We analyze a simple sequential algorithm (SA) for allocating indivisible items that are strictly ranked by n ≥ 2 players. It yields at least one Pareto-optimal allocation which, when n = 2, is envy-free unless no envy-free allocation exists. However, an SA allocation may not be maximin or...

An allocation of indivisible items among n ≥ 2 players is proportional if and only if each player receives a proportional subset — one that it thinks is worth at least 1/n of the total value of all the items. We show that a proportional allocation exists if and only if there is an allocation...

A cake is a metaphor for a heterogeneous, divisible good, such as land. A perfect division of cake is efficient (also called Pareto-optimal), envy-free, and equitable. We give an example of a cake in which it is impossible to divide it among three players such that these three properties are...

Assume that two players have strict rankings over an even number of indivisible items. We propose algorithms to find allocations of these items that are maximin — maximize the minimum rank of the items that the players receive — and are envy-free and Pareto-optimal if such allocations exist....

We analyze a class of proportional cake-cutting algorithms that use a minimal number of cuts (n-1 if there are n players) to divide a cake that the players value along one dimension. While these algorithms may not produce an envy-free or efficient allocation – as these terms are used in the...

This paper provides a distance based analysis of the Borda rule with respect to Condorcet’s criterion. It shows that the minimal Condorcet consistency present in the Borda rule, whenever a Condorcet winner (the alternative that wins against every other alternative in a pairwise contest)...

We analyze a class of proportional cake-cutting algorithms that use a minimal number of cuts (n-1 if there are n players) to divide a cake that the players value along one dimension. While these algorithms may not produce an envy-free or efficient allocation--as these terms are used in the...

A fair spanning tree of a graph maximizes the minimum satisfaction among individuals given their preferences over the edges of the graph. In this note we answer an open question about the computational complexity of determining fair spanning trees raised in Darmann et al. (2009). It is shown...

This paper analyzes the computational complexity involved in solving fairness issues on graphs, e.g., in the installation of networks such as water networks or oil pipelines. Based on individual rankings of the edges of a graph, we will show under which conditions solutions, i.e., spanning...