Individual disagreements are assumed to be reflected in the preferences. Distance functions, e.g., the well-known Kemeny (1959) distance, are used to measure these disagreements. However, a disagreement on how to rank the top two alternatives may be perceived more (or less) than a disagreement on how to rank the bottom two alternatives. We propose two conditions on distance functions which characterize a class of weighted distance functions. This class allows to quantify disagreements according to where they occur in preferences. We provide some examples within this class and show one of them to be the generalization of the Kemeny distance on strict preferences.JEL classification: C63, D71, D72, D74

The well-known swap distance (Kemeny (1959);Kendall (1938);Hamming (1950)) is analyzed. On weak preferences, this function was characterized by Kemeny (1959) with five conditions; metric, betweenness, neutrality, reducibility, and normalization. We show that the same result can be achieved without the reducibility condition, therefore, the original five conditions are not logically independent. We provide a new and logically independent characterization of the Kemeny distance and provide some insight to further analyze distance functions on preferences.JEL Classification: D63, D71, D72

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We consider one-to-one matching markets in which agents can either be matched as pairs or remain single. In these so-called roommate markets agents are consumers and resources at the same time. Klaus (Games Econ Behav 72:172-186, 2011) introduced two new "population sensitivity" properties that capture the effect newcomers have on incumbent agents: competition sensitivity and resource sensitivity. On various roommate market domains (marriage markets, no-odd-rings roommate markets, solvable roommate markets), we characterize the core using either of the population sensitivity properties in addition to weak unanimity and consistency. On the domain of all roommate markets, we obtain two associated impossibility results. 1 Introduction We consider one-to-one matching markets in which agents can either be matched as pairs or remain single. These markets are known as roommate markets and they include, as special cases, the well-known marriage markets (Gale and Shapley 1962; Roth and Sotomayor 1990). Furthermore, a roommate market is a simple example of hedonic coalition as well as network formation: in a "roommate coalition" situation, only coalitions of size one or two can be formed and in a "roommate network" situation, each agent is allowed or able to form only one link (for surveys and current

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