635 research outputs found
Complex Collective Decisions and the Probability of Collective Inconsistencies
Many groups are required to make collective decisions over multiple interconnected propositions. The "doctrinal paradox" or "discursive dilemma" shows that propostionwise majority voting can lead to inconsistent collective outcomes, even when the judgments of individual group members are consistent. How likely is the occurence of this paradox? This paper develops a simple model for determining the probability of the paradox's occurrence, given various assumptions about the probability of different individual judgments. Several convergence results will be proved, identifying conditions under which the probability of the paradox's occurrence converges to certainty as the number of individuals increases, and conditions under which that probability vanishes. The present model will also be used for assessing the "truth-tracking" performance of two escape-routes from the paradox, the premise- and conclusion-based procedures. Finally, the results on the probability of the doctrinal paradox will be compared with existing results on the probability of Condorcet's paradox of cyclical preferences. It will be suggested that the doctrinal paradox is more likely to occur than Condorcet's paradox.
Group deliberation and the transformation ofjudgments: an impossibility result
While a large social-choice-theoretic literature discusses the aggregation ofindividual judgments into collective ones, there is relatively little formalwork on the transformation of individual judgments in group deliberation. Idevelop a model of judgment transformation and prove a baselineimpossibility result: Any judgment transformation function satisfying someinitially plausible condition is the identity function, under which no opinionchange occurs. I identify escape routes from this impossibility result andargue that successful group deliberation must be 'holistic': individualscannot generally revise their judgments on a proposition based on judgmentson that proposition alone but must take other propositions into account too. Idiscuss the significance of these findings for democratic theory.group deliberation, judgment aggregation, judgmenttransformation, belief revision
What is special about the proportion? A research report on special majority voting and the classical Condorcet jury theorem
It is known that, in Condorcetâs classical model of jury decisions, the proportion of jurors supporting a decision is not a significant indicator of that decisionâs reliability: the probability that a particular majority decision is correct given the size of the majority depends only on the absolute margin between the majority and the minority, and is invariant under changes of the proportion in the majority if the absolute margin is held fixed. Here I show that, if we relax the assumption that juror competence is independent of the juryâs size, the proportion can be made significant: there are then conditions in which the probability that a given majority decision is correct depends only on the proportion of jurors supporting that decision, and is invariant under changes of the jury size. The proportion is significant in this way if and only if juror competence is a particular decreasing function of the jury size. However, the required condition on juror competence is not only highly special â thereby casting doubt on the significance of the proportion in realistic conditions â but it also has an adverse implication for the Condorcet jury theorem. If the proportion is significant, then the Condorcet jury theorem fails to hold; and if the Condorcet jury theorem holds, the proportion is not significant. I discuss the implications of these results for defining and justifying special majority voting from the perspective of an epistemic account of voting.Condorcet jury theorem, special majority voting, proportion, decreasing juror competence
The relation between degrees of belief and binary beliefs: A general impossibility theorem
Agents are often assumed to have degrees of belief (âcredencesâ) and also binary beliefs (âbeliefs simpliciterâ). How are these related to each other? A much-discussed answer asserts that it is rational to believe a proposition if and only if one has a high enough degree of belief in it. But this answer runs into the âlottery paradoxâ: the set of believed propositions may violate the key rationality conditions of consistency and deductive closure. In earlier work, we showed that this problem generalizes: there exists no local function from degrees of belief to binary beliefs that satisfies some minimal conditions of rationality and non-triviality. âLocalityâ means that the binary belief in each proposition depends only on the degree of belief in that proposition, not on the degrees of belief in others. One might think that the impossibility can be avoided by dropping the assumption that binary beliefs are a function of degrees of belief. We prove that, even if we drop the âfunctionalityâ restriction, there still exists no local relation between degrees of belief and binary beliefs that satisfies some minimal conditions. Thus functionality is not the source of the impossibility; its source is the condition of locality. If there is any non-trivial relation between degrees of belief and binary beliefs at all, it must be a âholisticâ one. We explore several concrete forms this âholisticâ relation could take
The Methodology of Political Theory
This article examines the methodology of a core branch of contemporary political theory or philosophy: âanalyticâ political theory. After distinguishing political theory from related fields, such as political science, moral philosophy, and legal theory, the article discusses the analysis of political concepts. It then turns to the notions of principles and theories, as distinct from concepts, and reviews the methods of assessing such principles and theories, for the purpose of justifying or criticizing them. Finally, it looks at a recent debate on how abstract and idealized political theory should be, and assesses the significance of disagreement in political theory. The discussion is carried out from an angle inspired by the philosophy of science
What Normative Facts Should Political Theory Be About? Philosophy of Science meets Political Liberalism
Just as different sciences deal with different factsâsay, physics versus biologyâso we may
ask a similar question about normative theories. Is normative political theory concerned
with the same normative facts as moral theory or different ones? By developing an analogy
with the sciences, we argue that the normative facts of political theory belong to a higherâ
more coarse-grainedâlevel than those of moral theory. The latter are multiply realizable by
the former: competing facts at the moral level can underpin the same facts at the political
one. Consequently, some questions that moral theories answer are indeterminate at the
political level. This proposal offers a novel interpretation of John Rawlsâs idea that, in public
reasoning, we should abstract away from comprehensive moral doctrines. We contrast our
distinction between facts at different levels with the distinction between admissible and
inadmissible evidence and discuss some implications for the practice of political theory
Where do preferences come from?
Rational choice theory analyzes how an agent can rationally act, given his or her preferences, but says little about where those preferences come from. Preferences are usually assumed to be fixed and exogenously given. Building on related work on reasons and rational choice (Dietrich and List, Nous, forthcoming), we describe a framework for conceptualizing preference formation and preference change. In our model, an agentâs preferences are based on certain âmotivationally salientâ properties of the alternatives over which the preferences are held. Preferences may change as new properties of the alternatives become salient or previously salient properties cease to be salient. Our approach captures endogenous preferences in various contexts and helps to illuminate the distinction between formal and substantive concepts of rationality, as well as the role of perception in rational choice
Majority voting on restricted domains
In judgment aggregation, unlike preference aggregation, not much is known about domain restrictions that guarantee consistent majority outcomes. We introduce several conditions on individual judgments sufficient for consistent majority judgments. Some are based on global orders of propositions or individuals, others on local orders, still others not on orders at all. Some generalize classic social-choice-theoretic domain conditions, others have no counterpart. Our most general condition generalizes Sen's triplewise value-restriction, itself the most general classic condition. We also prove a new characterization theorem: for a large class of domains, if there exists any aggregation function satisfying some democratic conditions, then majority voting is the unique such function. Taken together, our results support the robustness of majority rule
Framing as Path-Dependence
A âframingâ effect occurs when an agentâs choices are not invariant under changes in the way a choice problem is formulated, e.g. changes in the way the options are described (violation of description invariance) or in the way preferences are elicited (violation of procedure invariance). In this paper we examine precisely which classical conditions of rationality it is whose non-satisfaction may lead to framing effects. We show that (under certain conditions), if (and only if) an agent's initial dispositions on a set of propositions are âimplicitly inconsistentâ, her decisions may be âpath-dependentâ, i.e. dependent on the order in which the propositions are considered. We suggest that different ways of framing a choice problem may induce the order in which relevant propositions are considered and hence affect the decision made. This theoretical explanation suggests some observations about human psychology which are consistent with those made by psychologists and provides a unified framework for explaining violations of description and procedure invariance.framing, preference reversal, path-dependence, rationality, deductive closure
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