A social choice correspondence satisfies balancedness if, for every pair of alternatives, x and y, and every pair of individuals, i and j, whenever a profile has x adjacent to but just above y for individual i while individual j has y adjacent to but
just above x, then only switching x and y in the orderings for both of those two individuals leaves the choice set unchanged. We show how the balancedness condition interacts with other social choice properties, especially tops-only. We also use balancedness to characterize the Borda rule (for a fixed number of voters) within the class of scoring rules.
Determination of the range of a variety of social choice correspondences: Plurality voting, the Borda rule, the Pareto rule, the Copeland correspondence, approval voting, and the top cycle correspondence
A graph $G$ is called $3$-choice critical if $G$ is not $2$-choosable but any proper subgraph is $2$-choosable. A graph $G$ is strongly fractional $r$-choosable if $G$ is $(a,b)$-choosable for all positive integers $a,b$ for which $a/b ge r$. The str
ong fractional choice number of $G$ is $ch_f^s(G) = inf {r: G $ is strongly fractional $r$-choosable$}$. This paper determines the strong fractional choice number of all $3$-choice critical graphs.
Human decision making underlies data generating process in multiple application areas, and models explaining and predicting choices made by individuals are in high demand. Discrete choice models are widely studied in economics and computational socia
l sciences. As digital social networking facilitates information flow and spread of influence between individuals, new advances in modeling are needed to incorporate social information into these models in addition to characteristic features affecting individual choices. In this paper, we propose two novel models with scalable training algorithms: local logistics graph regularization (LLGR) and latent class graph regularization (LCGR) models. We add social regularization to represent similarity between friends, and we introduce latent classes to account for possible preference discrepancies between different social groups. Training of the LLGR model is performed using alternating direction method of multipliers (ADMM), and training of the LCGR model is performed using a specialized Monte Carlo expectation maximization (MCEM) algorithm. Scalability to large graphs is achieved by parallelizing computation in both the expectation and the maximization steps. The LCGR model is the first latent class classification model that incorporates social relationships among individuals represented by a given graph. To evaluate our two models, we consider three classes of data to illustrate a typical large-scale use case in internet and social media applications. We experiment on synthetic datasets to empirically explain when the proposed model is better than vanilla classification models that do not exploit graph structure. We also experiment on real-world data, including both small scale and large scale real-world datasets, to demonstrate on which types of datasets our model can be expected to outperform state-of-the-art models.
In large scale collective decision making, social choice is a normative study of how one ought to design a protocol for reaching consensus. However, in instances where the underlying decision space is too large or complex for ordinal voting, standard
voting methods of social choice may be impractical. How then can we design a mechanism - preferably decentralized, simple, scalable, and not requiring any special knowledge of the decision space - to reach consensus? We propose sequential deliberation as a natural solution to this problem. In this iterative method, successive pairs of agents bargain over the decision space using the previous decision as a disagreement alternative. We describe the general method and analyze the quality of its outcome when the space of preferences define a median graph. We show that sequential deliberation finds a 1.208- approximation to the optimal social cost on such graphs, coming very close to this value with only a small constant number of agents sampled from the population. We also show lower bounds on simpler classes of mechanisms to justify our design choices. We further show that sequential deliberation is ex-post Pareto efficient and has truthful reporting as an equilibrium of the induced extensive form game. We finally show that for general metric spaces, the second moment of of the distribution of social cost of the outcomes produced by sequential deliberation is also bounded.