The undercut procedure: an algorithm for the envy-free division of indivisible items

We propose a procedure for dividing a set of indivisible items between two players. We assume that each player’s preference over subsets of items is consistent with a strict ranking of the items, and that neither player has information about the other’s preferences. Our procedure ensures an envy-free division—each player receives a subset of items that it values more than the other player’s complementary subset—given that an envy-free division of “contested items,” which the players would choose at the same time, is possible. We show that the possibility of one player’s undercutting the other’s proposal, and implementing the reduced subset for himself or herself, makes the proposer “reasonable,” and generally leads to an envy-free division, even when the players rank items exactly the same. Although the undercut procedure is manipulable and its envy-free allocation may be Pareto-inferior, each player’s maximin strategy is to be truthful. Applications of the procedure are discussed briefly.     

A note on interdependent happiness

Based on two models of interdependent utilities [Becker, G., 1974. A theory of social interaction, Journal of Political Economy 82, 1064–1093; Fehr, E., Schmidt, K., 1999. A theory of fairness, competition, and cooperation, Quarterly Journal of Economics 114, 817–868] we derive a functional relationship between average happiness and the standard deviation of happiness within a country. This hypothesis is supported by an empirical investigation of 71 countries which shows that the average happiness in these countries depends only on income and on the standard deviation of happiness σ. The latter may be partly based on influences beyond income, for which no data are available. Income has the expected positive influence and σ has the expected negative influence, i.e. large differences in “autonomous” happiness have a dampening influence on “effective” happiness which also takes into account the happiness of others.     

A note on female ejaculation

We developed a 14‐item Attitudes Toward Sexuality Scale (ATSS) to compare the sexual attitudes of early, middle, and late adolescents and their parents. One hundred forty‐one adolescents between the ages of 12 and 20 and their parents completed a questionnaire consisting of the ATSS and demographic information. The Cronbach alpha reliability coefficient for the adolescents was .75, and for the parents it was .84. A principal components analysis revealed four major dimensions of the scale: a large General factor, Legality/Morality, Alternative Modes of Sexual Expression, and Individual Rights. The correlation pattern between the ATSS and subscales of the Sex Knowledge and Attitudes Test, as well as with certain demographic variables, supports the construct validity of the ATSS. This is, therefore, a scale which may be used for research in which the sexual attitudes of adults and adolescents of various ages are to be measured and compared.     

A note on the paradox of smaller coalitions

We consider hedonic coalition formation games that are induced by a simple TU-game and a cooperative solution. For such models, Shenoy’s (Int J Game Theory 8:133–164, 1979) absence of the paradox of smaller coalitions provides a sufficient condition for core existence. We present three different versions of his condition in order to compare it to the top coalition property of Banerjee et al. (Social Choice Welfare 18:135–153, 2001) that guarantees nonemptiness of the core in more general models. As it turns out, the top coalition property implies a condition in which Shenoy’s paradox is not present for at least one minimal winning coalition. Conversely, if for each non-null player Shenoy’s paradox is not present for at least one minimal winning coalition containing that player, then the induced hedonic game satisfies the top coalition property.     

A note on the non-emptiness of the stability set

Peleg (1978) presents a necessary and sufficient condition for the non-emptiness of the core, by considering quota games. The purpose of this paper is to present a similar result for the non-emptiness of another solution concept introduced by Rubinstein (1980) and called the stability set. Received: 25 January 1999/Accepted: 6 July 1999     

A note from the editor

A note from the editor     

A note from the editor

A note from the editor     

A note from the editor

A note from the editor     

A note on images of networks

Visual imagery and visual representations have proven very useful in some of the most important discoveries in the history of science. It is not surprising, therefore, that the earliest students of network phenomena often made use of visual representations (e.g. sociograms) to assist in the analysis, interpretation and illustration of complex relational data: by creating such visual representations, human faculties for visual imagery and pattern recognition could be more fully utilized in the search for structural patterns in sociometric networks. What is somewhat surprising, though, is that the techniques for creating visual representations of relational data have remained virtually unchanged since the study of social networks began: the slow, tedious, pen-and-ink approach of forty years ago is still very much the method of the day.Readily available computer graphics technology, however, introduces potentially powerful possibilities, and some of these are explored. The results of this initial exploration suggest that the time is ripe for forging new tools that will facilitate the analysis of complex relational data, stimulate the development of network theory, and provide new perspectives from which to view previously hidden facets of society.     

A note on continuous social choice

 We discuss continuous social choice functions defined on the set of the equivalence classes induced by profiles of individual preferences corresponding to anonymity. It is shown that we can at best obtain the equivalent result of Chichilnisky’s impossibility theorem when the set of an equivalence classes is endowed with various reasonable topologies. Received: 28 February 1994/Accepted: 22 April 1996