2,814 research outputs found
Ready for the design of voting rules?
The design of fair voting rules has been addressed quite often in the
literature. Still, the so-called inverse problem is not entirely resolved. We
summarize some achievements in this direction and formulate explicit open
questions and conjectures.Comment: 10 page
Fair Representation and a Linear Shapley Rule
When delegations to an assembly or council represent differently sized
constituencies, they are often allocated voting weights which increase in
population numbers (EU Council, US Electoral College, etc.). The Penrose square
root rule (PSRR) is the main benchmark for fair representation of all
bottom-tier voters in the top-tier decision making body, but rests on the
restrictive assumption of independent binary decisions. We consider intervals
of alternatives with single-peaked preferences instead, and presume positive
correlation of local voters. This calls for a replacement of the PSRR by a
linear Shapley rule: representation is fair if the Shapley value of the
delegates is proportional to their constituency sizes.Comment: 21 pages, 2 figure
Mostly sunny : a forecast of tomorrow's power index research
Power index research has been a very active field in the last decades. Will
this continue or are all the important questions solved? We argue that there
are still many opportunities to conduct useful research with and on power
indices. Positive and normative questions keep calling for theoretical and
empirical attention. Technical and technological improvements are likely to
boost applicability.Comment: 12 page
Minimal proper non-IRUP instances of the one-dimensional Cutting Stock Problem
We consider the well-known one dimensional cutting stock problem (1CSP).
Based on the pattern structure of the classical ILP formulation of Gilmore and
Gomory, we can decompose the infinite set of 1CSP instances, with a fixed
demand n, into a finite number of equivalence classes. We show up a strong
relation to weighted simple games. Studying the integer round-up property we
computationally show that all 1CSP instances with are proper IRUP,
while we give examples of a proper non-IRUP instances with . A gap larger
than 1 occurs for . The worst known gap is raised from 1.003 to 1.0625.
The used algorithmic approaches are based on exhaustive enumeration and integer
linear programming. Additionally we give some theoretical bounds showing that
all 1CSP instances with some specific parameters have the proper IRUP.Comment: 14 pages, 2 figures, 2 table
Are weighted games sufficiently good for binary voting?
Binary yes-no decisions in a legislative committee or a shareholder meeting
are commonly modeled as a weighted game. However, there are noteworthy
exceptions. E.g., the voting rules of the European Council according to the
Treaty of Lisbon use a more complicated construction. Here we want to study the
question if we lose much from a practical point of view, if we restrict
ourselves to weighted games. To this end, we invoke power indices that measure
the influence of a member in binary decision committees. More precisely, we
compare the achievable power distributions of weighted games with those from a
reasonable superset of weighted games. It turns out that the deviation is
relatively small.Comment: 7 pages, 2 tables; typos correcte
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