A Theorem on Preference Aggregation

I present a general theorem on preference aggregation. This theorem implies, as corollaries, Arrow's Impossibility Theorem, Wilson's extension of Arrow's to non-Paretian aggregation rules, the Gibbard-Satterthwaite Theorem and Sen's result on the Impossibility of a Paretian Liberal. The theorem shows that these classical results are not only similar, but actually share a common root. The theorem expresses a simple but deep fact that transcends each of its particular applications: it expresses the tension between decentralizing the choice of aggregate into partial choices based on preferences over pairs of alternatives, and the need for some coordination in these decisions, so as to avoid contradictory recommendations.NULL

Designing Decisions Rules for Transnational Infraestructure Projects

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Locating Public Facilities by Majority: Stability, Consistency and Group Formation

We consider the following allocation problem: A fixed number of public facilities must be located on a line. Society is composed of N agents, who must be allocated to one and only one of these facilities. Agents have single peaked preferences over the possible location of the facilities they are assigned to, and do not care about the location of the rest of facilities. There is no congestion. We show that there exist social choice correspondences that choose locations and assign agents to them in such a way that: (1) these decisions are Condorcet winners whenever one exists, (2) the majority of the users of each facility supports the choice of its location, and (3) no agent wishes to become a user of another facility, even if that could induce a change of its present location by majority voting.Social choice correspondences, condorcet rules, stability, Simpson Rule

Preference for Flexibility and the Opportunities of Choice

A decision-maker exhibits preference for flexibility if he always prefers any set of alternatives to its subsets, even when two of them contain the same best element. Desire for flexibility can be explained as the consequence of the agent's uncertainty along a two-stage process, where he must first preselect a subset of alternatives from which to make a final choice later on. We investigate conditions on the rankings of subsets that are compatible with the following assumptions: (1) the agent is endowed with a VN-M utility function of alternatives, (2) the agent attaches a subjective probability to the survival of each subset of alternatives, and (3) the agent will make a best choice out of any set which becomes available, and ranks sets ex-ante in terms of the expected utility of the best choices within them. We first prove that any total ordering respecting set inclusion is rationalizable in these terms. This result is essentially the same obtained by Kreps (1979) under an alternative interpretation. We also show that we cannot learn anything about the underlying utilities of agents unless we impose further restrictions on the admissible distributions of survival probabilities. Then we investigate the additional consequences of assuming that the survival probabilities of individual alternatives are independently distributed. We prove that this reduces significantly the class of set rankings which can be rationalized and that then one can infer some of the characteristics of the agentís preferences. We offer a full characterization for the case of three alternatives. We also provide necessary conditions for rationalizability in the general case.NULL

Preference for Flexibility and the Opportunities of Choice

A decision-maker exhibits preference for flexibility if he always prefers any set of alternatives to its subsets, even when two of them contain the same best element. Desire for flexibility can be explained as the consequence of the agent’s uncertainty along a two-stage process, where he must first preselect a subset of alternatives from which to make a final choice later on. We investigate conditions on the rankings of subsets that are compatible with the following assumptions: (1) the agent is endowed with a VN-M utility function on alternatives, (2) the agent attaches a subjective probability to the survival of each subset of alternatives, and (3) the agent will make a best choice out of any set which becomes available, and ranks sets ex-ante in terms of the expected utility of the best choices within them. We first prove that any total ordering respecting set inclusion is rationalizable in these terms. This result is essentially the same obtained by Kreps (1979) under an alternative interpretation. We also show that we cannot learn anything about the underlying utilities of agents unless we impose further restrictions on the admissible distributions of survival probabilities. Then we investigate the additional consequences of assuming that the survival probabilities of individual alternatives are independently distributed. We prove that this reduces significantly the class of set rankings which can be rationalized and that then one can infer some of the characteristics of the agent’s preferences. We offer a full characterization for the case of three alternatives. We also provide necessary conditions for rationalizability in the general case.

Free Triples, Large Indifference Classes and the Majority Rule

We consider situations in which agents are not able to completely distinguish between all alternatives. Preferences respect individual objective indifferences if any two alternatives are indifferent whenever an agent cannot distinguish between them. We present necessary and sufficient conditions of such a domain of preferences under which majority rule is quasi-transitive and thus Condorcet winners exist for any set of alternatives. Finally, we compare our proposed restrictions with others in the literature, to conclude that they are independent of any previously discussed domain restriction.Quasi-Transitivity

Top Monotonicity: A Common Root for Single Peakedness, Single Crossing and the Median Voter Result

When the members of a voting body exhibit single peaked preferences, majority winners exist. Moreover, the median(s) of the preferred alternatives of voters is (are) indeed the majority (Condorcet) winner(s). This important result of Duncan Black (1958) has been crucial in the development of public economics and political economy, even if it only provides a sufficient condition. Yet, there are many examples in the literature of environments where voting equilibria exist and alternative versions of the median voter results are satisfied while single peakedness does not hold. Some of them correspond to instances where other relevant conditions, apparently not connected with single eakedness, are satisfied. For example preferences may satisfy the single-crossing property (Mirrlees, 1971, Gans and Smart, 1996, and Milgrom and Shannon, 1994), intermediateness (Grandmont, 1978) or order restriction (Rothstein, 1990). Still other interesting cases of existence of voting equilibria do not fall in any of these categories. We present a new and weak domain restriction which encompasses all the above mentioned ones, llows for new cases, still guarantees the existence of Condorcet winners and preserves a version of the median voter result. We illustrate how this new condition, that we call top monotonicity, arises naturally in different economic contexts.Single peaked, single crossing and intermediate preferences, majority (Condorcet) winners

On the rule of K names

The rule of k names can be described as follows: given a set of candidates for office, a committee chooses k members from this set by voting, and makes a list with their names. Then a single individual from outside the committee selects one of the listed names for the office. Different variants of this method have been used since the distant past and are still used today in many countries and for different types of choices. After documenting this widespread use by means of actual examples, we provide a theoretical analysis. We concentrate on the plausible outcomes induced by the rule of k names when the agents involved act strategically. Our analysis shows how the parameter k, the screening rule and the nature of candidacies act as a means to balance the power of the committee with that of the chooser.employment by lotto, probabilistic mechanism, two-sided matching, stability

How to choose a non-controversial list with k names

Barberà and Coelho (2006) documented six screening rules associated with the rule of k names that are used by different institutions around the world. Here, we study whether these screening rules satisfy stability. A set is said to be a weak Condorcet set la Gehrlein (1985) if no candidate in this set can be defeated by any candidate from outside the set on the basis of simple majority rule. We say that a screening rule is stable if it always selects a weak Condorcet set whenever such set exists. We show that all of the six procedures which are used in reality do violate stability if the voters act not strategically. We then show that there are screening rules which satisfy stability. Finally, we provide two results that can explain the widespread use of unstable screening rules.NULL

A Note on the Impossibility of a Satisfactory Concept of Stability for Coalition Formation Games

In this note we show that no solution to coalition formation games can satisfy a set of axioms that we propose as reasonable. Our result points out that "solutions" to the coalition formation cannot be interpreted as predictions of what would be ìresting pointsî for a game in the way stable coalition structures are usually interpreted.Hedonic Game, Coalition Formation, Stability