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...

Arrow’s and the Gibbard-Satterthwaite theorems are proved using a common proof strategy based on a dictatorship result for choice functions. One of the instrumental results obtained shows the inconsistency between the basic assumption in each of these theorems and a mild majority principle.

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...

Two results showing the limitations of the “as if” methodology are proved under relatively mild assumptions. In an interpretation of the results, a competitive market cannot simulate the outcome of a market M in which the single price assumption does not hold. In a second interpretation, the...

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.