Objective rationality foundations for (dynamic) Alpha-MEU

We show how incorporating Gilboa, Maccheroni, Marinacci, and Schmeidler’s (2010) notion of objective rationality into the α-MEU model of choice under ambiguity can overcome several challenges faced by the baseline model without objective rationality. The decision-maker (DM) has a subjectively rational preference ≿^, which captures the complete ranking overacts the DM expresses when forced to make a choice; in addition, we endow the DM with a (possibly incomplete) objectively rational preference ≿*, which captures the rankings the DM deems uncontroversial. Under the objectively founded α-MEU model, ≿^ has an α-MEU representation and ≿*has a unanimity representation à la Bewley (2002), where both representations feature the same utility index and set of beliefs. While the axiomatic foundations of the baseline α-MEU model are still not fully understood, we provide a simple characterization of its objectively founded counterpart. Moreover, in contrast with the baseline model, the model parameters are uniquely identified. Finally, we provide axiomatic foundations for prior-by-prior Bayesian updating of the objectively founded α-MEU model, while we show that, for the baseline model, standard updating rules can be ill-defined

Objective rationality foundations for (dynamic) α-MEU

We show how incorporating Gilboa, Maccheroni, Marinacci, and Schmeidler’s (2010) notion of objective rationality into the alpha-MEU model of choice under ambiguity (Hurwicz, 1951) can overcome several challenges faced by the baseline model without objective rationality. The decision-maker (DM) has a subjectively rational preference $\succsim^\wedge$, which captures the complete ranking over acts the DM expresses when forced to make a choice; in addition, we endow the DM with a (possibly incomplete) objectively rational preference $\succsim^*$, which captures the rankings the DM deems uncontroversial. Under the objectively founded alpha-MEU model, $\succsim^\wedge$ has an alpha-MEU representation and $\succsim^*$ has a unanimity representation à la Bewley (2002), where both representations feature the same utility index and set of beliefs. While the axiomatic foundations of the baseline alpha-MEU model are still not fully understood, we provide a simple characterization of its objectively founded counterpart. Moreover, in contrast with the baseline model, the model parameters are uniquely identified. Finally, we provide axiomatic foundations for prior-by-prior Bayesian updating of the objectively founded alpha-MEU model, while we show that, for the baseline model, standard updating rules can be ill-defined

Objective Rationality Foundations for (Dynamic) α-MEU

We show how incorporating Gilboa, Maccheroni, Marinacci, and Schmeidler’s (2010) notion of objective rationality into the alpha-MEU model of choice under ambiguity (Hurwicz, 1951) can overcome several challenges faced by the baseline model without objective rationality. The decision-maker (DM) has a subjectively rational preference $\succsim^\wedge$, which captures the complete ranking over acts the DM expresses when forced to make a choice; in addition, we endow the DM with a (possibly incomplete) objectively rational preference $\succsim^*$, which captures the rankings the DM deems uncontroversial. Under the objectively founded alpha-MEU model, $\succsim^\wedge$ has an alpha-MEU representation and $\succsim^*$ has a unanimity representation à la Bewley (2002), where both representations feature the same utility index and set of beliefs. While the axiomatic foundations of the baseline alpha-MEU model are still not fully understood, we provide a simple characterization of its objectively founded counterpart. Moreover, in contrast with the baseline model, the model parameters are uniquely identified. Finally, we provide axiomatic foundations for prior-by-prior Bayesian updating of the objectively founded alpha-MEU model, while we show that, for the baseline model, standard updating rules can be ill-defined

Boolean Expected Utility

We propose a multiple-prior model of preferences under ambiguity that provides a unified lens through which to understand different formalizations of ambiguity aversion, as well as context-dependent negative and positive ambiguity attitudes documented in experiments. This model, Boolean expected utility (BEU), represents the belief the decision-maker uses to evaluate any uncertain prospect as the outcome of a game between two conflicting forces, Pessimism and Optimism. We prove, first, that BEU provides a novel representation of the class of invariant biseparable preferences (Ghirardato, Maccheroni, and Marinacci, 2004). Second, BEU accommodates rich patterns of ambiguity attitudes, which we characterize in terms of the relative power allocated to each force in the game

Enhanced Wavelet Analysis of Solar Magnetic Activity with Comparison to Global Temperature and the Central England Temperature Record

The continuous wavelet transform may be enhanced by deconvolution with the wavelet response function. After correcting for the cone-of-influence, the power spectral density of the solar magnetic record as given by the derectified yearly sunspot number is calculated, revealing a spectrum of odd harmonics of the fundamental Hale cycle, and the integrated instant power is compared to a reconstruction of global temperature in a normalized scatter plot displaying a positive correlation after the turn of the twentieth century. Comparison of the spectrum with that obtained from the Central England Temperature record suggests that some features are shared while others are not, and the scatter plot again indicates a possible correlation.Comment: 19 pages, 11 figure

Dual-self Representations of Ambiguity Preferences

We propose a class of multiple-prior representations of preferences under ambiguity, where the belief the decision-maker (DM) uses to evaluate an uncertain prospect is the outcome of a game played by two conflicting forces, Pessimism and Optimism. The model does not restrict the sign of the DM’s ambiguity attitude, and we show that it provides a unified framework through which to characterize different degrees of ambiguity aversion, and to represent the co-existence of negative and positive ambiguity attitudes within individuals as documented in experiments. We prove that our baseline representation, dual-self expected utility (DSEU), yields a novel representation of the class of invariant biseparable preferences (Ghirardato, Maccheroni, and Marinacci, 2004), which drops uncertainty aversion from maxmin expected utility (Gilboa and Schmeidler, 1989). Extensions of DSEU allow for more general departures from independence

Dual-self Representations of Ambiguity Preferences

We propose a class of multiple-prior representations of preferences under ambiguity, where the belief the decision-maker (DM) uses to evaluate an uncertain prospect is the outcome of a game played by two conflicting forces, Pessimism and Optimism. The model does not restrict the sign of the DM’s ambiguity attitude, and we show that it provides a unified framework through which to characterize different degrees of ambiguity aversion, and to represent the co-existence of negative and positive ambiguity attitudes within individuals as documented in experiments. We prove that our baseline representation, dual-self expected utility (DSEU), yields a novel representation of the class of invariant biseparable preferences (Ghirardato, Maccheroni, and Marinacci, 2004), which drops uncertainty aversion from maxmin expected utility (Gilboa and Schmeidler, 1989), while extensions of DSEU allow for more general departures from independence. We also provide foundations for a generalization of prior-by-prior belief updating to our model

Boolean Representations of Preferences under Ambiguity

We propose a class of multiple-prior representations of preferences under ambiguity where the belief the decision-maker (DM) uses to evaluate an uncertain prospect is the outcome of a game played by two conflicting forces, Pessimism and Optimism. The model does not restrict the sign of the DM’s ambiguity attitude, and we show that it provides a unified framework through which to characterize different degrees of ambiguity aversion, as well as to represent context-dependent negative and positive ambiguity attitudes documented in experiments. We prove that our baseline representation, Boolean expected utility (BEU), yields a novel representation of the class of invariant biseparable preferences (Ghirardato, Maccheroni, and Marinacci, 2004), which drops uncertainty aversion from maxmin expected utility (Gilboa and Schmeidler, 1989), while extensions of BEU allow for more general departures from independence

Multi-timescale Solar Cycles and the Possible Implications

Based on analysis of the annual averaged relative sunspot number (ASN) during 1700 -- 2009, 3 kinds of solar cycles are confirmed: the well-known 11-yr cycle (Schwabe cycle), 103-yr secular cycle (numbered as G1, G2, G3, and G4, respectively since 1700); and 51.5-yr Cycle. From similarities, an extrapolation of forthcoming solar cycles is made, and found that the solar cycle 24 will be a relative long and weak Schwabe cycle, which may reach to its apex around 2012-2014 in the vale between G3 and G4. Additionally, most Schwabe cycles are asymmetric with rapidly rising-phases and slowly decay-phases. The comparisons between ASN and the annual flare numbers with different GOES classes (C-class, M-class, X-class, and super-flare, here super-flare is defined as $\geq$ X10.0) and the annal averaged radio flux at frequency of 2.84 GHz indicate that solar flares have a tendency: the more powerful of the flare, the later it takes place after the onset of the Schwabe cycle, and most powerful flares take place in the decay phase of Schwabe cycle. Some discussions on the origin of solar cycles are presented.Comment: 8 pages, 4 figure