|M.Sc Student||Dokow Elad|
|Subject||Aggregation of Sets of Judgments|
|Department||Department of Mathematics||Supervisor||PROF. Ron Holzman|
In this research we
explore how to aggregate individual judgments into a collective judgment.
Suppose each member of a group of individuals has a certain judgment concerning a set of propositions Phi. In particular, for each proposition in Phi an individual can either accept it or reject it.
The question now is what kind of aggregation functions assign to each possible configuration of consistent individual judgments, a consistent 'group' judgment.
This line of research was initiated by Wilson (1975) who asked under what conditions the aggregation must be dictatorial, but gave only partial answers. Later, List and Pettit (2002) revived the interest in the problem. They proved an impossibility theorem under some strong assumptions on the aggregation rule (anonymity and systematicity).
By contrast, we only make assumptions analogous to those of Arrow's theorem (IIA and Pareto). We characterize proposition sets, for which there is no non-dictatorial decision method for aggregating sets of judgments in a logically consistent way.
In Arrow’s original context, the existence of at least three alternatives suffices for these two conditions to imply that the aggregation must be dictatorial. In our context, no simple condition on the number of propositions would lead to a similar impossibility result.
For Phi that is closed under atomic propositions we get not only a characterization of the conditions that imply that a function which is IIA and paretian must be dictatorial, but also a description of all IIA and paretian functions when the conditions do not hold.