14,635 research outputs found
A law of large numbers for weighted plurality
Consider an election between k candidates in which each voter votes randomly
(but not necessarily independently) and suppose that there is a single
candidate that every voter prefers (in the sense that each voter is more likely
to vote for this special candidate than any other candidate). Suppose we have a
voting rule that takes all of the votes and produces a single outcome and
suppose that each individual voter has little effect on the outcome of the
voting rule. If the voting rule is a weighted plurality, then we show that with
high probability, the preferred candidate will win the election. Conversely, we
show that this statement fails for all other reasonable voting rules.
This result is an extension of H\"aggstr\"om, Kalai and Mossel, who proved
the above in the case k=2
Majority Dynamics and Aggregation of Information in Social Networks
Consider n individuals who, by popular vote, choose among q >= 2
alternatives, one of which is "better" than the others. Assume that each
individual votes independently at random, and that the probability of voting
for the better alternative is larger than the probability of voting for any
other. It follows from the law of large numbers that a plurality vote among the
n individuals would result in the correct outcome, with probability approaching
one exponentially quickly as n tends to infinity. Our interest in this paper is
in a variant of the process above where, after forming their initial opinions,
the voters update their decisions based on some interaction with their
neighbors in a social network. Our main example is "majority dynamics", in
which each voter adopts the most popular opinion among its friends. The
interaction repeats for some number of rounds and is then followed by a
population-wide plurality vote.
The question we tackle is that of "efficient aggregation of information": in
which cases is the better alternative chosen with probability approaching one
as n tends to infinity? Conversely, for which sequences of growing graphs does
aggregation fail, so that the wrong alternative gets chosen with probability
bounded away from zero? We construct a family of examples in which interaction
prevents efficient aggregation of information, and give a condition on the
social network which ensures that aggregation occurs. For the case of majority
dynamics we also investigate the question of unanimity in the limit. In
particular, if the voters' social network is an expander graph, we show that if
the initial population is sufficiently biased towards a particular alternative
then that alternative will eventually become the unanimous preference of the
entire population.Comment: 22 page
Tactical Voting in Plurality Elections
How often will elections end in landslides? What is the probability for a
head-to-head race? Analyzing ballot results from several large countries rather
anomalous and yet unexplained distributions have been observed. We identify
tactical voting as the driving ingredient for the anomalies and introduce a
model to study its effect on plurality elections, characterized by the relative
strength of the feedback from polls and the pairwise interaction between
individuals in the society. With this model it becomes possible to explain the
polarization of votes between two candidates, understand the small margin of
victories frequently observed for different elections, and analyze the polls'
impact in American, Canadian, and Brazilian ballots. Moreover, the model
reproduces, quantitatively, the distribution of votes obtained in the Brazilian
mayor elections with two, three, and four candidates.Comment: 7 pages, 4 figure
Voting Power in the Australian Senate: 1901-2004
Indices of voting power are intended to measure the a priori degree of in.uence that a voter or party can expect to have in framing legislation or passing motions. Commonly used measures include those proposed by Shapley and Shubik (1954), Banzhaf (1965) and Deegan and Packel (1978). This paper computes these power indices for the Australian Senate for the period 1901-2004. The introduction of the Single Transferable Vote in the Senate in 1949 appears to have had a profound effect on the voting power of both major parties, as well as on the degree of concentration of voting power.
Analog hardware for delta-backpropagation neural networks
This is a fully parallel analog backpropagation learning processor which comprises a plurality of programmable resistive memory elements serving as synapse connections whose values can be weighted during learning with buffer amplifiers, summing circuits, and sample-and-hold circuits arranged in a plurality of neuron layers in accordance with delta-backpropagation algorithms modified so as to control weight changes due to circuit drift
Voces Populi and the Art of Listening
The strategy most damaging to many preferential election methods is to give insincerely low rank to the main opponent of one’s favorite candidate. Theorem 1 determines the 3-candidate Condorcet method that minimizes the number of noncyclic profiles allowing this strategy. Theorems 2, 3, and 4 establish conditions for an anonymous and neutral 3-candidate single-seat election to be monotonic and still avoid this strategy completely. Plurality elections combine these properties; among the others "conditional IRV" gives the strongest challenge to the plurality winner. Conditional IRV is extended to any number of candidates. Theorem 5 is an impossibility of Gibbard-Satterthwaite type, describing 3 specific strategies that cannot all be avoided in meaningful anonymous and neutral elections.Preferential Election methods; Plurality Election methods
The program for the simulation of electoral systems ALEX4.1: what it does and how to use it.
This paper illustrates ALEX4.1, the 2007 version of the program of simulation of electoral systems developed at ALEX, the Laboratory for Experimental and Simulative Economics of the Universitàdel Piemonte Orientale at Alessandria, Italy. The main features of the program have been described with reference to a previous version in Bissey, Carini and Ortona, 2004; the paper may be freely downloaded from the site of the journal where it has been published, or in its working paper version from the site http://polis.unipmn.it/. The organization of this paper is, consequently, rather unusual. The next section presents only the very basic traits of the simulation program, as most details and theoretical considerations may be read in the quoted (and easy-to-find) reference. Sections 3 and 4 are the most important: they illustrate the novelties of ALEX4.1 with respect to previous versions. Section 5 is very short, as it contains only the instructions for downloading the program, and some caveats regarding its use. The core of the paper is a large appendix that contains the readme file of the package ALEX4.1. Actually, this paper should be considered a handbook for the use of ALEX4.1.
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