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Vertical precedents in formal models of precedential constraint

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Abstract

The standard model of precedential constraint holds that a court is equally free to modify a precedent of its own and a precedent of a superior court—overruling aside, it does not differentiate horizontal and vertical precedents. This paper shows that no model can capture the U.S. doctrine of precedent without making that distinction. A precise model is then developed that does just that. This requires situating precedent cases in a formal representation of a hierarchical legal structure, and adjusting the constraint that a precedent imposes based on the relationship of the precedent court and the instant court. The paper closes with suggestions for further improvements of the model.

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Notes

  1. Though Horty (2015) was the first to formalize the standard model, he actually prefers the reason model that he develops in Horty (2011a), Horty (2011b), Horty and Bench-Capon (2012), Horty (2014), Horty (2015), Horty (2016), and Horty (2017). Intriguingly, Horty (2015, 12–13) argues that the reason model and the standard model are actually equivalent, in the sense that they permit precisely the same judicial behavior. He nevertheless prefers the reason model because he takes it to be more illuminating. For discussion, see Horty (2015, 13–23).

  2. Many theorists subscribe to a rule-based model of one form or another. See, for example, Raz (2009, chp. 10), Eisenberg (2007), Alexander and Sherwin (2007), Alexander and Sherwin (2001). Compare the “reason models” of Horty (2017), Rigoni (2017), Horty (2015, §4), Horty (2014, §4), Horty and Bench-Capon (2012), and Lamond (2005), and the “result models” of Horty (2017), Horty (2004), Levi (1949), and Paton (1946, 159).

  3. The implicit universal quantifier in the second sentence of (R) ranges over future courts in the same legal system. For now, I take the notion of a legal system for granted. For discussion, see Raz (2009, chp. 5), Raz (1970). Later, in Sect. 8, I will define a formal notion closely related to the informal notion of a legal system.

  4. See, for example, Garner et al. (2016, 44–96), Schauer (2009, 44–57, 180–184), Duxbury (2008, 58–92), Abramowicz and Stearns (2005), Cross and Harris (1991, chp. 2), Simpson (1959), Simpson (1958), Montrose (1957a), Montrose (1957b), Simpson (1957), Goodhart (1930b).

  5. See Llewellyn (2011, 38, 67, 103) for discussion of this conception of legal rules. I actually think that precedent rules should not generally be understood as directed to courts, as opposed to ordinary people in the relevant jurisdiction. See Hart (1994, 35–42). But I will set this concern aside for purposes of this essay.

  6. The strict rule model is defended as the normatively best doctrine of precedent, the one that ought to be adopted by the courts, in Alexander and Sherwin (2008, 42–50), Alexander and Sherwin (2007), Alexander and Sherwin (2001, 145–156), and Alexander (1989). When Alexander (1989, 53–54) turns to the descriptive question of the actual U.S. doctrine of precedent, however, he suggests that while vertical precedents are governed by the strict rule model, horizontal precedents are governed by something weaker. This is the position that I will be defending in Sect. 4.

  7. In fact, this sense is far more common in American courts than the one I adopt in this paper. I adopt the non-standard sense nevertheless in order to make contact with Horty (2015) and related work.

  8. So the term ‘applicable’ in (D) is redundant. I retain it as a reminder of the sense of ‘distinguish’ in play.

  9. For this use of the term, see, for example, Garner et al. (2016, 97), Raz (2009, 185), Duxbury (2008, 115), Hart (1994, 135). Compare the use of ‘narrowing’ in Re (2014), and the use of ‘stealth overruling’ in Friedman (2010).

  10. Cf. Dworkin (1977, 37): “If courts had discretion to change established rules, then these rules would of course not be binding upon them\(\ldots\)

  11. These conditions were first articulated in Raz (2009, 186). Compare Raz (1990, 140).

  12. Factors were introduced in Ashley (1990). They have since been adopted in a great deal of work on modeling legal reasoning. See, for example, Rigoni (2015), Horty and Bench-Capon (2012), Wyner et al (2011), Horty (2004), Prakken and Sartor (1998).

  13. See American Law Institute (2005, §13), American Law Institute (1965, §295A).

  14. See, for example, Aleven (1997, 20–24), Aleven and Ashley (1996). See also Al-Abdulkarim et al (2016), Grossi and Jones (2013), Lindahl and Odelstad (2013, §7), Roth and Verheij (2004), Ashley and Brüninghaus (2003), Brüninghaus and Ashley (2003), Bench-Capon (1999, 40–41), Branting (1994).

  15. On dimensions, see, for example, Bench-Capon (2017), Horty (2017), Rigoni (2017), Al-Abdulkarim et al (2015), Bench-Capon (1999), Ashley (1990).

  16. See Llewellyn (2008, 80), Llewellyn (1960, 84–91).

  17. Alternatives to the standard model are often built on similar assumptions. See, for example, Horty and Bench-Capon (2012, 199), Horty (2011b, 2, 3), Lamond (2005), Horty (2004, 20). Rigoni (2015, 134) may be an exception, however. He suggests that his reason model—rather than applying to both horizontal and vertical precedents, while setting aside the possibility of overruling—applies exclusively to vertical precedents. Yet Rigoni (2015, 157) seems to discuss the application of his model to cases in which the Supreme Court distinguishes its own past decisions. So it’s ultimately unclear where the model is supposed to apply.

  18. Note that this definition assumes that the case base \(\varGamma\) is consistent to begin with, in the sense that \(\varGamma ^+\) is a case base.

  19. Strictly speaking, the lowest level also includes the Court of International Trade and the Court of Federal Claims, which have nationwide jurisdiction to hear different sorts of specialized claims. We ignore these and other complications for ease of exposition.

  20. Indeed, this judicial structure is found in many western democracies. See Taruffo (1997, 437).

  21. A more general taxonomy might also allow for the possibility that a court is constrained by (3) a past decision of an inferior court, or (4) a past decision of a court to which it is neither superior nor inferior. (A court falling under (4) is not necessarily a coordinate court, a court at the same level in the judicial hierarchy. The Second Circuit Court of Appeals, for example, is not superior, inferior, or coordinate to the United States District Court for the Eastern District of Arkansas.) But U.S. courts are not generally constrained by such decisions.

  22. So long as an adequate formal model of the U.S. doctrine would be worth having, it doesn’t much matter whether past work on the standard model and its competitors was aimed at developing such a model. My concern is not ultimately to take issue with any particular claims that have been made on behalf of these models. Rather, it is simply to take up the standard model, and to ask, regardless of what may have motivated its development in the first instance, how well it captures the U.S. doctrine of precedent. Incidentally, though, I do think that the standard model and its competitors have often been taken to capture the U.S. doctrine of precedent (even if they have been employed for different purposes as well). While Raz (2009, 181) first presented the standard model (informally) as a descriptive model of the doctrine of precedent not in the U.S. but in England, subsequent discussions of the standard model and its competitors have taken the models to apply more generally. Horty (2011b, 1), for example, introduces the standard model, as well as his preferred reason model, as a specification of the doctrine of precedent along roughly Razian lines. Gone, though, is the explicit clarification that what is at issue is the doctrine of precedent in England. Instead, we find only generic mention of “the common law.” The suggestion—fairly explicit in Horty (2014, 337) but more often left in the background—is that substantially the same doctrine of precedent binds judges in the United Kingdom, the United States, Canada, India, Israel, and other common law jurisdictions. If these models are supposed to capture the doctrine of precedent in all of these jurisdictions, then, a fortiori, they are supposed to capture the doctrine in the U.S., which is all that was wanted. I should say, though, that the suggestion that substantially the same doctrine is at work in all these jurisdictions strikes me as implausible (although this will of course depend on just how much work is being done by “substantially”). Many scholars have noted differences between the doctrines of precedent in different common law jurisdictions—for example, MacCormick and Summers (1997), Cross (1991, 19ff.), Goodhart (1930a). But we don’t actually need to compare the doctrines of different common-law jurisdictions to see that there is no perfectly general doctrine of precedent baked into the very notion of common law reasoning. It’s enough to notice that the doctrine in any given jurisdiction changes over time. The U.K. doctrine famously changed in 1966 when the House of Lords gave itself the power to overrule its own precedents, a power it had lacked since at least 1898. But the U.S. doctrine has changed too. For example, as discussed in Bradford (1990), it used to be an open question whether a federal circuit court is required to follow an applicable Supreme Court precedent that the court is reasonably sure the current Court would overrule if given the chance. Then, after many years of confusion in the lower courts, the Supreme Court finally decided, in Rodriguez de Quijas v. Shearson/American Express, 490 U.S. 477 (1989), that inferior courts must follow applicable Supreme Court precedents until the Court actually overrules them. Now this is a settled component of the U.S. doctrine of precedent. Plainly, then, there is no single doctrine of precedent to be found in every common law system at every time. There are similarities, to be sure, and as we develop our formal models, it may well make sense to stave off parochialism for a while by starting with features common to many jurisdictions. Fairly soon, however, assuming that our aim is to describe the doctrine of precedent in some jurisdiction, progress will require that we attend to the doctrine of some particular jurisdiction. This paper, of course, focuses on the U.S. In spite of the real differences between the doctrines of precedent in different common law jurisdictions, however, I suspect that, even once the possibility of overruling is set aside, the distinction between vertical and horizontal precedent will need to be incorporated into formal models for many of them, although the precise doctrine for each sort of precedent will need to be different in different models. I make no argument for this claim here, but see, for example, Eng (1997, 204) (concerning Norway), Bankowski et al. (1997, 325–326, 328, 349) (concerning the United Kingdom).

  23. Compare Lewis (1975) and Lewis (1969) on “languages and language” (or “possible languages and actual languages”).

  24. To be clear, this is a stipulation, not a conceptual or linguistic claim. If it were a conceptual or linguistic claim, then one might reasonably object that it asks too little. For it is at least plausible that for a doctrine of precedent to be the doctrine of a legal system—in the ordinary, non-stipulative sense—we must have not only (i)–(iii), but also that the judges of the system (iv) generally act in accordance with the doctrine, and (v) generally think that they ought to act in accordance with the doctrine. Conditions (i)–(v) are closely related to the conditions that Hart (1994, 55–61) claims are necessary and sufficient for the existence of a social rule. Their plausibility in this context should hardly be surprising, of course, since Hart’s rule of recognition is a social rule, and Hart (1994, 101) thought that the doctrine of precedent—part of it, anyway—is included in the rule of recognition in most modern legal systems. Alternatively, one might plausibly say that (iv) and (v) alone are necessary and sufficient for a doctrine to be the doctrine of a given system. (Indeed, Hart is sometimes read in this way with respect to social rules generally.) On this account, the fact that judges in a particular legal system, in official statements, claim that they are required to follow a certain doctrine of precedent, criticize other judges for failing to follow that doctrine, and so on, would merely be relevant evidence that they (v) generally think that they ought to comply with the doctrine, i.e., that they accept the doctrine. In any case, I do not intend to engage in these sorts of debates here. While I do think that judges in the U.S. generally accept and comply with the doctrine of precedent that (DVP) describes, I will be directly concerned, in this section, only with whether they claim that they are required to comply with it, criticize violations of it, and appeal to it in order to justify their official decisions. (In the next section, I will briefly address whether judges in the U.S. generally follow the U.S. doctrine of precedent. But the issue is not a central concern of this essay.)

  25. Helvering v. Hallock, 309 U.S. 106, 119 (1940).

  26. Janus v. Am. Fed’n of State, Cty., & Mun. Employees, Council 31, 138 S. Ct. 2448, 2478 (2018).

  27. Payne v. Tennessee, 501 U.S. 808, 828 (1991). See also Hohn v. United States, 524 U.S. 236, 251 (1998); Seminole Tribe of Fla. v. Fla., 517 U.S. 44, 63 (1996); Planned Parenthood of SE Pennsylvania v. Casey, 505 U.S. 833, 854–855 (1992).

  28. Generally, the Court says that it must follow a horizontal precedent unless there is a “special justification” for departing from it. See, for example, Dickerson v. United States, 530 U.S. 428, 443 (2000). See also Kimble v. Marvel Entm’t, LLC, 135 S. Ct. 2401, 2409 (2015); Halliburton Co. v. Erica P. John Fund, Inc., 134 S. Ct. 2398, 2407 (2014); Michigan v. Bay Mills Indian Cmty., 134 S. Ct. 2024, 2036 (2014). What constitutes a special justification? For starters, there is a “positive” reason to depart from precedent if the case was wrongly decided (and perhaps badly reasoned), its continued application would result in harm or injustice, or the lower courts have struggled to apply the associated rule or standard. See Janus, 138 S. Ct. at 2479; Johnson v. United States, 135 S. Ct. 2551, 2562 (2015); Citizens United v. Federal Election Comm’n, 558 U.S. 310, 363 (2010); Montejo v. Louisiana, 556 U.S. 778, 785 (2009); United States v. South-Eastern Underwriters Ass’n, 322 U.S. 533, 580 (1944) (Stone C.J. dissenting). Whether there is a “special justification” in a given case may depend, in part, on just how great a harm or injustice the continued application of the precedent would produce, or just how unworkable the rule has proven to be. But it will usually depend also on the presence or absence of countervailing reasons to adhere to precedent. For instance, if people have arranged their affairs in reliance on a precedent, this is a good reason not to depart from it. Accordingly, a “special justification” is more likely to exist if reliance interests are absent. See, for example, Leegin Creative Leather Prod., Inc. v. PSKS, Inc., 551 U.S. 877, 925 (2007); Hohn, 524 U.S. at 251; Payne, 501 U.S. at 828. A handful of additional considerations are considered relevant, but the general idea is simply that the Court must “make certain that more harm will not be done in rejecting than in retaining a rule of even dubious validity.” South-Eastern Underwriters Ass’n, 322 U.S. at 580 (Stone C.J. dissenting). See also Citizens United, 558 U.S. at 378 (Roberts C.J. concurring) (“When considering whether to reexamine a prior erroneous holding, we must balance the importance of having constitutional questions decided against the importance of having them decided right.").

  29. 539 U.S. 558 (2003).

  30. Id. at 562–563. For additional examples of the Supreme Court overruling its own precedents, see Janus v. Am. Fed’n of State, Cty., & Mun. Employees, Council 31, 138 S. Ct. 2448, 2486 (2018) (overruling Abood v. Detroit Bd. of Ed., 431 U.S. 209 (1977)); S. Dakota v. Wayfair, Inc., 138 S. Ct. 2080, 2099 (2018) (overruling Quill Corp. v. North Dakota, 504 U.S. 298 (1992) and National Bellas Hess, Inc. v. Department of Revenue of Ill., 386 U.S. 753 (1967)); Johnson v. United States, 135 S. Ct. 2551, 2563 (2015) (overruling Sykes v. United States, 131 S. Ct. 2267 (2011) and James v. United States, 550 U.S. 192 (2007)); Obergefell v. Hodges, 135 S. Ct. 2584, 2605 (2015) (overruling Baker v. Nelson, 409 U.S. 810 (1972)); Adarand Constructors, Inc. v. Pena, 515 U.S. 200, 227 (1995) (overruling Metro Broadcasting, Inc. v. FCC, 497 U.S. 547 (1990)).

  31. 478 U.S. 186 (1986).

  32. See Lawrence, 539 U.S. at 579ff. (O’Connor J. concurring in the judgment).

  33. Id. at 578.

  34. 467 U.S. 649 (1984).

  35. 384 U.S. 436 (1966).

  36. Id. at 444.

  37. Quarles, 467 U.S. at 655. See also id., at 664–665 (O’Connor J. concurring in the judgment in part and dissenting in part) (noting the majority’s concession that Miranda applies).

  38. Id. at 655–656. See also id., at 679 (Marshall J. dissenting) (noting the majority’s candor concerning its modification of Miranda).

  39. See Miranda, 384 U.S. at 491–492.

  40. Quarles, 467 U.S. at 657.

  41. The Court has modified Miranda in other cases as well. See, for example, Berghuis v. Thompkins, 130 S. Ct. 2250 (2010); Oregon v. Elstad, 470 U.S. 298 (1985); Harris v. New York, 401 U.S. 222 (1971). See also Dickerson v. United States, 530 U.S. 428, 441 (describing Quarles and Harris as modifying the rule of Miranda). Additional examples of the Court (arguably, at least) modifying an applicable horizontal precedent include Arizona v. Gant, 556 U.S. 332 (2009) (modifying New York v. Belton, 453 U.S. 454 (1981)); Flast v. Cohen, 392 U.S. 83 (1968) (modifying Frothingham v. Mellon, 262 U.S. 447 (1923)).

  42. Hutto v. Davis, 454 U.S. 370, 375 (1982). Otherwise, the Court says, “anarchy [would] prevail within the federal judicial system.” Id.

  43. 460 U.S. 533 (1983) (per curiam).

  44. Thurston Motor Lines, Inc. v. Jordan K. Rand, Ltd., 682 F.2d 811 (9th Cir. 1982).

  45. Id. at 812.

  46. 247 U.S. 201 (1918).

  47. Id. at 202.

  48. Thurston Motor, 682 F.2d at 812.

  49. Id. at 814.

  50. Thurston Motor, 460 U.S. at 533.

  51. Id. at 534.

  52. Id.

  53. Id. Why “wholly unconvincing” and not, say, wholly inappropriate? Because the Ninth Circuit framed its attempt to modify a vertical precedent as an attempt to interpret it. And it is hardly inappropriate for an inferior court to interpret a superior court opinion in order to identify its holding.

  54. Id. at 535.

  55. County of Allegheny v. American Civil Liberties Union, Greater Pittsburgh Chapter, 492 U.S. 573, 668 (1989) (Kennedy J. concurring and dissenting). See also Bosse v. Oklahoma, 137 S. Ct. 1, 2 (2016); Ashcroft v. al-Kidd, 563 U.S. 731, 742 (2011); Seminole Tribe, 517 U.S. at 63; Rivers v. Roadway Exp., Inc., 511 U.S. 298, 312 (1994).

  56. Rodriguez de Quijas, 490 U.S. at 484. See also Bosse v. Oklahoma, 137 S. Ct. 1, 2, (2016); Jaffree v. Bd. of Sch. Comm’rs of Mobile Cty., 459 U.S. 1314, 1316 (1983); Hicks v. Miranda, 422 U.S. 332, 344–345 (1975).

  57. Hart v. Massanari, 266 F.3d 1155, 1171–1172 (9th Cir. 2001).

  58. See also United States v. Bd. of Cty. Commissioners of Cty. of Otero, 843 F.3d 1208, 1214 (10th Cir. 2016); United States v. Walker, 351 F. App’x 16, 18 (6th Cir. 2009); Omega S.A. v. Costco Wholesale Corp., 541 F.3d 982, 987 n. 5 (9th Cir. 2008); United States v. Sampson, 486 F.3d 13, 20 (1st Cir. 2007); Cardenas v. Dretke, 405 F.3d 244, 253 (5th Cir. 2005); Johnson v. DeSoto Cty. Bd. of Commissioners, 72 F.3d 1556 (11th Cir. 1996); Butts v. City of New York Dep’t of Hous. Pres. & Dev., 990 F.2d 1397, 1409 (2d Cir. 1993); Vujosevic v. Rafferty, 844 F.2d 1023, 1030 (3d Cir. 1988); U.S. ex rel Shore v. O’Leary, 833 F.2d 663, 667 (7th Cir. 1987).

  59. The implicit contrast, of course, is with the situation in which a court is faced with a horizontal precedent that the court would rather not apply to a new set of facts. In this situation, the court is not (always) required to follow the precedent.

  60. In fact, many circuit courts have also suggested that they have a duty to follow the dicta of the Supreme Court. See, for example, Utah Republican Party v. Cox, 892 F.3d 1066, 1079 (10th Cir. 2018); American Civil Liberties Union of Ky. v. McCreary Cnty., 607 F.3d 439, 447 (6th Cir. 2010) (“Lower courts are obligated to follow Supreme Court dicta, particularly where there is not substantial reason for disregarding it, such as age or subsequent statements undermining its rationale.”); Winslow v. F.E.R.C., 587 F.3d 1133, 1135 (D.C. Cir. 2009) (stating that “carefully considered language of the Supreme Court, even if technically dictum, generally must be treated as authoritative”); McCoy v. Massachusetts Inst. of Tech., 950 F.3d 13, 19 (1st Cir. 1991) (stating that “federal appellate courts are bound by the Supreme Court’s considered dicta almost as firmly as by the Court’s outright holdings, particularly when\(\ldots\)[they are] of recent vintage and not enfeebled by any subsequent statement”).

  61. See also Duvall, 740 F.3d at 617 (Kavanaugh J. concurring) (“[T]he Supreme Court is free to reconsider or refine or tweak its own precedents\(\ldots\)and it does so in appropriate cases. Lower courts, by contrast, are not free to reconsider or refine or tweak Supreme Court precedents.”).

  62. And in the federal district courts as well. See, for example, Poonjani v. Shanahan, 319 F. Supp. 3d 644, 650 (S.D.N.Y. 2018); McGary v. Crowley, 266 F. Supp. 3d 254, 261 (D.D.C. 2017); Exergen Corp. v. Kids-Med, Inc., 189 F. Supp. 3d 237, 243–244 (D. Mass. 2016); In re Ashai, 211 F. Supp. 3d 1215, 1221 (C.D. Cal. 2016); Haith ex rel. Accretive Health, Inc. v. Bronfman, 928 F. Supp. 2d 964, 971 (N.D. Ill. 2013) (“The reach of Supreme Court decisions are not limited to the particular facts and circumstances presented in the case being decided; lower courts must apply the reasoning of those decisions even to cases that are factually dissimilar.”); Panayoty v. Annucci, 898 F. Supp. 2d 469, 479–480 (N.D.N.Y. 2012); United States v. Rosenau, 870 F. Supp. 2d 1109, 1115 (W.D. Wash. 2012); Does 1–7 v. Round Rock Indep. Sch. Dist., 540 F. Supp. 2d 735, 749 (W.D. Tex. 2007); In re Reveal, 148 B.R. 288, 292 (Bankr. S.D. Ohio 1992).

  63. See also Evans v. Rockdale Hosp., LLC, 345 Ga. App. 511, 521 (2018); Harris v. State, 407 P.3d 348, 355 (Nev. App. 2017); People v. Etherton, 82 N.E.3d 693, 697 (Ill. 2017); Stringer v. Stringer, 544 S.W.3d 714, 723 (Tenn. Ct. App. 2017); George v. Hercules Real Estate Servs., Inc., 339 Ga. App. 843, 854 (2016); Rodriguez v. Nat’l City Bank, 277 FRD 148, 154 (E.D. Pa. 2011); State v. Hausmann, 277 Neb. 819, 824 (2009); Alaska Pub. Interest Research Grp. v. State, 167 P.3d 27, 43–44 (Alaska 2007); Sanford v. Clear Channel Broad, Inc., 14 Neb. App. 908, 915–916 (2006); Com v. Millner, 585 Pa. 237, 260 (2005); Howell Lumber Co. v. City of Tuscaloosa, 757 So.2d 1173 (Ala. Civ. App. 1997); Stephenson v. Perlitz, 524 S.W.2d 786, 788–789 (Tex. Civ. App. 1975).

  64. Although some may find it surprising, I do not think that (DVP) should be terribly controversial. In fact, it is so widely accepted among traditional legal scholars that it passes for a platitude in the law reviews. See, for example, Garner et al. (2016, 42, 101, 243), Kozel (2014, 203), Mead (2012, 791), Sloan (2009, 718), Abramowicz and Stearns (2005, 957), Lundmark (1998, 212), Summers (1997, 369–370, 374), Caminker (1994, 818), Dorf (1994, 2025), Alexander (1989, 53–54).

  65. While this paper focuses on the standard model, I also take the arguments in this section to show that if the reason model—elaborated in, for example, Horty (2017), Rigoni (2017), Horty (2015), Horty and Bench-Capon (2012), Horty (2011b), Lamond (2005)—is to capture the U.S. doctrine of precedent, then it too requires revision. An anonymous reviewer disagrees. In particular, the reviewer suggests that, for the reason model theorist, the prohibitions on modifying, tweaking, altering, and limiting vertical precedent—as found in Stop PAC, Pate, Casper, and elsewhere—do nothing to show that vertical precedents can’t be distinguished, because distinguishing, on the reason model, does not involve modifying precedent rules. (Instead, it involves strengthening, in a particular way, the priority ordering on reasons implicit in the case base.) The reviewer’s suggestion is, I think, mistaken. Before addressing the relevance to the reason model of the prohibitions on modifying vertical precedent rules, I will simply note that the conclusion that vertical precedents can’t be distinguished under the U.S. doctrine is supported by many judicial statements that make no reference to rule modification, including, for example, the statements in Rodriguez de Quijas, Duvall, and Hart that if the holding of a vertical precedent applies, the lower court must follow the rule. Thus, even if the prohibitions on modifying vertical precedent rules were irrelevant to the reason model, the evidence in this section would still indicate that the reason model can’t capture the U.S. doctrine of precedent without considerable revision. In fact, though, these prohibitions are as relevant to the reason model as they are to the standard model. To see this, note that, on the reason model, no court ever modifies a precedent rule, whether the precedent is horizontal or vertical. Yet courts in the U.S. certainly say that they can and do modify horizontal precedent rules. In Dickerson, for example, Chief Justice Rehnquist, writing for the Court, refers to the many “modifications” that the Court has made to the rule of Miranda and declares that “no constitutional rule is immutable.” 530 U.S. at 441. The reason model, if it is to capture the U.S. doctrine of precedent, can’t simply ignore all this talk of rule modification. There is evidently something, a certain way of treating precedents, that these courts are using the language of rule modification to talk about. And they are saying that it is permissible to treat horizontal precedents, but impermissible to treat vertical precedents, in that way. The reason model must account for this, presumably by translating talk of modifying rules into talk of strengthening priority orderings among reasons. Recall, in this connection, that Horty (2015) maintains that the reason model and the standard model are equivalent, in the sense that they permit precisely the same judicial decisions. If this is right, then if these judicial statements suffice to show that distinguishing vertical precedents is prohibited on the standard model, they also suffice to show that it is prohibited on the reason model. Even if the two models are not equivalent, however, or the term ‘distinguish’ is used differently by reason model theorists, I submit that accounting for the data canvassed in this section will require significant changes to the reason model.

  66. For recent work in AI & Law aimed at predicting judicial decisions, see, for example, Chen and Eagel (2017), Conrad and Al-Kofahi (2017), Grabmair (2017), Ashley and Brüninghaus (2003), Brüninghaus and Ashley (2003).

  67. The comparison I intend is between (i) models that capture the distinction between horizontal and vertical precedent and (ii) models that don’t capture that distinction but still appeal to a doctrine of precedent. It’s possible, of course, that the best predictive models would make no appeal to doctrinal considerations at all, although this seems unlikely if the models are intended to predict decisions outside the Supreme Court.

  68. See, for example, Epstein et al (2013), Klein and Devins (2013), Kassow et al (2012), Westerland et al (2010), Hansford and Spriggs (2006), Cross (2005), Haire et al (2003), Segal and Spaeth (2002), Reddick and Benesh (2000), Brenner and Spaeth (1995), Songer et al (1994). Two useful surveys are Hansford (2017) and Klein (2017).

  69. 93 F.3d 1358 (7th Cir. 1996) (Posner C.J.).

  70. Hovenkamp (2008) is a good introduction.

  71. The task of developing standards to determine just what should count as a restraint on trade was left to the courts. As a result, despite the underlying statute, antitrust law in the U.S. is effectively common law.

  72. 220 U.S. 373 (1911).

  73. See United States v. A. Schrader’s Son, 252 U.S. 85 (1920); Frey & Son v. Cudahy Packing Co., 256 U.S. 208, 210 (1921); Fed. Trade Comm’n v. Beech-Nut Packing Co., 257 U.S. 441, 452–453 (1922); United States v. Socony-Vacuum Oil Co., 310 U.S. 150, 223 (1940); United States v. Bausch & Lomb Optical Co., 321 U.S. 707, 721 (1944); Kiefer-Stewart Co. v. Joseph E. Seagram & Sons, 340 U.S. 211, 71 (1951); United States v. McKesson & Robbins, Inc., 351 U.S. 305, 76 (1956); United States v. Parke, Davis & Co., 362 U.S. 29 (1960); Simpson v. Union Oil Co., 377 U.S. 13 (1964).

  74. 390 U.S. 145 (1968).

  75. Id. at 152–153.

  76. See, for example, Posner (1979), Posner (1976), Posner (1975a), Posner (1975b), Posner (1970). So too was Judge Easterbrook, also of the Seventh Circuit. See, for example, Easterbrook (1984), Easterbrook (1982), Easterbrook (1981).

  77. (Posner 1975a, 290).

  78. Judge Posner was thinking of such cases as United States v. Colgate & Co., 250 U.S. 300 (1919); United States v. General Electric Co., 272 U.S. 476 (1926); and Parke, Davis, 362 U.S. at 29.

  79. Posner (1975b, 143).

  80. Posner (1975b, 141).

  81. Posner (1975a, 297).

  82. In the case of massive market power among the sellers, Posner suggested that the court ought to undertake the usual open-ended antitrust inquiry under the “rule of reason.” Posner (1975a, 298–299).

  83. In fact, Khan was not contractually prohibited from charging a higher price, so that if he did so he would be in breach. Rather, the contract provided that, if Khan did raise the price, then State Oil was entitled to the difference between the new price and the old multiplied by the number of gallons sold at the new price. Thus, the contract made it worthless for Khan to raise the price. See Khan, 93 F.3d at 1360.

  84. Notably, Judge Ripple wrote a concurring opinion to register that he too opposed the Court’s per se prohibition of maximum RPM agreements as a substantive matter. So, if the option to distinguish the Court’s precedents were really available, Judge Posner would evidently have had the votes to do so. See Khan, 93 F.3d at 1367 (Ripple J. concurring).

  85. Khan, 93 F.3d at 1362.

  86. See, for example, id. at 1363 (“Albrecht was unsound when decided, and is inconsistent with later decisions by the Supreme Court. It should be overruled. Someday, we expect, it will be.”).

  87. State Oil v. Khan, 522 U.S. 3 (1997).

  88. Id. at 20.

  89. An anonymous reviewer suggests that Judge Posner’s Khan opinion actually undermines(DVP). The objection can be paraphrased as follows.

    Posner says it’s not cricket to distinguish by pointing to a fact the precedent court mentioned but gave no weight. This implies that it would be “cricket” to distinguish by pointing to a novel reason, a relevant fact favoring the otherwise losing side. That’s exactly what the reason model says is required for distinguishing. If vertical precedent were strict, why would it matter that the fact was mentioned in the older opinion? Shouldn’t Posner just have to follow the rule?

    This strikes me as confused. State Oil was claiming—and Posner agreed—that its dispute with Khan presented a novel reason, not present in Albrecht, to find the contract enforceable. The reason, present in Khan but absent in Albrecht, was that the dispute was entirely “vertical,” in the sense that it involved a single supplier and a single dealer. The dispute in Albrecht, by contrast, was more “horizontal,” in the sense that it involved multiple dealers. So Posner’s suggestion that it’s not cricket to distinguish a vertical precedent by pointing to a fact the precedent court mentioned but gave no weight does not imply that it’s permissible to distinguish a vertical precedent by pointing to a novel reason. It implies that it’s permissible to distinguish a vertical precedent—in the thin sense of ‘distinguish’—by pointing to a factor that was given weight by the precedent court, a factor whose presence or absence the precedent court relied on by incorporating into its holding. The holding in Albrecht, Posner tells us, was: “Maximum price fixing is illegal per se.” Had the Court relied on the “horizontal flavor” of the dispute in finding an antitrust violation, then it might have held: “Maximum price fixing schemes involving multiple dealers [in some specified way] are illegal per se.” If the Court had taken this tack, then State Oil could rightly have pointed out that Albrecht did not apply in Khan, since Khan did not involve multiple dealers.

    The objection seems to assume that distinguishing a precedent involves either pointing to some fact about the precedent dispute or pointing to some fact about the instant dispute, but not both. This is a mistake. A precedent can be distinguished (in either the thick sense or the thin sense) only if there is some factual difference between the precedent dispute and the instant dispute. And to show that two things are different, one must say something about each of them. A member of a law school admissions committee does not differentiate two candidates, after all, merely by pointing out that one aced the LSAT. Rather, she must somehow indicate that the other did not. Similarly, to differentiate its dispute with Khan from the dispute in Albrecht, State Oil needed to say something about its dispute with Khan, and it needed to say something about the dispute in Albrecht. What it said was that its dispute with Khan was entirely “vertical,” while the dispute in Albrecht was more “horizontal.” Why did State Oil think that the dispute in Albrecht was more horizontal? Because the Supreme Court said so in its Albrecht opinion. “If vertical precedent were really strict,” the objection asks, “then why would it matter that the Albrecht Court mentioned that the case involved multiple dealers?" But the very point that Judge Posner is making is that it doesn’t matter. What matters, he tells us, is the holding in Albrecht, the rule of the case: Maximum price fixing is illegal per se. Since the contract in Khan fixed maximum prices, that was the ballgame.

  90. Leiter (2007a, 88). See also Shapiro (2011, chp. 8).

  91. Llewellyn (2011, 41) refers to these as “trade techniques.”

  92. This phenomenon is noted by Llewellyn (2008, 44–45).

  93. There is also the possibility that the authoritative methods themselves conflict, thus producing rather than removing indeterminacy, a possibility advanced in Llewellyn (2008, 68–69), Llewellyn (1950), Llewellyn (1940, 210). For discussion, see Leiter (2007b, 73–79), Leiter (2005, 64).

  94. See, for example, Prakken and Sartor (2013), Wyner et al (2011), Bench-Capon and Sartor (2003), Bench-Capon (1999), Ashley (1989).

  95. I’m assuming a background requirement that \(\langle X, r, s\rangle\) constitute a case, in the sense that \(X \vDash Premise(r)\) and \(Conclusion(r) = s\).

  96. Cf. Bergholtz and Peczenik (1997, 311) on conflicting precedents in Swedish law.

  97. We might say that the court is required to invoke something like the reason model of Horty (2015) as a tie-breaker. (Notice, though, that this would not help the court faced with \(X_{6}\) in the context of \(\varGamma _3\). So we would need further tie-breakers beyond the reason model.)

  98. See Garner et al. (2016, 300–307).

  99. See, for example, United States v. Snyder, 5 F. Supp. 3d 1258, 1262 (D. Or. 2014) (“When a Ninth Circuit decision becomes clearly irreconcilable with the reasoning or theory of intervening higher authority, this court must follow the higher authority.”) (internal quotation marks omitted).

  100. United States v. Madden, 733 F.3d 1314, 1319 (11th Cir. 2013) (stating that “our prior precedent is no longer binding once it has been substantially undermined or overruled by Supreme Court jurisprudence”) (internal quotation marks and ellipses omitted); U.S. v. Singletary, 268 F.3d 196 (3d Cir. 2001) (stating that “our respect for the uniformity of decisions within this Court yields when a prior panel’s holding conflicts with a holding of the Supreme Court”).

  101. See, for example, Luhman v. Beecher, 144 Wis.2d 781, 787–788 (1988) (“If decisions of the supreme court are inconsistent, we follow the court’s practice of relying on the most recent pronouncement.”). To be clear, the inferior court must determine that both precedent rules directly apply to the present dispute. If an earlier supreme court precedent directly applies, and a later supreme court precedent, while casting doubt on the reasoning of the earlier case, does not directly apply (and does not explicitly overrule the earlier holding), then an inferior court is generally required to follow the earlier case. See, for example, U.S. v. Leija-Sanchez, 602 F.3d 797, 799 (7th Cir. 2010) (Easterbrook C.J.).

  102. United States v. Madden, 733 F.3d 1314, 1319 (11th Cir. 2013) (“When we have conflicting case law, we follow our oldest precedent.”); Mader v. U.S., 654 F.3d 794, 800 (8th Cir. 2011); Rios v. City of Del Rio, Tex., 444 F.3d 417, 427 (5th Cir. 2006); McMellon v. U.S., 387 F.3d 329, 333 (4th Cir. 2004).

  103. Theile v. Michigan, 891 F.3d 240, 245 (6th Cir. 2018); White v. Chafin, 862 F.3d 1065, 1067 (10th Cir. 2017); Jackson v. Ault, 452 F.3d 734, 736 (8th Cir. 2006) (stating that “one panel may not overrule an earlier decision by another”).

  104. See, for example, Rios, 444 F.3d at 427 (“No panel is empowered to hold that a prior decision applies only on the limited set of facts set forth in that opinion, and a prior panel’s explication of the rules of law governing its holdings may not generally be disregarded as dictum.”) (internal quotation marks and citations omitted). For discussion, see Garner et al. (2016, 37ff.).

  105. Actually, some circuit courts have so many active judges that en banc cases may be heard by a proper subset. But we can ignore such details.

  106. For more work in AI & Law that takes up, in one way or another, the temporal context of legal decisions, see, for example, Al-Abdulkarim et al (2016), Grabmair (2016), Governatori et al (2005), and Berman and Hafner (1995).

  107. If \(c'\) was not decided before c, then \(c' =c\) and obviously the substitution is harmless.

  108. Or, at any rate, a quadruple consisting of a court, a set of facts, a rule, and a side. Whenever a court has failed to follow binding precedent, this quadruple will fail to be a case in our technical sense.

  109. There may, of course, be other sorts of constraints placed on the \(\mathbf{c }_1\) court—by constitutional provisions or legislation, for example. The point is just that there are no precedential constraints placed on the \(\mathbf{c }_1\) court.

  110. Again, the definition actually uses the correction\(^\Downarrow\) of \(\mathbf{c }_{i+1}\) to refine this set, but, as we’ve seen, if either (i) there were no applicable vertical precedents for \(\mathbf{c }_{i+1}\) in \(\varGamma ^{i}\), or (ii) there were applicable vertical precedents for \(\mathbf{c }_{i+1}\) in \(\varGamma ^{i}\), but the \(\mathbf{c }_{i+1}\) court applied the top applicable precedent rule and decided accordingly, then the correction\(^\Downarrow\) of \(\mathbf{c }_{i+1}\) is simply \(\mathbf{c }_{i+1}\).

  111. We might put this differently. We might say that the Court is at least sometimes permitted to decide for the defendant in this context. The question, then, would be whether the Court is always permitted to decide for the defendant in this context. We could then continue to speak in terms of the doctrine of precedent permitting and prohibiting decisions, rather than switching to talk of the doctrine “discouraging” decisions and “placing a thumb on the scale.” I’m speaking here in terms of discouragement simply because it seems more natural. Frankly, though, I’m not sure that it’s the best way to go from an analytical perspective.

  112. Seminole Tribe, 517 U.S. at 67 (internal quotation marks and citations omitted). Accord Cty of Allegheny v. Am. Civil Liberties Union Greater Pittsburgh Chapter, 492 U.S. 573, 668 (1989). See also United States v. Virginia, 518 U.S. 515, 596 (1996) (“The Supreme Court of the United States does not sit to announce “unique” dispositions. Its principal function is to establish precedent—that is, to set forth principles of law that every court in America must follow. As we said only this Term, we expect both ourselves and lower courts to adhere to the rationale upon which the Court based the results of its earlier decisions.”).

  113. Dickerson, 530 U.S. at 443. See also Citizens United v. Fed. Election Comm’n, 558 U.S. 310, 362 (2010) (“Our precedent is to be respected unless the most convincing of reasons demonstrates that adherence to it puts us on a course that is sure error.”). To be sure, most of the Court’s explicit discussion of the “special justification” requirement has taken place in the context of decisions whether to overrule a precedent. But see, for example, Quarles, 467 U.S. at 660 (O’Connor J. concurring in the judgment in part and dissenting in part), for the suggestion that a special justification is required even to distinguish (in the thick sense) a horizontal precedent.

  114. See Planned Parenthood of SE Pa. v. Casey, 505 U.S. 833, 864 (1992).

  115. It’s hard to say what impact, if any, this additional constraint built into the doctrine of horizontal precedent has on the actual practice of the Court. Certainly there are many cases in which the Court appears to have departed from a horizontal precedent based on nothing more than the bare policy preferences of the majority. And indeed the evidence suggests that precedent in general influences the decisions of Supreme Court justices far less than it influences the decisions of lower court judges. See, for example, Epstein et al. (2013, chp. 3), Segal (2008, 23), Segal and Spaeth (2002, 298), Segal and Spaeth (1996), Brenner and Spaeth (1995, 109). (Of course, there are a variety of reasons to predict this result. For discussion, see Klein (2017, 238–239), Posner (2008, chp. 10).) But even staunch attitudinalists acknowledge that the doctrine of precedent has some influence on the decisions of (some) Supreme Court justices. See Segal and Spaeth (2002, 295, 302–03), Segal and Spaeth (1996, 977). Our question, however, concerns the causal effects of a particular component of the doctrine of horizontal precedent, and this question has not, to my knowledge, been studied empirically.

  116. Consider, in this regard, the suggestion in Strauss (2010, 40) that common law reasoning is about “attitudes, not algorithms.” Note that similar difficulties will arise once the hierarchical model is expanded, as it presumably ought to be, to account for the overruling of horizontal precedents.

  117. The Seventh Circuit, however, allows one panel to depart from the holding of another whenever there are “compelling reasons” to do so. United States v. Reyes-Hernandez, 624 F.3d 405, 413–414 (7th Cir. 2010). And this sounds quite like the doctrine of horizontal precedent in the Supreme Court.

  118. United States v. Rodriguez-Pacheco, 475 F.3d 434, 442 (1st Cir. 2007) (quotation marks and internal citations omitted).

  119. Martinez v. State, 82 N.E.3d 261, 266 (Ind. Ct. App. 2017) (stating that “this court does not recognize horizontal stare decisis”); In re F.S., 53 N.E.3d 582, 596 (Ind. Ct. App. 2016) (“[W]e do not recognize horizontal stare decisis in Indiana.”); Smith v. State, 21 N.E.3d 121, 126 (Ind. Ct. App. 2014).

  120. Camreta v. Greene, 563 U.S. 692, 709 n.7 (2011) (internal citations omitted). See also Smentek v. Dart, 683 F.3d 373, 377 (7th Cir. 2012) (Posner J.) (stating that “a district court decision does not have precedential effect”); Threadgill v. Armstrong World Indus., Inc., 928 F.2d 1366, 1371 (3d Cir. 1991) (stating that “there is no such thing as ‘the law of the district”’).

  121. Erie R.R. v. Tompkins, 304 U.S. 64, 78 (1938). See also Commissioner v. Estate of Bosch, 387 U.S. 456, 465 (1967); Williams v. Kaiser, 323 U.S. 471, 473 (1945).

References

  • Abramowicz M, Stearns M (2005) Defining dicta. Stanf Law Rev 57:1–142

    Google Scholar 

  • Al-Abdulkarim L, Atkinson K, Bench-Capon T (2015) Factors, issues and values: revisiting reasoning with cases. In: Proceedings of the fifteenth international conference on artificial intelligence and law (ICAIL-15), pp 3–12

  • Al-Abdulkarim L, Atkinson K, Bench-Capon T (2016) Accomodating change. Artif Intell Law 24:409–427

    Article  Google Scholar 

  • Aleven V (1997) Teaching case-based argumentation through a model and examples. Ph.D. thesis, Intelligent Systems Program, University of Pittsburgh

  • Aleven V, Ashley KD (1996) How different is different? Arguing about the significance of similarities and differences. In: Smith I, Faltings B (eds) Advances in case-based reasoning. Springer, New York, pp 1–15

    Google Scholar 

  • Alexander L (1989) Constrained by precedent. Calif Law Rev 63:1–64

    Google Scholar 

  • Alexander L, Sherwin E (2001) The rule of rules. Duke University Press, Durham

    Book  Google Scholar 

  • Alexander L, Sherwin E (2007) Judges as rule makers. In: Edlin DE (ed) Common law theory. Cambridge University Press, Cambridge, pp 27–50

    Chapter  Google Scholar 

  • Alexander L, Sherwin E (2008) Demystifying legal reasoning. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • American Law Institute (1965) Restatement (second) of torts. American Law Institute Publishers, Philadelphia

    Google Scholar 

  • American Law Institute (2005) Restatement (third) of torts. American Law Institute Publishers, Philadelphia

    Google Scholar 

  • Ashley K (1989) Toward a computational theory of arguing with precedents. In: Proceedings of the second international conference on artificial intelligence and law (ICAIL-89), pp 93–102

  • Ashley K (1990) Modeling legal argument. MIT Press, Cambridge

    Google Scholar 

  • Ashley KD, Brüninghaus S (2003) A predictive role for intermediate legal concepts. In: Bourcier D (ed) Legal knowledge and information systems: JURIX 2003. IOS Press, Amsterdam, pp 153–162

    Google Scholar 

  • Bankowski Z, MacCormick DN, Marshall G (1997) Precedent in the United Kingdom. In: MacCormick DN, Summers RS, Goodhart AL (eds) Interpreting precedents. Routledge, London, pp 325–326

    Google Scholar 

  • Bench-Capon T (1999) Some observations on modelling case based reasoning with formal argument models. In: Proceedings of the seventh international conference on artificial intelligence and law (ICAIL-99), pp 36–42

  • Bench-Capon T (2017) HYPO’S legacy: introduction to the virtual special issue. Artif Intell Law 25:205–250

    Article  Google Scholar 

  • Bench-Capon T, Sartor G (2003) A model of legal reasoning with cases incorporating theories and values. Artif Intell 150(1–2):97–143

    Article  MATH  Google Scholar 

  • Bergholtz G, Peczenik A (1997) Precedent in Sweden. In: MacCormick DN, Summers RS, Goodhart AL (eds) Interpreting precedents. Routledge, London, pp 293–314

    Google Scholar 

  • Berman DH, Hafner CD (1995) Understanding precedents in a temporal context of evolving legal doctrine. In: Proceedings of the fifth international conference on artificial intelligence and law (ICAIL-95), pp 42–51

  • Bradford CS (1990) Following dead precedent. Fordham Law Rev 59:39–90

    Google Scholar 

  • Branting LK (1994) A computational model of ratio decidendi. Artif Intell Law 2:1–31

    Article  Google Scholar 

  • Brenner S, Spaeth HJ (1995) Stare indecisis. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Brüninghaus S, Ashley KD (2003) Predicting outcomes of case-based legal arguments. In: Proceedings of the ninth international conference on artificial intelligence and law (ICAIL-11), pp 233–242

  • Caminker EH (1994) Why must inferior courts obey superior court precedents? Stanf Law Rev 46:817–873

    Article  Google Scholar 

  • Chen DL, Eagel J (2017) Can machine learning help predict the outcome of asylum adjudications? In: Proceedings of the sixteenth international conference on artificial intelligence and law (ICAIL-17), pp 237–240

  • Conrad JG, Al-Kofahi K (2017) Scenario analytics. In: Proceedings of the sixteenth international conference on artificial intelligence and law (ICAIL-17), pp 29–39

  • Cross F (2005) Appellate court adherence to precedent. J Empir Leg Stud 2(2):369–405

    Article  Google Scholar 

  • Cross R, Harris J (1991) Precedent in English law. Oxford University Press, Oxford

    Google Scholar 

  • Dorf MC (1994) Dicta and article III. Univ Pa Law Rev 142:1997–2069

    Article  Google Scholar 

  • Duxbury N (2008) The nature and authority of precedent. Oxford University Press, Oxford

    Book  Google Scholar 

  • Dworkin R (1977) Taking rights seriously. Harvard University Press, Cambridge

    Google Scholar 

  • Easterbrook FH (1981) Maximum price fixing. Univ Chic Law Rev 48:886–910

    Article  Google Scholar 

  • Easterbrook FH (1982) Is there a ratchet in antitrust law? Tex Law Rev 60:705–720

    Google Scholar 

  • Easterbrook FH (1984) Vertical arrangements and the rule of reason. Antitrust Law J 53(1):135–173

    Google Scholar 

  • Eisenberg MA (2007) The principles of legal reasoning in the common law. In: Edlin DE (ed) Common lawtheory. Cambridge University Press, Cambridge, pp 81–101

    Google Scholar 

  • Eng S (1997) Precedent in Norway. In: MacCormick DN, Summers RS, Goodhart AL (eds) Interpreting precedents. Routledge, London, pp 189–217

    Google Scholar 

  • Epstein L, Landes WM, Posner RA (2013) The behavior of federal judges. Harvard University Press, Cambridge

    Google Scholar 

  • Friedman B (2010) The wages of stealth overruling (with particular attention to Miranda v. Arizona). Georget Law J 99(1):1–64

    Google Scholar 

  • Garner BA, Bea C, Berch RW, Gorsuch NM, Hartz HL, Hecht NL, Kavanaugh BM, Kozinski A, Lynch SL, Pryor WH Jr, Reavley TM, Sutton JS, Wood DP (2016) The law of judicial precedent. Thomson Reuters, Toronto

    Google Scholar 

  • Goodhart AL (1930a) Case law in England and America. Cornell Law Rev 15(2):173–193

    Google Scholar 

  • Goodhart AL (1930b) Determining the ratio decidendi of a case. Yale Law J 40:161–183

    Article  Google Scholar 

  • Governatori G, Palmirani M, Riveret R, Rotolo A, Sartor G (2005) Norm modifications in defeasible logic. In: Moens MF, Spyne P (eds) Legal knowledge and information systems: JURIX 2005. IOS Press, Amsterdam, pp 13–22

    Google Scholar 

  • Grabmair M (2016) Modeling purposive legal argumentation and case outcome prediction using argument schemes in the value judgment formalism. Ph.D. dissertation, University of Pittsburgh

  • Grabmair M (2017) Predicting trade secret case outcomes using argument schemes and learned quantitative value effect tradeoffs. In: Proceedings of the sixteenth international conference on artificial intelligence and law (ICAIL-17), pp 89–99

  • Grossi D, Jones AJI (2013) Constitutive norms and counts-as conditionals. In: Gabbay D, Horty J, Parent X, van der Meyden R, van der Torre L (eds) Handbook of deontic logic and normative systems. College Publications, London, pp 407–441

    Google Scholar 

  • Haire SB, Songer DR, Lindquist SA (2003) Appellate court supervision in the federal judiciary. Law Soc Rev 37(1):143–168

    Article  Google Scholar 

  • Hansford TG (2017) Vertical stare decisis. In: Epstein L, Lindquist SA (eds) Oxford handbook of U.S. judicial behavior. Oxford University Press, Oxford

    Google Scholar 

  • Hansford TG, Spriggs JF (2006) The politics of precedent on the U.S. Supreme Court. Princeton University Press, Princeton

    Book  Google Scholar 

  • Hart H (1994) The concept of law. Oxford University Press, Oxford

    Google Scholar 

  • Horty J (2004) The result model of precedent. Leg Theory 10:19–31

    Article  Google Scholar 

  • Horty J (2011a) Reasons and precedent. In: Proceedings of the thirteenth international conference on artificial intelligence and law (ICAIL-11). Association for Computing Machinery Press, pp 41–50

  • Horty J (2011b) Rules and reasons in the theory of precedent. Leg Theory 17:1–33

    Article  Google Scholar 

  • Horty J (2014) Norm change in the common law. In: Hansson SO (ed) David Makinson on classical methods for non-classical problems. Springer, New York, pp 335–355

    Chapter  Google Scholar 

  • Horty J (2015) Constraint and freedom in the common law. Philos Impr 15(25):1–27

    Google Scholar 

  • Horty J (2016) Reasoning with precedents as constrained natural reasoning. In: Lord E, Maguire B (eds) Weighing reasons. Oxford University Press, Oxford, pp 193–212

    Chapter  Google Scholar 

  • Horty J (2017) Reasoning with dimensions and magnitudes. In: Proceedings of the sixteenth international conference on artificial intelligence and law (ICAIL-17), pp 1–10

  • Horty J, Bench-Capon J (2012) A factor-based definition of precedential constraint. Artif Intell Law 20:181–214

    Article  Google Scholar 

  • Hovenkamp H (2008) The antitrust enterprise. Harvard University Press, Cambridge

    Google Scholar 

  • Kassow B, Songer DR, Fix MP (2012) The influence of precedent on state supreme courts. Polit Res Q 65(2):372–384

    Article  Google Scholar 

  • Klein D (2017) Law in judicial decision-making. In: Epstein L, Lindquist SA (eds) Oxford handbook of U.S. judicial behavior. Oxford University Press, Oxford

    Google Scholar 

  • Klein D, Devins N (2013) Dicta, schmicta. William Mary Law Rev 54:2021–2054

    Google Scholar 

  • Kozel RJ (2014) The scope of precedent. Michi Law Rev 113:179–230

    Google Scholar 

  • Lamond G (2005) Do precedents create rules? Leg Theory 11:1–26

    Article  Google Scholar 

  • Leiter B (2005) American legal realism. In: Golding MP, Edmundson WA (eds) Blackwell guide to the philosophy of law and legal theory. Wiley, New York, pp 50–66

    Google Scholar 

  • Leiter B (2007a) Is there an “American” jurisprudence? In: Naturalizing jurisprudence. Oxford University Press, pp 81–102

  • Leiter B (2007b) Legal realism and legal positivism reconsidered. In: Naturalizing jurisprudence. Oxford University Press, pp 59–80

  • Leiter B (2009) Explaining theoretical disagreement. Univ Chic Law Rev 76:1215–1250

    Google Scholar 

  • Levi EH (1949) An introduction to legal reasoning. University of Chicago Press, Chicago

    Google Scholar 

  • Lewis D (1969) Convention. Wiley, New York

    Google Scholar 

  • Lewis D (1975) Languages and language. In: Philosophical papers, vol 1. Oxford University Press, pp 163–188

  • Lindahl L, Odelstad J (2013) The theory of joining systems. In: Gabbay D, Horty J, Parent X, van der Meyden R, van der Torre L (eds) Handbook of deontic logic and normative systems. College Publications, London, pp 545–634

    MATH  Google Scholar 

  • Llewellyn K (1940) The status of the rule of judicial precedent. Univ Cincinnati Law Rev 14:207–251

    Google Scholar 

  • Llewellyn K (1950) Remarks on the theory of appellate decision and the rules or canons about how statutes are to be construed. Vanderbilt Law Rev 3:395–406

    Google Scholar 

  • Llewellyn K (1960) The common law tradition. Little, Brown and Company, Boston

    Google Scholar 

  • Llewellyn K (2008) The bramble bush. Oxford University Press, Oxford

    Google Scholar 

  • Llewellyn K (2011) The theory of rules. University of Chicago Press, Chicago

    Book  Google Scholar 

  • Lundmark T (1998) Interpreting precedents: a comparative study (review). Am J Comp Law 46:211–224

    Article  Google Scholar 

  • MacCormick DN, Summers RS (eds) (1997) Interpreting precedents: a comparative study. Ashgate, Farnham

    Google Scholar 

  • Mead JW (2012) Stare decisis in the inferior courts of the United States. Nev Law J 12:787–830

    Google Scholar 

  • Montrose J (1957a) Ratio decidendi and the House of Lords. Mod Law Rev 20(2):124–130

    Article  Google Scholar 

  • Montrose J (1957b) The ratio decidendi of a case. Mod Law Rev 20(6):587–595

    Article  Google Scholar 

  • Paton GW (1946) A textbook of jurisprudence. Oxford University Press, Oxford

    Google Scholar 

  • Posner RA (1970) A program for the Antitrust Division. Univ Chic Law Rev 38:500–536

    Article  Google Scholar 

  • Posner RA (1975a) Antitrust policy and the Supreme Court. Columbia Law Rev 75:282–327

    Article  Google Scholar 

  • Posner RA (1975b) The Supreme Court and antitrust policy: a new direction? Antitrust Law J 44(1):10–12

    Google Scholar 

  • Posner RA (1976) Antitrust law. University of Chicago Press, Chicago

    Google Scholar 

  • Posner RA (1979) The Chicago school of antitrust analysis. Univ Pa Law Rev 127:925–948

    Article  Google Scholar 

  • Posner RA (2001) Antitrust law, 2nd edn. University of Chicago Press, Chicago

    Book  Google Scholar 

  • Posner RA (2008) How judges think. Harvard University Press, Cambridge

    Google Scholar 

  • Prakken H, Sartor G (1998) Reasoning with precedents in a formal dialogue game. Artif Intell Law 6:231–287

    Article  Google Scholar 

  • Prakken H, Sartor G (2013) Formalising arguments about norms. In: Ashley K (ed) Legal knowledge and information systems: JURIX 2013. IOS Press, Amsterdam, pp 121–130

    Google Scholar 

  • Raz J (1970) The concept of a legal system. Oxford University Press, Oxford

    Google Scholar 

  • Raz J (1990) Practical reason and norms. Oxford University Press, Oxford

    Google Scholar 

  • Raz J (2009) The authority of law. Oxford University Press, Oxford

    Google Scholar 

  • Re RM (2014) Narrowing precedent in the Supreme Court. Columbia Law Rev 114(7):1861–1911

    Google Scholar 

  • Reddick M, Benesh SC (2000) Norm violation by the lower courts in the treatment of Supreme Court precedent. Justice Syst J 21(2):117–142

    Google Scholar 

  • Rigoni A (2015) An improved factor based approach to precedential constraint. Artif Intell Law 23:133–160

    Article  Google Scholar 

  • Rigoni A (2017) Representing dimensions within the reason model of precedent. Artif Intell Law. https://doi.org/10.1007/s10506-017-9216-7

    Article  Google Scholar 

  • Roth B, Verheij B (2004) Cases and dialectical arguments: an approach to case-based reasoning. In: Meersman R, Tari Z, Corsaro A (eds) OTM workshops. Springer, New York, pp 634–651

    Google Scholar 

  • Schauer F (2009) Thinking like a lawyer. Harvard University Press, Cambridge

    Google Scholar 

  • Segal JA (2008) Judicial behavior. In: Caldeira GA, Keleman RD, Whittington KE (eds) Oxford handbook of law and politics. Oxford University Press, Oxford, pp 19–31

    Google Scholar 

  • Segal JA, Spaeth HJ (1996) The influence of stare decisis on the votes of United States Supreme Court justices. Am J Polit Sci 40(4):971–1003

    Article  Google Scholar 

  • Segal JA, Spaeth HJ (2002) The Supreme Court and the attitudinal model revisited. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Shapiro SJ (2011) Legality. Harvard University Press, Cambridge

    Book  Google Scholar 

  • Simpson A (1957) The ratio decidendi of a case. Mod Law Rev 20(4):413–415

    Google Scholar 

  • Simpson A (1958) The ratio decidendi of a case. Mod Law Rev 21(2):155–60

    Article  Google Scholar 

  • Simpson A (1959) The ratio decidendi of a case. Mod Law Rev 22(5):453–457

    Article  Google Scholar 

  • Sloan AE (2009) The dog that didn’t bark: stealth procedures and the erosion of stare decisis in the federal courts of appeals. Fordham Law Rev 78:713–772

    Google Scholar 

  • Songer DR, Segal JA, Cameron CM (1994) The hierarchy of justice. Am J Polit Sci 38(3):673–696

    Article  Google Scholar 

  • Strauss DA (2010) The living constitution. Oxford University Press, Oxford

    Google Scholar 

  • Summers RS (1997) Precedent in the United States (New York state). In: MacCormick DN, Summers RS, Goodhart AL (eds) Interpreting precedents. Routledge, London, pp 355–406

    Google Scholar 

  • Taruffo M (1997) Institutional factors influencing precedents. In: MacCormick DN, Summers RS, Goodhart AL (eds) Interpreting precedents. Routledge, London, pp 437–460

    Google Scholar 

  • Westerland C, Segal JA, Epstein L, Cameron CM, Comparato S (2010) Strategic defiance and compliance in the U.S. courts of appeals. Am J Polit Sci 54(4):891–905

    Article  Google Scholar 

  • Wyner AZ, Bench-Capon J, Atkinson KM (2011) Towards formalising argumentation about legal cases. In: Proceedings of the thirteenth international conference on artificial intelligence and law (ICAIL-11), pp 1–10

Cases

  • Abood v. Detroit Bd. of Ed., 431 U.S. 209 (1977)

  • Adarand Constructors, Inc. v. Pena, 515 U.S. 200 (1995)

  • Alaska Pub. Interest Research Grp. v. State, 167 P.3d 27 (Alaska 2007)

  • Albrecht v. Herald Co., 390 U.S. 145 (1968)

  • American Civil Liberties Union of Ky. v. McCreary Cnty., 607 F.3d 439 (6th Cir. 2010)

  • Amgen, Inc. v. F. Hoffmann-La Roche Ltd., 494 F. Supp. 2d 54 (D. Mass. 2007)

  • Arecibo Cmty Health Care, Inc. v. Commonwealth of Puerto Rico, 270 F.3d 17 (1st Cir. 2001)

  • Arizona v. Gant, 556 U.S. 332 (2009)

  • Ashcroft v. al-Kidd, 563 U.S. 731 (2011)

  • Axcell v. Phillips, 473 S.W.2d 554 (Tex. Civ. App. 1971)

  • Baker v. Nelson, 409 U.S. 810 (1972)

  • Baltimore & Carolina Line v. Redman, 295 U.S. 654 (1935)

  • Berghuis v. Thompkins, 130 S. Ct. 2250 (2010)

  • Bosse v. Oklahoma, 137 S. Ct. 1 (2016)

  • Bowers v. Hardwick, 478 U.S. 186 (1986)

  • Butts v. City of New York Dep’t of Hous. Pres. & Dev., 990 F.2d 1397 (2d Cir. 1993)

  • Camreta v. Greene, 563 U.S. 692 (2011)

  • Cardenas v. Dretke, 405 F.3d 244 (5th Cir. 2005)

  • Casper v. Am. Int’l S. Ins. Co., 336 Wis. 2d 267 (2011)

  • Citizens United v. Fed. Election Comm’n, 558 U.S. 310 (2010)

  • Com. v. Millner, 585 Pa. 237 (2005)

  • Commissioner v. Estate of Bosch, 387 U.S. 456 (1967)

  • County of Allegheny v. American Civil Liberties Union, Greater Pittsburgh Chapter, 492 U.S. 573 (1989)

  • Davis v. Starkenburg, 5 Wash. 2d 273 (1940)

  • Dickerson v. United States, 530 U.S. 428 (2000)

  • Does 1–7 v. Round Rock Indep. Sch. Dist., 540 F. Supp. 2d 735 (W.D. Tex. 2007)

  • Dr. Miles Medical Co. v. John D. Park & Sons Co., 220 U.S. 373 (1911)

  • EI DuPont De Nemours & Co. v. United States, 460 F.3d 515 (3d Cir. 2006)

  • Erie R.R. v. Tompkins, 304 U.S. 64 (1938)

  • Evans v. Rockdale Hosp., LLC, 345 Ga. App. 511 (2018)

  • Exergen Corp. v. Kids-Med, Inc., 189 F. Supp. 3d 237 (D. Mass. 2016)

  • Fed. Trade Comm’n v. Beech-Nut Packing Co., 257 U.S. 441 (1922)

  • Flast v. Cohen, 392 U.S. 83 (1968)

  • Frey & Son v. Cudahy Packing Co., 256 U.S. 208 (1921)

  • Frothingham v. Mellon, 262 U.S. 447 (1923)

  • George v. Hercules Real Estate Servs., Inc., 339 Ga. App. 843 (2016)

  • Haith ex rel. Accretive Health, Inc. v. Bronfman, 928 F. Supp. 2d 964 (N.D. Ill. 2013)

  • Halliburton Co. v. Erica P. John Fund, Inc., 134 S. Ct. 2398 (2014)

  • Harris v. New York, 401 U.S. 222 (1971)

  • Harris v. State, 407 P.3d 348 (Nev. App. 2017)

  • Hart v. Massanari, 266 F.3d 1155 (9th Cir. 2001)

  • Helvering v. Hallock, 309 U.S. 106 (1940)

  • Hicks v. Miranda, 422 U.S. 332 (1975)

  • Hohn v. United States, 524 U.S. 236 (1998)

  • Howell Lumber Co. v. City of Tuscaloosa, 757 So. 2d 1173 (Ala. Civ. App. 1997)

  • Hutto v. Davis, 454 U.S. 370 (1982)

  • In re Ashai, 211 F. Supp. 3d 1215 (C.D. Cal. 2016)

  • In re F.S., 53 N.E.3d 582 (Ind. Ct. App. 2016)

  • In re Marriage of Kaufman, 299 Ill. App. 3d 508 (1998)

  • In re Reveal, 148 B.R. 288 (Bankr. S.D. Ohio 1992)

  • Jackson v. Ault, 452 F.3d 734 (8th Cir. 2006)

  • Jaffree v. Bd. of Sch. Comm’rs of Mobile Cty., 459 U.S. 1314 (1983)

  • James v. United States, 550 U.S. 192 (2007)

  • Janus v. Am. Fed’n of State, Cty., & Mun. Employees, Council 31, 138 S. Ct. 2448 (2018)

  • Johnson v. DeSoto Cty. Bd. of Commissioners, 72 F.3d 1556 (11th Cir. 1996)

  • Johnson v. United States, 135 S. Ct. 2551 (2015)

  • Khan v. State Oil Co., 93 F.3d 1358 (7th Cir. 1996)

  • Kiefer-Stewart Co. v. Joseph E. Seagram & Sons, 340 U.S. 211 (1951)

  • Kimble v. Marvel Entm’t, LLC, 135 S. Ct. 2401 (2015)

  • Lawrence v. Texas, 539 U.S. 558 (2003)

  • Leegin Creative Leather Prod., Inc. v. PSKS, Inc., 551 U.S. 877 (2007)

  • Local 8599, United Steelworkers of America v. Board of Education, 162 Cal. App. 3d 823 (1984)

  • Luhman v. Beecher, 144 Wis. 2d 781 (1988)

  • Mader v. U.S., 654 F.3d 794 (8th Cir. 2011)

  • Martinez v. State, 82 N.E.3d 261 (Ind. Ct. App. 2017)

  • McCoy v. Massachusetts Inst. of Tech., 950 F.3d 13 (1st Cir. 1991)

  • McGary v. Crowley, 266 F. Supp. 3d 254 (D.D.C. 2017)

  • McMellon v. U.S., 387 F.3d 329 (4th Cir. 2004)

  • Metro Broadcasting, Inc. v. FCC, 497 U.S. 547 (1990)

  • Michigan v. Bay Mills Indian Cmty., 134 S. Ct. 2024 (2014)

  • Montejo v. Louisiana, 556 U.S. 778 (2009)

  • National Bellas Hess, Inc. v. Department of Revenue of Ill., 386 U.S. 753 (1967)

  • New York v. Belton, 453 U.S. 454 (1981)

  • Nunez-Reyes v. Holder, 646 F.3d 684 (9th Cir. 2011)

  • Obergefell v. Hodges, 135 S. Ct. 2584 (2015)

  • Omega S.A. v. Costco Wholesale Corp., 541 F.3d 982 (9th Cir. 2008)

  • Oregon v. Elstad, 470 U.S. 298 (1985)

  • Osaka Shosen Kaisha Line v. United States, 300 U.S. 98 (1937)

  • Palmore v. Sidoti, 466 U.S. 429 (1984)

  • Panayoty v. Annucci, 898 F. Supp. 2d 469 (N.D.N.Y. 2012)

  • Payne v. Tennessee, 501 U.S. 808 (1991)

  • Pellegrino v. AMPCO Sys. Parking, 486 Mich. 330 (2010)

  • People v. Etherton, 82 N.E.3d 693 (Ill. 2017)

  • Planned Parenthood of SE Pa. v. Casey, 505 U.S. 833 (1992)

  • Poonjani v. Shanahan, 319 F. Supp. 3d 644 (S.D.N.Y. 2018)

  • Quill Corp. v. North Dakota, 504 U.S. 298 (1992)

  • Reiser v. Residential Funding Corp., 380 F.3d 1027 (7th Cir. 2004)

  • Rios v. City of Del Rio, Tex., 444 F.3d 417 (5th Cir. 2006)

  • Rivers v. Roadway Exp., Inc., 511 U.S. 298 (1994)

  • Rodriguez de Quijas v. Shearson/Am. Exp., Inc., 490 U.S. 477 (1989)

  • Rodriguez v. Nat’l City Bank, 277 FRD 148 (E.D. Pa. 2011)

  • Sanchez v. Carter, 343 Ga. App. 187 (2017)

  • Sanford v. Clear Channel Broad, Inc., 14 Neb. App. 908 (2006)

  • Sell v. Gama, 231 Ariz. 323 (2013)

  • Seminole Tribe of Florida v. Florida, 517 U.S. 44 (1996)

  • Simpson v. Union Oil Co., 377 U.S. 13 (1964)

  • Smentek v. Dart, 683 F.3d 373 (7th Cir. 2012)

  • Smith v. State, 21 N.E.3d 121 (Ind. Ct. App. 2014)

  • S. Dakota v. Wayfair, Inc., 138 S. Ct. 2080 (2018)

  • State Oil v. Khan, 522 U.S. 3 (1997)

  • State v. Frazier, 181 Conn. App. 1 (2018)

  • State v. Hausmann, 277 Neb. 819 (2009)

  • State v. Menzies, 889 P.2d 393 (Utah 1994)

  • Stephenson v. Perlitz, 524 S.W.2d 786 (Tex. Civ. App. 1975)

  • Stop Reckless Economic Instability Caused by Democrats v. Federal Election Com’n, 814 F.3d 221 (4th Cir. 2016)

  • Stringer v. Stringer, 544 S.W.3d 714 (Tenn. Ct. App. 2017)

  • Sykes v. United States, 131 S. Ct. 2267 (2011)

  • Tate v. Showboat Marina Casino Partnership, 431 F.3d 580 (2005)

  • Theile v. Michigan, 891 F.3d 240 (6th Cir. 2018)

  • Threadgill v. Armstrong World Indus., Inc., 928 F.2d 1366 (3d Cir. 1991)

  • Thurston Motor Lines, Inc. v. Jordan K. Rand, Ltd., 682 F.2d 811 (9th Cir. 1982)

  • Thurston Motor Lines, Inc. v. Jordan K. Rand, Ltd., 460 U.S. 533 (1983)

  • United States ex rel Shore v. O’Leary, 833 F.2d 663 (7th Cir. 1987)

  • United States v. A. Schrader’s Son, 252 U.S. 85 (1920)

  • United States v. Bausch & Lomb Optical Co., 321 U.S. 707 (1944)

  • United States v. Bd. of Cty. Commissioners of Cty. of Otero, 843 F.3d 1208 (10th Cir. 2016)

  • United States v. Colgate & Co., 250 U.S. 300 (1919)

  • United States v. Danielczyk, 638 F.3d 611 (4th Cir. 2012)

  • United States v. Duvall, 740 F.3d 604 (D.C. Cir. 2013)

  • United States v. General Electric Co., 272 U.S. 476 (1926)

  • United States v. Leija-Sanchez, 602 F.3d 797 (7th Cir. 2010)

  • United States v. Madden, 733 F.3d 1314 (11th Cir. 2013)

  • United States v. McKesson & Robbins, Inc., 351 U.S. 305 (1956)

  • United States v. Parke, Davis & Co., 362 U.S. 20 (1960)

  • United States v. Pate, 754 F.3d 550 (8th Cir. 2014)

  • United States v. Reyes-Hernandez, 624 F.3d 405 (7th Cir. 2010)

  • United States v. Rodriguez-Pacheco, 475 F.3d 434 (1st Cir. 2007)

  • United States v. Rosenau, 870 F. Supp. 2d 1109 (W.D. Wash. 2012)

  • United States v. Sampson, 486 F.3d 13 (1st Cir. 2007)

  • United States v. Singletary, 268 F.3d 196 (3d Cir. 2001)

  • United States v. Snyder, 5 F. Supp. 3d 1258 (D. Or. 2014)

  • United States v. Socony-Vacuum Oil Co., 310 U.S. 150 (1940)

  • United States v. South-Eastern Unerwriters Ass’n, 322 U.S. 533 (1944)

  • United States v. Trenton Potteries Co., 273 U.S. 392 (1927)

  • United States v. Virginia, 518 U.S. 515 (1996)

  • United States v. Walker, 351 F. App’x 16 (6th Cir. 2009)

  • Utah Republican Party v. Cox, 892 F.3d 1066 (10th Cir. 2018)

  • Vujosevic v. Rafferty, 844 F.2d 1023 (3d Cir. 1988)

  • White v. Chafin, 862 F.3d 1065 (10th Cir. 2017)

  • Wilder v. Apfel, 153 F.3d 799 (7th Cir. 1998)

  • Williams v. Kaiser, 323 U.S. 471 (1945)

  • Winslow v. F.E.R.C., 587 F.3d 1133 (D.C. Cir. 2009)

  • Wygant v. Jackson Bd. of Educ., 476 U.S. 267 (1986)

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Acknowledgements

Thanks to Alexia Brancato, Beth Dalmut, Adam Elga, John Horty, Gideon Rosen, Michael Smith, and two anonymous referees.

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Broughton, G.L. Vertical precedents in formal models of precedential constraint. Artif Intell Law 27, 253–307 (2019). https://doi.org/10.1007/s10506-019-09244-1

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