33 research outputs found
Redividing the Cake
A heterogeneous resource, such as a land-estate, is already divided among
several agents in an unfair way. It should be re-divided among the agents in a
way that balances fairness with ownership rights. We present re-division
protocols that attain various trade-off points between fairness and ownership
rights, in various settings differing in the geometric constraints on the
allotments: (a) no geometric constraints; (b) connectivity --- the cake is a
one-dimensional interval and each piece must be a contiguous interval; (c)
rectangularity --- the cake is a two-dimensional rectangle or rectilinear
polygon and the pieces should be rectangles; (d) convexity --- the cake is a
two-dimensional convex polygon and the pieces should be convex.
Our re-division protocols have implications on another problem: the
price-of-fairness --- the loss of social welfare caused by fairness
requirements. Each protocol implies an upper bound on the price-of-fairness
with the respective geometric constraints.Comment: Extended IJCAI 2018 version. Previous name: "How to Re-Divide a Cake
Fairly
Multiagent negotiation for fair and unbiased resource allocation
This paper proposes a novel solution for the n agent cake cutting (resource allocation) problem. We propose a negotiation protocol for dividing a resource among n agents and then provide an algorithm for allotting portions of the resource. We prove that this protocol can enable distribution of the resource among n agents in a fair manner. The protocol enables agents to choose portions based on their internal utility function, which they do not have to reveal. In addition to being fair, the protocol has desirable features such as being unbiased and verifiable while allocating resources. In the case where the resource is two-dimensional (a circular cake) and uniform, it is shown that each agent can get close to l/n of the whole resource.Utility theory ; Utility function ; Bargaining ; Artificial intelligence ; Resource allocation ; Multiagent system
Multiagent Negotiation for Fair and Unbiased Resource Allocation
This paper proposes a novel solution for the n agent cake cutting (resource allocation) problem. We propose a negotiation protocol for dividing a resource among n agents and then provide an algorithm for allotting portions of the resource. We prove that this protocol can enable distribution of the resource among n agents in a fair manner. The protocol enables agents to choose portions based on their internal utility function, which they do not have to reveal. In addition to being fair, the protocol has desirable features such as being unbiased and verifiable while allocating resources. In the case where the resource is two-dimensional (a circular cake) and uniform, it is shown that each agent can get close to l/n of the whole resource
Mind the Gap: Cake Cutting With Separation
We study the problem of fairly allocating a divisible resource, also known as
cake cutting, with an additional requirement that the shares that different
agents receive should be sufficiently separated from one another. This
captures, for example, constraints arising from social distancing guidelines.
While it is sometimes impossible to allocate a proportional share to every
agent under the separation requirement, we show that the well-known criterion
of maximin share fairness can always be attained. We then establish several
computational properties of maximin share fairness -- for instance, the maximin
share of an agent cannot be computed exactly by any finite algorithm, but can
be approximated with an arbitrarily small error. In addition, we consider the
division of a pie (i.e., a circular cake) and show that an ordinal relaxation
of maximin share fairness can be achieved. We also prove that an envy-free or
equitable allocation that allocates the maximum amount of resource exists under
separation.Comment: Appears in the 35th AAAI Conference on Artificial Intelligence
(AAAI), 202
חטאת as interpolative gloss: a solution to Gen 4,7
This note suggests that Gen 4,7 can be rendered comprehensible by the removal of the term ht't, understanding its appearance as an interpolative gloss, and the interpretation of the remaining rbts as the subject of a nominal clause. This eliminates the lack of agreement between the feminine singular ht't and the three masculine singulars which follow, and it allows an interpretation of the verse which sees Cain being offered the option of reversing the decision made by Eve when she ate from the tree of the knowledge of good and evil
Multiagent negotiation for fair and unbiased resource allocation
This paper proposes a novel solution for the n agent cake cutting (resource allocation) problem. We propose a negotiation protocol for dividing a resource among n agents and then provide an algorithm for allotting portions of the resource. We prove that this protocol can enable distribution of the resource among n agents in a fair manner. The protocol enables agents to choose portions based on their internal utility function, which they do not have to reveal. In addition to being fair, the protocol has desirable features such as being unbiased and verifiable while allocating resources. In the case where the resource is two-dimensional (a circular cake) and uniform, it is shown that each agent can get close to l/n of the whole resource