Let the cake be represented by the unit interval and let each player have a valuation expressed by a nonatomic probability measure. A cake division is said to be equitable if the value of the piece ...assigned to a player by his measure is the same for all players. We show that for any number n of players in any order an equitable division exists, giving each player a contiguous cake piece. Moreover, there is at least one order in which the common value is not smaller than 1/n.
Let the cake be represented by the unit interval of reals, with players having private valuations expressed by nonatomic probability measures. The aim is to find a cake division which assigns to each ...of n players one contiguous piece (a simple division) in such a way that the value each player receives (by her own measure) is the same for all players and this common value is at least 1/n. It is known that such divisions always exist, however, we show that there is no finite algorithm to find them already for three players. Therefore we propose an algorithm that for any given ε>0 finds, in a finite number of steps, a simple division such that the values assigned to players differ by at most ε>0.
Simple fair division of a square Legut, Jerzy
Journal of mathematical economics,
January 2020, 2020-01-00, 20200101, Letnik:
86
Journal Article
Recenzirano
Odprti dostop
Suppose we are given a cake represented by the unit interval to be divided among agents evaluating the pieces of the cake by nonatomic probability measures. It is known that we can divide the unit ...interval into contiguous and connected pieces and assign them to the agents in such a way that the values of the pieces are equal according to the individual agents measures. Such division is said to be equitable and simple. In this paper we show that an equitable and simple division also exists in the case of dividing two-dimensional cake represented by the unit square. In this case, by simple division we mean dividing the unit square firstly by horizontal cuts, and then partition the resulting rectangles by vertical cuts. We give a method of obtaining a proportional and simple division of this cake. Furthermore, we prove the existence of proportional, equitable and simple division.
Upon divorce, marital assets in most U.S. states are divided equitably, often with the underlying legal purpose of equalizing outcomes. To examine whether decisionmakers value economic ...considerations, such as opportunity cost, specialization, and bargaining power, we conducted a vignette study in which we asked subjects to divide marital assets equitably between an employed husband and a wife without labor market income in a wealthy household. Subjects award less than 50 percent of assets to the wife, regardless of her education or the level of marital assets. Men award lower shares but, unlike women, award a larger share to a more educated wife. Equitable division can lead to unequal outcomes for wives who opt out of the labor force. These findings imply that the objective of equalizing post-divorce outcomes would be better accomplished through legal directives that nudge towards equal asset division and assign greater weight to nonmonetary contributions.
This thesis attempts to resolve the deadlock to achieve an equitable division of taxes, and thereby internation equity. As the present tax laws were not negotiated, it is not considered here as fair. ...In this thesis it is proposed that an equitable division could be achieved through a division based on the levels of human development (combining Rawlsian schema and Sen’s capability approach). Therefore, it is argued that such a division would be equitable; because it would be based on entitlements (territorial claims), it would generate cooperation and thereby lead to greater efficiency. Importantly, this thesis establishes that the present tax treaties neither generate cooperation nor cohere with global welfare. Similarly, it is also found that the other institutions (OECD, IMF, WB and Dispute Settlement) related the tax regime presently do not promote development based on human capabilities. This could help developing countries to pursue a division favouring development (laws favouring development) and understand the institutions better suited to pursue such goals.
PDF
