A short step between democracy and dictatorship

The majority rule and the hierarchically dictatorial rule are both characterized when preferences are defined over two alternatives. The majority rule is characterized in terms of seven axioms. The hierarchically dictatorial rule is characterized in terms of six of these seven axioms and the negation of the seventh, so each rule can be seen as obtained from the other by negating just one of the axioms. The pivotal axiom holds that, for societies with at least three members, the frequency with which indifference is the result of the preference aggregation must be smaller than the frequency with which one of the alternatives is declared preferred to the other.Social welfare function; majority rule; dictatorship; axiomatic characterization; two alternatives.

Trade, expropriation and allocation

Allocation rules map preference profiles into allocations, whereas trading rules map preference profiles and allocations into allocations. It is shown that no allocation rule can derive from a trading rule based on voluntary trade and satisfying a weak efficiency condition. If the trading rule allows compulsory trade then the only allocation rules that can derive from a trading rule satisfying certain additional mild conditions are those having a hierarchy of dictators. These results contribute to accentuate the difference between centralized and decentralized allocation mechanisms.Allocation rules, Compulsory trade, Hierarchy of dictators, Trading rules

Decision by majority and the right to vote

The (relative) majority rule is a benchmark collective decision norm. This paper provides a simple characterization of the majority rule, for the two-alternative case, that relies on the following property: the choice prescribed by the rule to a group I of individuals must be the one that would be prescribed in at least 50% of the strict subgroups that can be formed in I. This property means if some subgroup is denied the right to participate in the collective decision, the most likely event is that the exclusion of the subgroup will have no effect on the decision.Social welfare function; majority rule; axiomatic characterization; two alternatives; manipulation.

Two axioms for the majority rule

Two axioms are shown to characterize the relative majority rule when preferences are defined over two alternatives. According to one axiom, if all the individuals in a group are indifferent, then the associated group preference is indifference. The second axiom states that a group S prefers alternative a to alternative b if and only if there is a subgroup T whose members unanimously prefer a to b and such that, if S ≠ T, indifference represents the preference of the group ST.Social welfare function, relative majority rule, axiomatic characterization, two alternatives.

Parallel axiomatizations of majority and unanimity

The relative majority rule and the unanimity rule are characterized for the case in which there are only two alternatives. The main axioms are motivated by a principle of binary representativeness: the aggregation of the preferences of n voters is the result of splitting the n voters into two groups, aggregating the preferences of the voters of each group, selecting for each group a representative that adopts the preference of the group, and finally aggregating the preferences of the two representatives. The two characterizations are shown to differ from each other in just one axiom, expressing strategyproofness (unanimity) or group strategyproofness (majority).Social welfare function; relative majority rule; unanimity rule; representativeness; axiomatic characterization; two alternatives.

From social choice functions to dictatorial social welfare functions

A procedure to construct a social welfare function from a social choice function is suggested and it is shown that the dictatorial are the only unanimous social welfare functions that can be reconstructed from a social choice function that does not change the social choice when a defeated alternative is moved to the last position in all the individual preferences.

Merging discrete measurements

A merging function synthesizes a vector of numbers (representing measurements, scores or quantitative opinions) into a single number (representing a consensus or collective measurement, score or quantitative opinion). Assuming that all the involved numbers are drawn from a discrete set, it is shown that projection functions are the only merging functions satisfying three properties satisfied by the arithmetic mean (defined for real numbers). Another projection result is obtained under alternative assumptions when merging functions are assumed to transform matrices of numbers from a discrete set to a vector of numbers from the discrete set.Aggregation of measurements; merging functions; interdependent measurements; social choice.

Networks and market laws

The effects on the market price of a change in the number of buyers, in the number of sellers, in the prices sellers set and in the buyers’ reservation prices are established in a simple network model of a market.Market, Market price, Network, Price changes

Allocation by coercion

The problem of allocating indivisible goods is considered when groups of individuals can make use of their power to plunder other groups. A monarch in a group of individuals is an individual who always obtains one of his most preferred goods. A Paretian condition together with a requirement of robust stability lead to the existence of monarchs in all subsets of individuals, except possibly one.Allocation rule; dictator; indivisible good; power; coalition formation.

Allocation of objects with conditional property rights

This paper considers the allocation of indivisible goods among members of a collective assuming that individuals are given the right to retain certain goods when some individuals alter the allocation problem. The assignment of rights is exhaustive in that, for every good x, either individual i can exercise a right over x against j or j against i. It is shown that the only Pareto efficient allocation rules satisfying these requirements are those having a hierarchy of diarchies.Allocation rule; hierarchy of diarchies; indivisible good; property right.