Anonymous voting and minimal manipulability

We compare the manipulability of different choice rules by considering the number of manipulable profiles. We establish the minimal number of such profiles for tops-only, anonymous, and surjective choice rules, and show that this number is attained by unanimity rules with status quo.public economics ;

Minimal Manipulability: Anonymity and Unanimity

This paper is concerned with the minimal number of profiles at which a unanimous and anonymous social choice function is manipulable. The lower bound is derived when there are three alternatives to choose from. Examples of social choice functions attaining the lower bound are given. We conjecture that these examples are in fact all minimally manipulable social choice functions. Since some of these examples are even Pareto optimal, we have also derived the lower bound for Pareto optimal and anonymous social choice functions. Some of the minimally manipulable Pareto optimal and anonymous social choice functions can be interpreted as status quo voting.mathematical economics;

Minimal Manipulability: Anonymity and Surjectivity

Gibbard''s (1973) and Satterthwaite''s (1975) result implies that anonymous surjective social choice functions on more than two alternatives are manipulable. Placing some mild constraints on the number of agents compared to the number of alternatives, we show what the minimal number of manipulable profiles of such social choice functions is. Moreover, all such social choice functions attaining the lower bound are characterized. They show a trade off between minimizing manipulability and treating alternatives neutrally.mathematical economics;

Strategy-proof voting for single issues and cabinets

In a model with a continuum of voters with symmetric single-peaked preferences on the one-dimensional unit interval (representing the political spectrum) a voting rule assigns to each profile of votes a point in the interval. We characterize all voting rules that are strategy-proof, anonymous, Pareto optimal, and which satisfy a weak form of continuity. This result paves the way for studying cabinet formation rules. A cabinet is an interval which has obtained sufficiently many votes. The main result on cabinet formation is a characterization of all cabinet formation rules that are strategy-proof with respect to the endpoints of the cabinet, anonymous, Pareto optimal, and continuous.public economics ;

Minimal manipulability: Unanimity and Nondictatorship

This paper is concerned with the number of profiles at which a nondictatorial social choice function is manipulable. For three or more alternatives the lower bound is derived when the social choice function is nondictatorial and unanimous. In the case of three alternatives the lower bound is also derived when the social choice function is nondictatorial and surjective. In both cases all social choice functions reaching that lower bound are characterized when there are at least three agents. In the case of two agents the characterized social choice functions are only a subset of the set of all social choice functions reaching the minimum.mathematical economics;

Rule-based multi-level modeling of cell biological systems

<p>Abstract</p> <p>Background</p> <p>Proteins, individual cells, and cell populations denote different levels of an organizational hierarchy, each of which with its own dynamics. Multi-level modeling is concerned with describing a system at these different levels and relating their dynamics. Rule-based modeling has increasingly attracted attention due to enabling a concise and compact description of biochemical systems. In addition, it allows different methods for model analysis, since more than one semantics can be defined for the same syntax.</p> <p>Results</p> <p>Multi-level modeling implies the hierarchical nesting of model entities and explicit support for downward and upward causation between different levels. Concepts to support multi-level modeling in a rule-based language are identified. To those belong rule schemata, hierarchical nesting of species, assigning attributes and solutions to species at each level and preserving content of nested species while applying rules. Further necessities are the ability to apply rules and flexibly define reaction rate kinetics and constraints on nested species as well as species that are nested within others. An example model is presented that analyses the interplay of an intracellular control circuit with states at cell level, its relation to cell division, and connections to intercellular communication within a population of cells. The example is described in ML-Rules - a rule-based multi-level approach that has been realized within the plug-in-based modeling and simulation framework JAMES II.</p> <p>Conclusions</p> <p>Rule-based languages are a suitable starting point for developing a concise and compact language for multi-level modeling of cell biological systems. The combination of nesting species, assigning attributes, and constraining reactions according to these attributes is crucial in achieving the desired expressiveness. Rule schemata allow a concise and compact description of complex models. As a result, the presented approach facilitates developing and maintaining multi-level models that, for instance, interrelate intracellular and intercellular dynamics.</p