We provide the first social choice theory approach to the question of what constitutes a community in a social network. Inspired by social choice theory in voting and other contexts [2], we start from an abstract social network framework, called preference networks [3]; these consist of a finite set of members and a vector giving a total ranking of the members in the set for each of them (repre...

We define a family of rules for dividing m indivisible goods among agents, parameterized by a scoring vector and a social welfare aggregation function. We assume that agents’ preferences over sets of goods are additive, but that the input is ordinal: each agent simply ranks single goods. Similarly to positional scoring voting rules in voting, a scoring vector s = (s1, . . . ,sm) consists of m n...

To aggregate rankings into a social ranking, one can use scoring systems such as Plurality, Veto, and Borda. We distinguish three types of methods: ranking by score, repeatedly choosing winner that we delete rank at the top, loser bottom. The latter method captures frequently studied voting rules Single Transferable Vote (aka Instant Runoff Voting), Coombs, Baldwin. In an experimental analysis,...

In this paper, we consider a typical voting situation where a group of agents show their preferences over a set of alternatives. Under our approach, such preferences are codified into individual positional values which can be aggregated in several ways through particular functions, yielding positional voting rules and providing a social result in each case. We show that scoring rules belong to ...

An aggregation rule maps each profile of individual strict preference orderings over a set of alternatives into a social ordering over that set. We call such a rule strategyproof if misreporting one’s preference never produces a different social ordering that is between the original ordering and one’s own preference. After describing two examples of manipulable rules, we study in some detail th...

Classical voting rules output a winning alternative (or a nonempty set of tied alternatives). Social welfare functions output a ranking over alternatives. There are many practical situations where we have to output a different structure than a winner or a ranking: for instance, a ranked or non-ranked set of k winning alternatives, or an ordered partition of alternatives. We define three classes...