We introduce a new probability model, namely Impartial, Anonymous and Neutral Culture model (IANC), for sampling public preferences concerning a given set of alternatives. IANC treats public preferences through a class of preference profiles named roots, where both names of the voters and of the alternatives are immaterial. The general framework along with the theoretical formulation through group actions, an exact formula for the number of roots, and the description of a symbolic algebra package that allows for the generation of roots uniformly are presented. In order to be able to obtain uniform distribution of roots for large electorate size and high number of alternatives which lead to combinatorial explosions, the machinery we developed involves elements of symmetric functions and an application of the Dixon-Wilf algorithm. Using Monte-Carlo methods, the model we develop allows for a testbed that can be used to answer various questions about the properties and behaviors of anonymous and neutral social choice rules for large parameters. As applications of the method, the results of two MonteCarlo experiments are presented: the likelihood of the existence of Condorcet winners, and the probability of Condorcet and Plurality rules to choose the same winner. 1The Impartial, Anonymous and Neutral Culture Model: A Probability Model for Sampling Public Preference StructuresAbstract We introduce a new probability model, namely Impartial, Anonymous and Neutral Culture model (IANC), for sampling public preferences concerning a given set of alternatives. IANC treats public preferences through a class of preference profiles named roots, where both names of the voters and of the alternatives are immaterial. The general framework along with the theoretical formulation through group actions, an exact formula for the number of roots, and the description of a symbolic algebra package that allows for the generation of roots uniformly are presented. In order to be able to obtain uniform distribution of roots for large electorate size and high number of alternatives which lead to combinatorial explosions, the machinery we developed involves elements of symmetric functions and an application of the Dixon-Wilf algorithm. Using Monte-Carlo methods, the model we develop allows for a testbed that can be used to answer various questions about the properties and behaviors of anonymous and neutral social choice rules for large parameters. As applications of the method, the results of two MonteCarlo experiments are presented: the likelihood of the existence of Condorcet winners, and the probability of Condorcet and Plurality rules to choose the same winner.
Given that n voters report only the first r (1 ≤ r < m) ranks of their linear preference rankings over m alternatives, the likelihood of implementing Borda outcome is investigated. The information contained in the first r ranks is aggregated through a Borda-like method, namely the r-Borda rule. Monte-Carlo simulations are run to detect changes in the likelihood of r-Borda winner(s) to coincide with the original Borda winner(s) as a function of m, n and r. The voters' preferences are generated through the Impartial Anonymous and Neutral Culture Model, where both the names of the alternatives and voters are immaterial. It is observed that, for a given r, the likelihood of choosing the Borda winner decreases down to zero independent of n as m increases within the computed range of parameter values, 1 ≤ m, n ≤ 30. For n = 30, this likelihood is given as an approximating function of r and m through least square fit method.
In many areas of social life, individuals receive information about a particular issue of interest from multiple sources. When these sources are connected through a network, then proper aggregation of this information by an individual involves taking into account the structure of this network. The inability to aggregate properly may lead to various types of distortions. In our experiment, four agents all want to find out the value of a particular parameter unknown to all. Agents receive private signals about the parameter and can communicate their estimates of the parameter repeatedly through a network, the structure of which is known by all players. We present results from experiments with three different networks. We find that the information of agents who have more outgoing links in a network gets more weight in the information aggregation of the other agents than under optimal updating. Our results are consistent with the model of "persuasion bias" of DeMarzo et al. (2003).
We study competition in experimental markets in which two incumbents face entry by three other firms. Our treatments vary with respect to three factors: sequential vs. block or simultaneous entry, the cost functions of entrants and the amount of time during which incumbents are protected from entry. Before entry incumbents are able to collude in all cases. When all firms' costs are the same entry always leads consumer surplus and profits to their equilibrium levels. When entrants are more efficient than incumbents, entry leads consumer surplus to equilibrium. However, total profits remain below equilibrium, due to the fact that the inefficient incumbents produce too much and efficient entrants produce too little. Market behavior is satisfactory from the consumers' standpoint, but does not yield adequate signals to other potential entrants. These results are not affected by whether entry is simultaneous or sequential. The length of the incumbency phase does have some subtle effects.
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