On the Welfare of Cardinal Voting Mechanisms

A voting mechanism is a method for preference aggregation that takes as input preferences over alternatives from voters, and selects an alternative, or a distribution over alternatives. While preferences of voters are generally assumed to be cardinal utility functions that map each alternative to a real value, mechanisms typically studied assume coarser inputs, such as rankings of the alternatives (called ordinal mechanisms). We study cardinal mechanisms, that take as input the cardinal utilities of the voters, with the objective of minimizing the distortion - the worst-case ratio of the best social welfare to that obtained by the mechanism. For truthful cardinal mechanisms with m alternatives and n voters, we show bounds of Theta(mn), Omega(m), and Omega(sqrt{m}) for deterministic, unanimous, and randomized mechanisms respectively. This shows, somewhat surprisingly, that even mechanisms that allow cardinal inputs have large distortion. There exist ordinal (and hence, cardinal) mechanisms with distortion O(sqrt{m log m}), and hence our lower bound for randomized mechanisms is nearly tight. In an effort to close this gap, we give a class of truthful cardinal mechanisms that we call randomized hyperspherical mechanisms that have O(sqrt{m log m}) distortion. These are interesting because they violate two properties - localization and non-perversity - that characterize truthful ordinal mechanisms, demonstrating non-trivial mechanisms that differ significantly from ordinal mechanisms. Given the strong lower bounds for truthful mechanisms, we then consider approximately truthful mechanisms. We give a mechanism that is delta-truthful given delta in (0,1), and has distortion close to 1. Finally, we consider the simple mechanism that selects the alternative that maximizes social welfare. This mechanism is not truthful, and we study the distortion at equilibria for the voters (equivalent to the Price of Anarchy, or PoA). While in general, the PoA is unbounded, we show that for equilibria obtained from natural dynamics, the PoA is close to 1. Thus relaxing the notion of truthfulness in both cases allows us to obtain near-optimal distortion

Interpretation of the diphoton excess at CMS and ATLAS

We consider the diphoton resonance at the 13 TeV LHC in a consistent model with new scalars and vector-like fermions added to the Standard Model (SM), which can be constructed from orbifold grand unified theories and string models. The gauge coupling unification can be achieved, neutrino masses can be generated radiatively, and electroweak vacuum stability problem can be solved. To explain the diphoton resonance, we study a spin-0 particle, and discuss various associated final states.Comment: 8 pages, 6 figures, 3 tables; v2: typos corrected, references adde

Exploring the Jet Multiplicity in the 750 GeV Diphoton Excess

The recent diphoton excess at the LHC has been explained tentatively by a Standard Model (SM) singlet scalar of 750 GeV in mass, in the association of heavy particles with SM gauge charges. These new particles with various SM gauge charges induce loop-level couplings of the new scalar to $WW$, $ZZ$, $Z\gamma$, $\gamma\gamma$, and $gg$. We show that the strength of the couplings to the gauge bosons also determines the production mechanism of the scalar particle via $WW,\, ZZ,\, Z\gamma,\, \gamma\gamma,\, gg$ fusion which leads to individually distinguishable jet distributions in the final state where the statistics will be improved in the ongoing run. The number of jets and the leading jet's transverse momentum distribution in the excess region of the diphoton signal can be used to determine the coupling of the scalar to the gauge bosons arising from the protons which subsequently determine the charges of the heavy particles that arise from various well-motivated models.Comment: 4 pages, 4 figures, 1 tabl

Diaspora and postmodern fecundity

Central to the experience of postmodernity is the increase in, and the intensification of, transnational encounters. The globalization of capital, culture, work-forces, and identities leads to patterns of homogenization whose totalizing tendency is undercut by intense fragmentation and the local play of differences. The increased productivity in economic and cultural terms marks the postmodern as remarkably fecund. This perception of fecundity comes from the various, and often opposing, groups on the political continuum.1 The \u27triumph\u27 of transnational capital in Asia and the entry of Eastern Europe into the capitalist fold have created unprecedented economic and financial flows. Simultaneously, the antifoundational dismantling of epistemological hierarchies release long-repressed energies that create new flows and open up fresh possibilities. These new flows and structuration’s require cognitive refrigeration, as older modes of knowing the world have become inadequate. The nation is one social and cultural formation that has come to be rigorously Interrogated in the light of the global-local· dynamisms. A rise in the volume of migrations and the increasing visibility of varied diasporas - communities that transcend the geopolitical boundaries of the nation-state - demand a new sense of national belonging: national heritage, essence, tradition etc. have lost their immanent valences. For instance, Chow (1993) stresses the need to "unlearn Chinese ness" in order to foster Chinese diasporic identity

Exploring the Doubly Charged Higgs of the Left-Right Symmetric Model using Vector Boson Fusion-like Events at the LHC

This paper studies the pair production of the doubly charged Higgs boson of the left-right symmetric models using multilepton final state in the vector boson fusion (VBF)-like processes. The study is performed in the framework consistent with the model's correction to the standard model $\rho_{EW}$ parameter. VBF topological cuts, number of leptons in the final state and $p_T$ cuts on the leptons are found to be effective in suppressing the background. Significant mass reach can be achieved for exclusion/discovery of the doubly charge Higgs boson for the upcoming LHC run with a luminosity of $\mathcal{O}(10^3)$ fb$^{-1}$.Comment: 13 pages, 8 figures, 2 tables; Version 2:Journal matched versio