arXiv subjects

Ross Hyman

Publications and source records attributed to Ross Hyman.

4 recordsLinked to original sources

arXiv2025

A House Monotone, Coherent, and Droop Proportional Ranked Candidate Voting Method

A Ranked candidate voting method based on Phragmen's procedure is described that can be used to produce a top-down proportional candidate list. The method complies with the Droop proportionality criterion satisfied by Single Transferable Vote. It also complies with house monotonicity and coherence, which are the ranked-candidate analogs of the divisor methods properties of always avoiding the Alabama and New State paradoxes. The highest ranked candidate in the list is the Instant Runoff winner, which is in at least one Droop proportional set of N winners for all N.

econ.TH↗

arXiv2023

A Majority Rule Philosophy for Instant Runoff Voting

We present the core support criterion, a voting criterion satisfied by Instant Runoff Voting (IRV) that is analogous to the Condorcet criterion but reflective of a different majority rule philosophy. Condorcet methods can be thought of as conducting elections between each pair of candidates, counting all ballots to determine the winner of each pair-election. IRV can also be thought of as conducting elections between all pairs of candidates but for each pair-election only counting ballots from voters who do not prefer another major candidate (as determined self-consistently from the IRV social ranking) to the two candidates in contention. The appropriateness of including all ballots or a subset of ballots for a pair-election, depends on whether the society deems the entire or a selected ballot set in compliance with freedom of association (which implies freedom of non-association) for a given pair election. Arguments based on freedom of association rely on more information about an electorate than can be learned from ranked ballots alone. We present a freedom-of-association based argument to explain why IRV may be preferable to Condorcet in some circumstances, including the 2022 Alaska special congressional election, based on the political context of that election.

econ.TH↗

arXiv2022

A New Perspective on Impartial and Unbiased Apportionment

How to fairly apportion congressional seats to states has been debated for centuries. We present an alternative perspective on apportionment, centered not on states but "families" of state, sets of states with "divisor-method" quotas with the same integer part. We develop ``impartial" and ``unbiased" apportionment methods. Impartial methods apportion the same number of seats to families of states containing the same total population, whether a family consists of many small-population states or a few large-population states. Unbiased methods apportion seats so that if states are drawn repeatedly from the same distribution, the expected number of seats apportioned to each family equals the expected divisor-method quota for that family.

econ.GN↗

arXiv2020

d'Alembert Digitized: A Wave Pulse Method for Visualizing Electromagnetic Waves in Matter and for Deriving the Finite Difference Time Domain Method for Numerically Solving Maxwell's Equations

An alternative way of visualizing electromagnetic waves in matter and of deriving the Finite Difference Time Domain method (FDTD) for simulating Maxwell's equations for one dimensional systems is presented. The method uses d'Alembert's splitting of waves into forward and backward pulses of arbitrary shape and allows for grid spacing and material properties that vary with position. Constant velocity of waves in dispersionless dielectric materials, partial reflection and transmission at boundaries between materials with different indices of refraction, and partial reflection, transmission, and attenuation through conducting materials are derived without recourse to exponential functions, trigonometric functions, or complex numbers. Placing d'Alembert's method on a grid is shown to be equivalent to FDTD and allows for a simple and visual proof that FDTD is exact for dielectrics when the ratio of the spatial and temporal grid spacing is the wave speed, a straightforward way to incorporate reflectionless boundary conditions, and a derivation that FDTD retains second order accuracy when the grid spacing varies with position and the material parameters make sudden jumps across layer boundaries.

physics.optics↗