Anarchy, hierarchy and order

Abstract

We advocate a new approach to study models of fermion masses and mix-ings, namely anarchy proposed in Ref. [1]. In this approach, we scan the O(1) coefficients randomly. We argue that this is the correct approach when the fundamental theory is sufficiently complicated. Assuming there is no physical distinction among three generations of neutrinos, the probability distributions in MNS mixing angles can be predicted independent of the choice of the measure. This is because the mixing angles are distributed according to the Haar measure of the Lie groups whose elements diagonalize the mass matrices. The near-maximal mixings, as observed in the atmospheric neutrino data and as required in the LMA solution to the solar neutrino problem, are highly probable. A small hierarchy between the ∆m 2 for the atmospheric and the solar neutrinos is obtained very easily; the complex seesaw case gives a hierarchy of a factor of 20 as the most probable one, even though this conclusion is more measure-dependent. U e3 has to be just below the current limit from the CHOOZ experiment. The CP-violating parameter sin δ is preferred to be maximal. We present a simple SU (5)-like extension of anarchy to the charged-lepton and quark sectors which works well phenomenologically.

China’s engagement with Kazakhstan and Russia’s Zugzwang: Why is Nur-Sultan incurring regional power hedging?

“…The “anarchy-hierarchy” dichotomy as a concept has long existed under the rubric of international relations, yet it has recently gained prominence as a significant alternative to the dominance of formal legal sovereignty approaches centering on a “culture of anarchy” (Kang, 2004; Lake, 2009; Mearsheimer, 2001; Morgenthau, 1948; Waltz, 1979). Alternatively, through the lens of various hierarchical literature, anarchy and hierarchy operate as opposite poles, with varying gradients of authority: anarchy <–> loose hierarchy <–> tight hierarchy (Parent & Erikson, 2009, pp. 136–137).…”

“…Doing so, subordinates will consistently seek to obtain the best sets of net benefits, while not offsetting the political order provided that the order conforms to interests, incentives and preferences (Clapton, 2009; Kang, 2003; Lake, 2009, p. 26). Strong alignment of interests and preferences produces a strong social contract with tighter alignment, whereas lesser alignment of interests and preferences produce a weaker social contract with a looser order (Parent & Erikson, 2009, pp. 136–137).…”

International Legitimacy Lost? Rule and Resistance When America Is First

“… 4 See Clark 1989; Cooley 2005; Donnelly 2006; Dunne 2003; Goh 2013; Hancock 2009; Hobson and Sharman 2005; Kang 2003/04; McDonald 2015; Parent and Erikson 2009; Reus-Smit 2005; Weber 2000. For a review, see Bially Mattern and Zarakol 2016. …”

Reconstructing hierarchy as the key international relations concept and its implications for the study of Japanese national identity

“…There are but a few international relations (IR) concepts that have been recently so widely examined and discussed as anarchy. Contemporary IR approaches treat anarchy as a fundamental, defining, and analytical central feature of IR (see i.e., Schmidt, 1998; Deudney, 2000, 2007; Bell, 2002; Donelly, 2006, 2015; Lake, 2009a; Parent and Erikson, 2009; Holmes, 2011). Virtually all scholars agree that ‘relations between states are anarchic and that this is one of the most unique, important, and enduring features of world politics’ (Lake, 2009 a : 2).…”