Combinatorial Voting

We study elections that simultaneously decide multiple issues, where voters have independent private values over bundles of issues. The innovation is in considering nonseparable preferences, where issues may be complements or substitutes. Voters face a political exposure problem: the optimal vote for a particular issue will depend on the resolution of the other issues. Moreover, the probabilities that the other issues will pass should be conditioned on being pivotal. We prove that equilibrium exists when distributions over values have full support or when issues are complements. We then study large elections with two issues. There exists a nonempty open set of distributions where the probability of either issue passing fails to converge to either 1 or 0 for all limit equilibria. Thus, the outcomes of large elections are not generically predictable with independent private values, despite the fact that there is no aggregate uncertainty regarding fundamentals. While the Condorcet winner is not necessarily the outcome of a multi-issue election, we provide sufficient conditions that guarantee the implementation of the Condorcet winner. © 2012 The Econometric Society

Aggregation of endogenous information in large elections

We study aggregation of information when voters can collect information of different precision, with increased precision entailing an increasing marginal cost. In order to properly understand the incentives to collect information we introduce another dimension of heterogeneity: on top of the ideological dimension we allow for different levels of intensity in preferences. Contrary to traditional models of endogenous information, in equilibrium, there are voters collecting information of different qualities. After characterizing all symmetric Bayesian equilibria in pure strategies for arbitrary rules of election and fairly general distribution of types. We study information aggregation in symmetric electorates and show that information aggregates even when voters collect information of different qualities

Power Brokers: Middlemen in Legislative Bargaining

We consider a model of decentralized bargaining among three parties. Parties meet one-on-one after being randomly matched, and can sell or buy votes to one another. The party with a majority of the votes can decide to implement its preferred policy or extend negotiations to capture additional rents. We provide necessary and sufficient conditions for the existence of an equilibrium in which a party acts as an intermediary, transferring resources and voting rights among parties that wouldn't negotiate directly with one another. These conditions are generic, do not require special frictions, and include `well-behaved' (i.e., single-peaked) preference profiles

Approval Voting and Scoring Rules with Common Values

Consider the problem of deciding a winner among three alternatives when voters have common values, but private information regarding the values of the alternatives. We compare approval voting with other scoring rules. For any finite electorate, the best equilibrium under approval voting is more efficient than either plurality rule or negative voting. If any scoring rule yields a sequence of equilibria that aggregates information in large elections, then approval voting must do so as well

The Condorcet Jur(ies) Theorem

Should two issues be decided jointly by a single committee or in separately by different committees? Similarly, should two defendants be tried together in a joint trial or tried separately in severed trials? Multiplicity of issues or defendants introduces novel strategic considerations. As in the standard Condorcet Jury Theorem, we consider large committees with common values and incomplete information. Our main result is that the joint trial by a single committee can aggregate information if and only if the severed trials by separate committees can aggregate information. Specifically, suppose that either for the joint trial or for the severed trials there exists an sequence of equilibria that implements the optimal outcome with probability approaching one as the number of voters goes to infinity. Then a sequence of equilibria with similar asymptotic efficiency exists for the other format. Thus, the advantage of either format cannot hinge on pure information aggregation with many signals

Helioseismic and Magnetic Imager observations of linear polarization from a loop prominence system

White-light observations by the Solar Dynamics Observatory's Helioseismic and Magnetic Imager of a loop-prominence system occurring in the aftermath of an X-class flare on 2013 May 13 near the eastern solar limb show a linearly polarized component, reaching up to $\sim$20% at an altitude of $\sim$33 Mm, about the maximal amount expected if the emission were due solely to Thomson scattering of photospheric light by the coronal material. The mass associated with the polarized component was 8.2$\times$10$^{14}$ g. At 15 Mm altitude, the brightest part of the loop was 3(+/-0.5)% linearly polarized, only about 20% of that expected from pure Thomson scattering, indicating the presence of an additional unpolarized component at wavelengths near Fe I (617.33 nm), probably thermal emission. We estimated the free electron density of the white-light loop system to possibly be as high as 1.8$\times$10$^{12}$ cm$^{-3}$.Comment: 9 pages, 5 figure

A statistical correlation of sunquakes based on their seismic and white-light emission

Several mechanisms have been proposed to explain the transient seismic emission, i.e. “sunquakes,” from some solar flares. Some theories associate high-energy electrons and/or white-light emission with sunquakes. High-energy charged particles and their subsequent heating of the photosphere and/or chromosphere could induce acoustic waves in the solar interior. We carried out a correlative study of solar flares with emission in hard X-rays, enhanced continuum emission at 6173 Å, and transient seismic emission. We selected those flares observed by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) with a considerable flux above 50 keV between 1 January 2010 and 26 June 2014. We then used data from the Helioseismic and Magnetic Imager onboard the Solar Dynamic Observatory to search for excess visible-continuum emission and new sunquakes not previously reported. We found a total of 18 sunquakes out of 75 flares investigated. All of the sunquakes were associated with an enhancement of the visible continuum during the flare. Finally, we calculated a coefficient of correlation for a set of dichotomic variables related to these observations. We found a strong correlation between two of the standard helioseismic detection techniques, and between sunquakes and visible-continuum enhancements. We discuss the phenomenological connectivity between these physical quantities and the observational difficulties of detecting seismic signals and excess continuum radiation