M.Sc Thesis | |

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.