90,126 research outputs found
What majority decisions are possible with possible abstaining
Suppose we are given a family of choice functions on pairs from a given
finite set. The set is considered as a set of alternatives (say candidates for
an office) and the functions as potential "voters". The question is, what
choice functions agree, on every pair, with the majority of some finite
subfamily of the voters? For the problem as stated, a complete characterization
was given in \citet{shelah2009mdp}, but here we allow each voter to abstain.
There are four cases.Comment: 23 page
Consensus Strategies for Signed Profiles on Graphs
The median problem is a classical problem in Location Theory: one searches for a location that minimizes the average distance to the sites of the clients. This is for desired facilities as a distribution center for a set of warehouses. More recently, for obnoxious facilities, the antimedian was studied. Here one maximizes the average distance to the clients. In this paper the mixed case is studied. Clients are represented by a profile, which is a sequence of vertices with repetitions allowed. In a signed profile each element is provided with a sign from {+,-}. Thus one can take into account whether the client prefers the facility (with a + sign) or rejects it (with a - sign). The graphs for which all median sets, or all antimedian sets, are connected are characterized. Various consensus strategies for signed profiles are studied, amongst which Majority, Plurality and Scarcity. Hypercubes are the only graphs on which Majority produces the median set for all signed profiles. Finally, the antimedian sets are found by the Scarcity Strategy on e.g. Hamming graphs, Johnson graphs and halfcubes.median;consensus function;median graph;majority rule;plurality strategy;Graph theory;Hamming graph;Johnson graph;halfcube;scarcity strategy;Discrete location and assignment;Distance in graphs
Graphical potential games
We study the class of potential games that are also graphical games with
respect to a given graph of connections between the players. We show that,
up to strategic equivalence, this class of games can be identified with the set
of Markov random fields on .
From this characterization, and from the Hammersley-Clifford theorem, it
follows that the potentials of such games can be decomposed to local
potentials. We use this decomposition to strongly bound the number of strategy
changes of a single player along a better response path. This result extends to
generalized graphical potential games, which are played on infinite graphs.Comment: Accepted to the Journal of Economic Theor
Sharp Thresholds for Monotone Non Boolean Functions and Social Choice Theory
A key fact in the theory of Boolean functions is
that they often undergo sharp thresholds. For example: if the function is monotone and symmetric under a transitive action with
\E_p[f] = \eps and \E_q[f] = 1-\eps then as .
Here \E_p denotes the product probability measure on where each
coordinate takes the value independently with probability . The fact
that symmetric functions undergo sharp thresholds is important in the study of
random graphs and constraint satisfaction problems as well as in social
choice.In this paper we prove sharp thresholds for monotone functions taking
values in an arbitrary finite sets. We also provide examples of applications of
the results to social choice and to random graph problems. Among the
applications is an analog for Condorcet's jury theorem and an indeterminacy
result for a large class of social choice functions
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