Sequential Payment Rules: Approximately Fair Budget Divisions via Simple
Spending Dynamics
0
Citation
0
Reference
10
Related Paper
Abstract:
In approval-based budget division, a budget needs to be distributed to some candidates based on the voters' approval ballots over these candidates. In the pursuit of simple, well-behaved, and approximately fair rules for this setting, we introduce the class of sequential payment rules, where each voter controls a part of the budget and repeatedly spends his share on his approved candidates to determine the final distribution. We show that all sequential payment rules satisfy a demanding population consistency notion and we identify two particularly appealing rules within this class called the maximum payment rule (MP) and the $\frac{1}{3}$-multiplicative sequential payment rule ($\frac{1}{3}$-MP). More specifically, we prove that (i) MP is, apart from one other rule, the only monotonic sequential payment rule and gives a $2$-approximation to a fairness notion called average fair share, and (ii) $\frac{1}{3}$-MP gives a $\frac{3}{2}$-approximation to average fair share, which is optimal among sequential payment rules.Keywords:
Dynamics
In this article, we present new results on simple points, minimal non-simple sets (MNS) and P-simple points. In particular, we propose new characterizations which hold in dimensions 2, 3 and 4, and which lead to efficient algorithms for detecting such points or sets. This work is settled in the framework of cubical complexes, and some of the main results are based on the properties of critical kernels.
SIMPLE algorithm
Cite
Citations (6)
Abstract We show that a Kueker simple theory eliminates ∃ ∞ and densely interprets weakly minimal formulas. As part of the proof we generalize Hrushovski's dichotomy for almost complete formulas to simple theories. We conclude that in a unidimensional simple theory an almost-complete formula is either weakly minimal or trivially-almost-complete. We also observe that a small unidimensional simple theory is supersimple of finite SU -rank.
Rank (graph theory)
Cite
Citations (5)
Simple concepts are defined as closed constructions which do
not contain other constructions. The hypothesis that any simple
expressions express a simple concept is wrong. Many simple
expressions of a natural language came into being as
abbreviations, due to some definition so that the corresponding
conceptis given by the (not simple!) definiens.
Cite
Citations (2)
We investigate simple endotrivial modules of finite quasi-simple groups and classify them in several important cases. This is motivated by a recent result of Robinson showing that simple endotrivial modules of most groups come from quasi-simple groups.
Cite
Citations (0)
Abstract We investigate simple endotrivial modules of finite quasi-simple groups and classify them in several important cases. This is motivated by a recent result of Robinson [Bull. Lond. Math. Soc. 43 (2011), 712–716] showing that simple endotrivial modules of most groups come from quasi-simple groups.
Cite
Citations (30)
Cite
Citations (25)
We consider the fundamental relations β and γ in simple and 0-simple semihypergroups, especially in connection with certain minimal cardinality questions. In particular, we enumerate and exhibit all simple and 0-simple semihypergroups having order 3 where β is not transitive, apart of isomorphisms. Moreover, we show that the least order for which there exists a strongly simple semihypergroup where β is not transitive is 4. Finally, we prove that γ is transitive in all simple semihypergroups, and determine necessary and sufficient conditions for a 0-simple semihypergroup to have γ transitive. The latter results obviously hold also for simple and 0-simple semigroups.
Cardinality (data modeling)
Existential quantification
Cite
Citations (8)
Cite
Citations (0)
In this paper, we investigate the properties of the [0-simple] simple subsemigroups of nonnegative matrices and show that the [0-simple] simple subsemigroups of Mn(S) are completely [0-simple] simple, where S is a strong ideal subset of R+ which has no ele- ments less than 1 except 0. Finally, we illustrate that the semigroup of nonnegative matriles is interesting.
Cite
Citations (0)
We investigate simple endotrivial modules of finite quasi-simple groups and classify them in several important cases. This is motivated by a recent result of Robinson showing that simple endotrivial modules of most groups come from quasi-simple groups.
Cite
Citations (4)