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Fair division of graphs and of tangled cakes
[article]
2021
arXiv
pre-print
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In this case, moving knife methods seem unsuited for obtaining connected allocations (see Brams, Taylor, and Zwicker [6] ; Barbanel and Brams [2] ; and see the related conjecture in Brânzei and Nisan ...
Case 8 − → deg(T ) = t, 0, r, s , s ≥ 1, t + r + s ≥ 2: Then (T ) − σ 3 (T ) ≥ t+3[r+(s−1)]+4 2 − (r + s) = t+r+s+1 2 ≥ 2. ...
arXiv:2102.08560v1
fatcat:gie4facmybaavasqn7uqfslyd4
Coalition formation games with separable preferences
2003
Mathematical Social Sciences
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∩ T, if it is true that T Â p i S and T Â p k S, then T Â p j S. ...
and T with p i , p j , p k ∈ T ∩ S such that T Â p i S and T Â p k S. ...
doi:10.1016/s0165-4896(02)00082-3
fatcat:s5uwr6pnuffs3mb7f52mknwetm
Weighted voting, abstention, and multiple levels of approval
2003
Social Choice and Welfare
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S. ...
Zwicker 2 favor of the alternative or against it and the motion is passed or not depending of the collective strength of members who vote ''yes.'' ...
doi:10.1007/s00355-003-0212-3
fatcat:wvpvzm76l5gxnf7x5dmyyhohuy
Trading properties and Alexandrov kernels for Boolean functions
2000
Discrete Applied Mathematics
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The coalition S x , so reduced, is now S x , and the coalition S y , so enlarged, is now S y . We will refer to this as a "one-way transfer" of voters. ...
If x = (x 1 ; : : : ; x n ) is a Boolean vector, then {i: x i = 1} will be called the support S x of x. Conversely, if S ⊆ N , then x S will denote the unique Boolean vector with support S. ...
doi:10.1016/s0166-218x(00)00247-x
fatcat:w7365vi5jzabpp44znyqhayena
Aggregation of binary evaluations: a Borda-like approach
2015
Social Choice and Welfare
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Brams, Kilgour and Zwicker (1998) consider the "paradox of multiple elections" where voters vote yes/no on a sequence of propositions on a referendum. ...
labels), as the vector of scores also encodes the number n of voters, while from v cocycle it is not possible to recover n. 28 We are using "large enough" as a loose metaphor here -the precise version (Zwicker ...
One then shows that with the addition of one new alternative one can construct at least one more cocycle, which maintains linear independence of S cocycle when added in, expanding |S cocycle | to m, and ...
doi:10.1007/s00355-015-0914-3
fatcat:7fywphqvxvc5jox3j5ps3p2s4q
Cycles and Intractability in a Large Class of Aggregation Rules
[article]
2018
arXiv
pre-print
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The equivalence will be discussed by Zwicker (2018) . ...
for which γ i ∈ P s . ...
arXiv:1608.03999v2
fatcat:riupoubkjfh3dfliwym5h7jn5m
The geometry of voting power: Weighted voting and hyper-ellipsoids
2014
Games and Economic Behavior
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Then the member(s) y of Y closest to q minimize(s) r j=1 y − s j 2 among members of Y . ...
is a set of points in Euclidean space, q(S) denotes the mean location of the points in S, and L[S] denotes the set image of S, then L(q(S)) = q(L[S]). 17 We will no longer always be careful to distinguish ...
doi:10.1016/j.geb.2013.12.001
fatcat:hk35nwyt4ffkbn3ybtasazw6ey
One-way monotonicity as a form of strategy-proofness
2009
International Journal of Game Theory
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A voting rule F is two-way monotonic if such an effect is only possible when v moves t from below s (according to σ) to above s (according to τ). ...
One-way monotonicity is the strictly weaker requirement that such an effect never occur when v makes the opposite switch, by moving s from below t to above t. ...
Net(s > x) x" A#{s} $ of the pairwise net majorities for s (see, for example, Zwicker [1991] ). The Borda count is thus a net pairwise rule (but is well known to not be a Condorcet extension). ...
doi:10.1007/s00182-009-0170-9
fatcat:4jf36wvj4ffjfbofdc3uxaxrsy
Almost Envy-Free Allocations with Connected Bundles
[article]
2018
arXiv
pre-print
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However, for n = 4, several moving-knife procedures exist that only need few cuts; for example, the Brams-Taylor-Zwicker [1997] procedure requires 11 cuts, and a protocol of Barbanel and Brams [2004 ...
By de nition of s, agent s did not shout in the previous step. By (4.5), u s ({ r } ∪ R) u s (L), so together with (4.6), we have u s ({ +1 } ∪ M) u s (L), so s does not envy s le . ...
Since P k and the I j r 's are all intervals of a path, the middle interval must be completely contained in P k , that is, I j r ⊆ P k for some r . Hence j r ∈ P k , contradicting the choice of P k . ...
arXiv:1808.09406v1
fatcat:qssvgwctmzd43jask6nldshrta
Cycles and Intractability in a Large Class of Aggregation Rules
2018
The Journal of Artificial Intelligence Research
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The equivalence will be discussed by Zwicker (2018) . ...
for which γ i ∈ P s . ...
doi:10.1613/jair.5657
fatcat:crqysuspqjajbj2kenjlzu4pf4
Anonymous yes–no voting with abstention and multiple levels of approval
2009
Games and Economic Behavior
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nonascending strength of approval) approve at a level of s or stronger. ...
In this connection, see a number of comments in Freixas and Zwicker (2003) . ...
doi:10.1016/j.geb.2008.09.035
fatcat:wfnykigqdbdrdkjcpflsqo5pje
Voting with rubber bands, weights, and strings
2012
Mathematical Social Sciences
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Definition 3.4 Let S be a set of voters, P be any profile for the voters in S, v be a voter not in S, and P ∧ σ be the profile obtained by adding, to P , one additional ballot of σ, cast by v. ...
clear: v ranks s over t according to her sincere ballot. ...
doi:10.1016/j.mathsocsci.2011.08.003
fatcat:d4xegosvvzbzdez6d77l6x4agm
Almost Envy-Free Allocations with Connected Bundles
2018
Innovations in Theoretical Computer Science
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However, for n = 4, several moving-knife procedures exist that only need few cuts; for example, the Brams-Taylor-Zwicker [11] procedure requires 11 cuts, and a protocol of Barnabel and Brams [3] requires ...
a block B adjacent to three different cut vertices s 1 , s 2 , and s 3 . ...
doi:10.4230/lipics.itcs.2019.14
dblp:conf/innovations/BiloCFIMPVZ19
fatcat:julkjuspr5dxdjzlvsb3axhtqq
Nonmanipulable Selections from a Tournament
2010
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A tournament is a binary dominance relation on a set of alternatives. Tournaments arise in many contexts that are relevant to AI, most notably in voting (as a method to aggregate the preferences of agents). There are many works that deal with choice rules that select a desirable alternative from a tournament, but very few of them deal directly with incentive issues, despite the fact that game-theoretic considerations are crucial with respect to systems populated by selfish agents. We deal with
doi:10.4230/dagsemproc.10101.5
fatcat:6xnlztcsgvckjfvrtr6wbas2se
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... he problem of the manipulation of choice rules by considering two types of manipulation. We say that a choice rule is emph{monotonic} if an alternative cannot get itself selected by losing on purpose, and emph{pairwise nonmanipulable} if a pair of alternatives cannot make one of them the winner by reversing the outcome of the match between them. Our main result is a combinatorial construction of a choice rule that is monotonic, pairwise nonmanipulable, and onto the set of alternatives, for any number of alternatives besides three.
Page 23 of American Sportswear & Knitting Times Vol. 30, Issue 37
[page]
1961
American Sportswear & Knitting Times
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INiES
—_— ——
ll be ‘arter, 1 mer- Cour- >i the yvelop- s. ...
The business meet- ing preceding dinner was brief. \ telegram was received from
Sidney S. ...
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