At a Rational Expectations Equilibrium (REE), individuals are assumed to know the map from states to prices. This hypothesis has two components, that agents agree (consensus) and that they have point expectations (degeneracy). We consider economies where agents' beliefs are described by a joint distribution on states and prices, and these beliefs are fulfilled at equilibrium. Beliefs are self-f...

We propose Meshcash, a new framework for cryptocurrency protocols that combines a novel, proof-of-work based, permissionless byzantine consensus protocol (the tortoise) that guarantees eventual consensus and irreversibility, with a possibly-faulty but quick consensus protocol (the hare). The construction is modular, allowing any suitable “hare” protocol to be plugged in. The combined protocol e...

the principle of sovereignty of will is taken into consideration in jurisprudence and law as one fundamental, significant principle. one instant of declaring sovereignty of will is the right to cancel the contract through option of condition. that the contracts are subject to the option of condition is easily accepted – though whether this is acceptable with some instants of contracts such as m...

In group decision making (GDM) processes, prior to the selection of the best alternative(s), it would be desirable that experts achieve a high degree of consensus or agreement between them. Due to the complexity of most decision making problems, individuals’ preferences may not satisfy formal properties. ‘Consistency’ is one of such properties, and it is associated with the transitivity propert...

In recent years there has been a growing consensus that ordinary reasoning does not conform to the laws of classical logic but is rather nonmonotonic in the sense that conclusions previously drawn may well be removed upon acquiring further information Even so rational belief formation has up to now been modelled as conforming to some important principles that are classically valid The counterex...

Bayesianism is a theory of inductive inference that makes use of the mathematical theory of probability. Bayesians usually hold that the relevant probabilities should be interpreted in terms of rational degrees of belief. This still leaves much scope for disagreement, since there is no consensus about what norms govern rational degrees of belief. In this chapter, we first provide an introductio...

In framing the concept of rational consensus, decision theorists have tended to defer to an older, established literature on social welfare theory for guidance on how to proceed. But the uncritical adoption of standards meant to regulate the reconciliation of differing interests has unduly burdened the development of rational methods for the synthesis of differing judgments. In particular, the ...

Mathematical concepts and systems of notation are intertwined with human cultural history. The discovery (or invention) of 0, understanding of negative, rational, and real numbers, and development of the calculus took place over thousands of years. But what of those most fundamental of mathematical objects, the positive integers: 1, 2, 3, 4, 5, ...? Until recently, the consensus was that the ca...