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.

What is special about the proportion? A research report on special majority voting and the classical Condorcet jury theorem

It is known that, in Condorcet’s classical model of jury decisions, the proportion of jurors supporting a decision is not a significant indicator of that decision’s 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 jury’s 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 – thereby casting doubt on the significance of the proportion in realistic conditions – 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

What Normative Facts Should Political Theory Be About? Philosophy of Science meets Political Liberalism

Just as different sciences deal with different facts—say, physics versus biology—so 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 higher— more coarse-grained—level 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 Rawls’s 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

Friend or Foe? A Natural Experiment of the Prisoner's Dilemma

This study examines data drawn from the game show Friend or Foe?, which is similar to the classic prisoner%u2019s dilemma tale: partnerships are endogenously determined, players work together to earn money, after which, they play a one-shot prisoner%u2019s dilemma game over large stakes: varying from $200 to (potentially) more than$22,000. If one were to conduct such an experiment in the laboratory, the cost to gather the data would be well over $350,000. The data reveal several interesting insights; perhaps most provocatively, they suggest that even though the game is played in front of an audience of millions of viewers, there is some evidence consistent with a model of discrimination. The observed patterns of social discrimination are unanticipated, however. For example, there is evidence consistent with the notion that certain populations have a general %u201Cdistaste%u201D for older participants.

Testing Neoclassical Competitive Theory in Multi-Lateral Decentralized Markets+

This study presents results from a pilot field experiment that tests predictions of competitive market theory. A major advantage of this particular field experimental design is that my laboratory is the marketplace: subjects are engaged in buying, selling, and trading activities whether I run an exchange experiment or am a passive observer. In this sense, I am gathering data in a natural environment while still maintaining the necessary control to execute a clean comparison between treatments. The main results of the study fall into two categories. First, the competitive model predicts reasonably well in some market treatments: the expected price and quantity levels are approximated in many market rounds. Second, the data suggest that market composition is important: buyer and seller experience levels impact not only the distribution of rents but also the overall level of rents captured. An unexpected result in this regard is that average market efficiency is lowest in markets that match experienced buyers and experienced sellers and highest when experienced buyers engage in bargaining with inexperienced sellers. Together, these results suggest that both market experience and market composition play an important role in the equilibrium discovery process.

Neoclassical Theory Versus Prospect Theory: Evidence from the Marketplace

Neoclassical theory postulates that preferences between two goods are independent of the consumer's current entitlements. Several experimental studies have recently provided strong evidence that this basic independence assumption, which is used in most theoretical and applied economic models to assess the operation of markets, is rarely appropriate. These results, which clearly contradict closely held economic doctrines, have led some influential commentators to call for an entirely new economic paradigm to displace conventional neoclassical theory e.g., prospect theory, which invokes psychological effects. This paper pits neoclassical theory against prospect theory by investigating three clean tests of the competing hypotheses. In all three cases, the data, which are drawn from nearly 500 subjects actively participating in a well-functioning marketplace, suggest that prospect theory adequately organizes behavior among inexperienced consumers, whereas consumers with intense market experience behave largely in accordance with neoclassical predictions. The pattern of results indicates that learning primarily occurs on the sell side of the market: agents with intense market experience are more willing to part with their entitlements than lesser-experienced agents.

Substitutability, Experience, and the Value Disparity: Evidence from the Marketplace

Recent empirical evidence suggests that important disparities exist between willingness to pay and compensation demanded for the same good. These results, which clearly contradict closely held economic doctrines, have led some influential commentators to call for an entirely new economic paradigm to displace conventional neoclassical theory. This study examines the generality of these experimental findings by going to a well-functioning marketplace and examining more than 350 individual decisions across two incentive-compatible elicitation mechanisms. The data suggest that behavior of individuals with intense experience approaches neoclassical predictions: any observed WTA/WTP disparity amongst this group is negligible.WTP/WTA disparity, Field experiment, Marketlike experience