncertainty reduction. • We can approximate these behaviors using dynamic equations.
II. Model • ΔVt = g(L-Vt)
L (upper limit)
Vt 1 0.8 0.6 Vt
0.4 0.2 0 1981 1982 1983 1984 1985 1986 1987 1988
II. Model • ΔRt = f(B-Vt)
B (upper limit)
Rt 1 0.8 0.6 Rt
0.4 0.2 0 1981 1982 1983 1984 1985 1986 1987 1988
II. Model • Total Uncertainty (At) = Vt-Rt Rt 1 0.8 0.6 Rt
0.4 0.2 0 1981 1982 1983 1984 1985 1986 1987 1988
II. Model • Finally, we will represent our expected number of cases in a given category as total uncertainty (At) multiplied by the sensitivity of the court (p). • Xt = pAt
III. Data • Court: Oklahoma Supreme Court • Topic: Support Alimony • Dates: 1890-2010
1890 1895 1900 1905 1910 1915 1920 1925 1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
III. Data
Total OK S.C. Cases
1400
1200
1000
800
600
400
200
0
1890 1895 1900 1905 1910 1915 1920 1925 1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
III. Data
Total Alimony Cases
30
25
20
15
10
5
0
1890 1895 1900 1905 1910 1915 1920 1925 1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
III. Data
Alimony Cases as Percent of Total
14.00%
12.00%
10.00%
8.00%
6.00%
4.00%
2.00%
0.00%
III. Data Alimony Cases as Percent of Total (Subset) 4.50%
4.00% 3.50% 3.00% 2.50% 2.00%
1.50% 1.00% 0.50% 1920 1922 1924 1926 1928 1930 1932 1934 1936 1938 1940 1942 1944 1946 1948 1950 1952 1954 1956 1958 1960 1962 1964
0.00%
IV. Making Predictions Remember our original formulas: • ΔVt = g(L-Vt) • ΔRt = f(B-Vt) • Xt = pAt Rearrange as: • (Δ+g)Vt = gL • (Δ+f)Rt = fB • Xt-pVt+pRt = 0
IV. Making Predictions Rewritten in matrix format: (Δ+g) 0 -p
0 (Δ+f) p
0 0 1
Vt Rt Xt
= = =
gL fB 0
IV. Making Predictions Using Cramer’s Rule, we derive: • Xt+2 + (f+g-2)Xt+1 + (1-f-g+fg)Xt = pgf(L-B)
• Notice that Vt and Rt are absent.
V. Summary • The model, which attempts to explain appealed case acceptance rates in terms of doctrinal uncertainty and uncertainty reduction, finds marginal support from the data. • If the model is reliable, we should be able to estimate the number of cases of a given type that a supreme court will accept in an upcoming year.
V. Summary Benefits of independent research: • Chance to integrate my major with my minor • Opportunity to conduct self-study • Reason to familiarize self with new topics
VI. Sample Prediction Example: • 1983 – 40 alimony cases • 1984 – 64 alimony cases • 1985 – ? Xt+2 = (200)(.6)(.4)(.8-.6)-(.4+.6-2)(64)-(1-.4-.6(.4)(.6))(40) = 64
References •
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12 O.S. § Rule 1.178. This statute contains a short list of criteria which the Oklahoma Supreme Court may use to identify an appealed case as one that deserves certiorari. Characteristics which may distinguish a case as being particularly deserving of review include the presence of a substantial question that the court has not yet considered and the presence of conflict between the instant case and a previous Court of Civil Appeals Case. 20 O.S. § 30.1. This statute grants the Oklahoma Supreme Court authority to review a decision by the Court of Civil Appeals. According to the statute, a majority of the Oklahoma Supreme Court’s justices must elect to grant certiorari before the case can be considered. 24 Am. Jur. 2d Divorce §§ 607-928. (1998). This lengthy legal encyclopedia article provides an in-depth introduction to support alimony. Information of immediate importance includes a comprehensive definition of alimony and the necessity of separation of the spouses.
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Jay M. Zitter, Annotation, Excessiveness or Adequacy of Amount of Money Awarded as Permanent Alimony Following Divorce, 28 A.L.R. 4th 786 (1984). This article will be useful to the reader who is interested in developing a better understanding of the mechanics of alimony determination. The article refers the reader to cases which have deemed various amounts of alimony to be appropriate or inappropriate. Khan, S. (2008, June 7). Introduction to Matrices. Retrieved January 27, 2011, from http://www.khanacademy.org/video/introduction-tomatrices?playlist=Linear%20Algebra This online video is the first in a series of video tutorials that explain the basic principles of linear algebra. Proficiency in algebra is a prerequisite to understanding the series. Lipshutz, S., & Lipson, M. (2009). Linear algebra (4th ed.). New York: McGraw Hill. This text provides a comprehensive introduction to the topic of linear algebra. A working knowledge of college-level algebra is likely a prerequisite to completing the book.
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National Center for State Courts. (n.d.). Oklahoma: (Court structure as of fiscal year 2008). Retrieved January 27, 2011, from http://www.ncsconline.org/D_Research/ Ct_Struct/state_inc.asp?STATE=OK This document provides a pictorial representation of Oklahoma’s court structure. It also specifies the number of justices that sit on each court. O.K. Const. art. VII, § 4. This section of Oklahoma’s Constitution establishes the jurisdiction of the Oklahoma Supreme Court. It also establishes the jurisdiction of Oklahoma’s Court of Criminal Appeals. Oklahoma State Courts Network. Oklahoma Supreme Court Cases. Retrieved January 27, 2011, from http://www.oscn.net/applications/oscn/Index.asp?ftdb=STOKCSSC&level=1 This site indexes Oklahoma Supreme Court cases by year. Cases span from 1890 to present.
