Aggregation of Probabilities and Illogic

Classical logic and probability theory produce in law thetroublesome paradox of aggregation of claims: On theother hand, logic seems to tell us that the aggregatedlikelihood of alternative claims elevates in response toprobability\u27s rules; thus, if the plaintiff almost provesclaim A and almost proves an alternative but independentclaim B, then the plaintiff should win one. On the otherhand, because the law requires each claim to meet thestandard of proof, and thus refuses to apply the proofstandard to the aggregation, the plaintiff loses inactuality; legal scholars despair in consequences-including Ariel Porat and Eric Posner in their new articleAggregation and Law.Fuzzy Logic, however, eradicates the paradox, byshowing that the claims\u27 aggregate likelihood equals themost likely claim\u27s likelihood. The law is correct inapplying this approach

Beliefs and Probabilities: The Errors That Remain Are Mine Alone

Imagine that the preface to a professor’s book implicitly asserts that all the propositions in the rest of his or her book are true, but explicitly acknowledges that experience would suggest some errors remain among those propositions. The prof thereby seems paradoxically to believe inconsistent statements. But in fact this famous preface paradox is an illusion. The first statement is a belief reflecting epistemic uncertainty, while the second is a probabilistic statement about aleatory uncertainty. If one were to convert the probability into a belief, one would see that the author rationally holds perfectly consistent beliefs. Likewise the lottery paradox resolves. Remarkably, resolution of these philosophy paradoxes sheds important light on legal evidence and proof: once one realizes that legal factfinding deals in beliefs, not probabilities, many of the law’s proof paradoxes vaporize. All those paradoxes reveal a generally applicable and powerful principle of rational thought: if in the presence of epistemic uncertainty a person believes fact x and believes fact y because each passes the threshold for belief, then the person believes x AND y together. The explanation lies in the fact that epistemic uncertainty calls for nonadditive logic, which employs the MIN rule for conjunction rather than the product rule. The significance is broad, as it maps where one can logically believe a string of beliefs as a narrative chain

Fuzzy Logic and the Sliding Scale Theorem

The law operates principally in the context of ordinary transactions and relationships. Consequently it is important to develop insights into how it operates in the everyday world. To resolve recurring legal issues in everyday affairs, judges and other decision-makers sometimes use formulas. When a legal formula contains two elements, as several do, a process of fuzzy logic produces a result that is a function of a sliding scale between the elements. Thus, if physical presence in a new state + intent to remain = change of domicile, there will be degrees of each element, such that the degree of physical presence (which could be treated as a fraction between zero and one or as a point on a diagram where each of two axes runs from zero to one) combines with the degree of intent to remain, to produce a result - either acquisition of a new domicile or retention of the old one. The process and the result can best be illustrated by a diagram that, in most instances, resembles an economist\u27s demand curve. The placement and slope of the curve will depend on the particular formula, and the curve may shift depending on what is at stake. The process is at work in several fields of law, including (at least) contracts, civil procedure and conflict of laws

On the ‘residuum of powers’ in the great Anglo-American Federations: a neo-Bagehotian-Coasean gloss

In some constitutional designs, federation is based on the doctrine of ‘residuum of powers,’ where one level of government is privileged vis-à-vis the other, and where a concomitant enumeration of powers gives rise to a presumption of a restricted capacity to legislate outside powers so specified. The quintessential examples of this approach are the Federal Constitutions of the United States, Canada and Australia. The Coase theorem explains how and why efficiency in the allocation of these powers emerges regardless of the initial allocation of residuum powers. The analysis confirms this Coasean proposition in an evolutionary context. In all three jurisdictions, regardless of the initial allocation of powers, there is a neo-Bagehotian (evolutionary) shift from the canonical constitution and towards an ‘efficient constitution’—an institution that avoids (transaction) costs. Bargaining between general and special purpose governments allocates powers such that transaction costs are avoided. The paper provides an efficiency definition based on the distinction between symmetric federalism (as seen in the United States and Australia) and asymmetric federalism (as seen in Canada). On aggregate, the locus of this efficiency is either central (as in the case of the United States and Australia), or distributed (as in the case of Canada). Specific examples from all three jurisdictions provide further illustrations. Normatively, further efficiency gains could come from developing (constitutional) legal doctrines that dialogue directly with this evolution