Single-switch preferences and the Ostrogorski paradox

http://directory.umm.ac.id/Data%20Elmu/jurnal/M/Mathematical%20Social%20Sciences/Vol39.Issue1.Jan2000/931.pdf

Representation in majority tournaments

I present an original model in judgment aggregation theory that demonstrates the general impossibility of consistently describing decision-making purely at the group level Only a type of unanimity rule can guarantee a group decision is consistent with supporting reasons, and even this possibility is limited to a small class of reasoning methods The key innovation is that this result holds when individuals can reason in different ways, an allowance not previously considered in the literature This generalizes judgment aggregation to subjective decision situations, implying that the discursive dilemma persists without individual agreement on the logical constraints Notably, the model mirrors the typical method of choosing political representatives, and thus suggests that no voting procedure other than unanimity rule can guarantee representation that reflects electorate opinion Finally, I apply the results to a normative argument for unanimity rule in contract theory and juries, as well as to problems posed for deliberative democratic theory and the concept of representation

Judgment aggregation and subjective decision-making*

The public choice literature has paid little attention to altruism, and the few works that do deal with it usually focus on the tradeoff between selfish and unselfish preferences, assuming some shared set of unselfish preferences. This focus leaves the question open as to whether unselfish but conflicting beliefs can be the source of public choice problems. This paper examines conflicting ethical beliefs among purely altruistic individuals to show that many of the problems that appear to go away if people are altruistic (assuming notions of the public interest are shared) return if notions of the public interest conflict no matter how altruistic people may be.

/pdf/public-choice-and-altruism-1woq1bo1en.pdf

Public choice and altruism

Suppose n Bayesian agents need to make a decision as a group. The groupas a whole is also supposed to be a Bayesian agent whose probabilities andutilities are derived or aggregated in reasonable ways from the probabilitiesand utilities of the group members. The aggregation could beex ante, i.e., interms of expected utilities, or it could be ex post, i.e., in terms of utilitiesonly, or in terms of utilities and probabilities separately. This study exploresthe ex post approach. Using the Bolker/Jeffrey framework, we show thatex post aggregation is subject to an instability phenomenon. That is, it mayhappen that the group preference between actions ``flips back and forth'' dependingon the level of detail in which the decision problem is described. Structurally verysimilar phenomena also occur elsewhere in social choice theory, in statistics (Simpson'sParadox), and in voting theory (Ostrogorski's Paradox).

Instability Of Ex Post Aggregation In The Bolker–Jeffrey Framework And Related Instability Phenomena

Motivated by certain paradoxa that have been discussed in the literature (Ostrogorski paradox), we prove an impossibility theorem for two-stage aggregation procedures for discrete data. We consider aggregation procedures of the following form: The whole population is partitioned into subgroups. First we aggregate over each subgroup, and in a second step we aggregate the subgroup aggregates to obtain a total aggregate. The data are either dichotomous (1 — 0; yes-no) or take values in a finite ordered set of possible attributes (e.g., exam grades A, B,...F). Examples are given by multistage voting procedures (indirect democracy, federalism), or by the forming of partial grades and overall grades in academic examinations and similar evaluation problems (sports competitions, consumer reports). It is well known from standard examples that the result of such a two-stage aggregation procedure depends, in general, not only on the distribution of attributes in the whole population, but also on how the attributes are distributed across the various subgroups (in other words: how the subgroups are defined). This dependence leads to certain “paradoxa”. The main result of the present paper is that these paradoxa are not due to the special aggregation rules employed in the examples, but are unavoidable in principle, provided the aggregators satisfy certain natural assumptions. More precisely: the only aggregator functions for which the result of a two-stage (a fortiori: multi-stage) aggregation does not depend on the partitioning are “degenerate” aggregators of the following form: there exists a partial order (“dominance”) on the set of possible attributes such that the aggregate over any collection of data is always equal to the supremum (w.r.t. dominance) of the attributes occurring in the data, regardless of the relative frequnencies of these occurrences. In the voting context, degeneracy corresponds to the unanimity principle. Our theorem is true for arbitrary partitionings of arbitrary (finite) sets and generalizes the results of Deb & Kelsey (for the matrix case with dichotomous variables and majority voting) to general two-stage aggregation procedures for attributes belonging to a finite ordered set. The general result is illustrated by some examples.

Two-stage discrete aggregation: the Ostrogorski paradox and related phenomena

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Two-stage discrete aggregation: the Ostrogorski paradox and related phenomena